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Heuristic Method

Heuristic Method: this article explains the concept of the Heuristic Method , developed by George Pólya in a practical way. After reading it, you will understand the basics of this powerful Problem Solving tool.

What is the Heuristic Method?

A heuristic method is an approach to finding a solution to a problem that originates from the ancient Greek word ‘eurisko’, meaning to ‘find’, ‘search’ or ‘discover’. It is about using a practical method that doesn’t necessarily need to be perfect. Heuristic methods speed up the process of reaching a satisfactory solution.

Previous experiences with comparable problems are used that can concern problem situations for people, machines or abstract issues. One of the founders of heuristics is the Hungarian mathematician György (George) Pólya , who published a book about the subject in 1945 called ‘How to Solve It’. He used four principles that form the basis for problem solving.

Heuristic method: Four principles

Pólya describes the following four principles in his book:

• try to understand the problem
• make a plan
• carry out this plan
• evaluate and adapt

If this sequence doesn’t lead to the right solution, Pólya advises to first look for a simpler problem.

A solution may potentially be found by first looking at a similar problem that was possible to solve. With this experience, it’s possible to look at the current problem in another way.

First principle of the heuristic method: understand the problem

It’s more difficult than it seems, because it seems obvious. In truth, people are hindered when it comes to finding an initially suitable approach to the problem.

It can help to draw the problem and to look at it from another angle. What is the problem, what is happening, can the problem be explained in other words, is there enough information available, etc. Such questions can help with the first evaluation of a problem issue.

Second principle of the heuristic method: make a plan

There are many ways to solve problems. This section is about choosing the right strategy that best fits the problem at hand. The reversed ‘working backwards’ can help with this; people assume to have a solution and use this as a starting point to work towards the problem.

It can also be useful to make an overview of the possibilities, delete some of them immediately, work with comparisons, or to apply symmetry. Creativity comes into play here and will improve the ability to judge.

Third principle of the heuristic method: carry out the plan

Once a strategy has been chosen, the plan can quickly be implemented. However, it is important to pay attention to time and be patient, because the solution will not simply appear.

If the plan doesn’t go anywhere, the advice is to throw it overboard and find a new way.

Fourth principle of the heuristic method: evaluate and adapt

Take the time to carefully consider and reflect upon the work that’s already been done. The things that are going well should be maintained, those leading to a lesser solution, should be adjusted. Some things simply work, while others simply don’t.

There are many different heuristic methods, which Pólya also used. The most well-known heuristics are found below:

1. Dividing technique

The original problem is divided into smaller sub-problems that can be solved more easily. These sub-problems can be linked to each other and combined, which will eventually lead to the solving of the original problem.

2. Inductive method

This involves a problem that has already been solved, but is smaller than the original problem. Generalisation can be derived from the previously solved problem, which can help in solving the bigger, original problem.

3. Reduction method

Because problems are often larger than assumed and deal with different causes and factors, this method sets limits for the problem in advance. This reduces the leeway of the original problem, making it easier to solve.

4. Constructive method

This is about working on the problem step by step. The smallest solution is seen as a victory and from that point consecutive steps are taken. This way, the best choices keep being made, which will eventually lead to a successful end result.

5. Local search method

This is about the search for the most attainable solution to the problem. This solution is improved along the way. This method ends when improvement is no longer possible.

Exact solutions versus the heuristic method

The heuristic approach is a mathmatical method with which proof of a good solution to a problem is delivered. There is a large number of different problems that could use good solutions. When the processing speed is equally as important as the obtained solution, we speak of a heuristic method.

The Heuristic Method only tries to find a good, but not necessarily optimal, solution. This is what differentiates heuristics from exact solution methods, which are about finding the optimal solution to a problem. However, that’s very time consuming, which is why a heuristic method may prove preferable. This is much quicker and more flexible than an exact method, but does have to satisfy a number of criteria.

It’s Your Turn

What do you think? Is the Heuristic Method applicable in your personal or professional environment? Do you recognize the practical explanation or do you have more suggestions? What are your success factors for solving problems

Share your experience and knowledge in the comments box below.

More information

• Groner, R., Groner, M., & Bischof, W. F. (2014). Methods of heuristics . Routledge .
• Newell, A. (1983). The heuristic of George Polya and its relation to artificial intelligence . Methods of heuristics, 195-243.
• Polya, G. (2014, 1945). How to solve it: A new aspect of mathematical method . Princeton university press .

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Published on: 29/05/2018 | Last update: 04/03/2022

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Heuristic Problem Solving: A comprehensive guide with 5 Examples

What are heuristics, advantages of using heuristic problem solving, disadvantages of using heuristic problem solving, heuristic problem solving examples, frequently asked questions.

• Speed: Heuristics are designed to find solutions quickly, saving time in problem solving tasks. Rather than spending a lot of time analyzing every possible solution, heuristics help to narrow down the options and focus on the most promising ones.
• Flexibility: Heuristics are not rigid, step-by-step procedures. They allow for flexibility and creativity in problem solving, leading to innovative solutions. They encourage thinking outside the box and can generate unexpected and valuable ideas.
• Simplicity: Heuristics are often easy to understand and apply, making them accessible to anyone regardless of their expertise or background. They don’t require specialized knowledge or training, which means they can be used in various contexts and by different people.
• Cost-effective: Because heuristics are simple and efficient, they can save time, money, and effort in finding solutions. They also don’t require expensive software or equipment, making them a cost-effective approach to problem solving.
• Real-world applicability: Heuristics are often based on practical experience and knowledge, making them relevant to real-world situations. They can help solve complex, messy, or ill-defined problems where other problem solving methods may not be practical.
• Potential for errors: Heuristic problem solving relies on generalizations and assumptions, which may lead to errors or incorrect conclusions. This is especially true if the heuristic is not based on a solid understanding of the problem or the underlying principles.
• Limited scope: Heuristic problem solving may only consider a limited number of potential solutions and may not identify the most optimal or effective solution.
• Lack of creativity: Heuristic problem solving may rely on pre-existing solutions or approaches, limiting creativity and innovation in problem-solving.
• Over-reliance: Heuristic problem solving may lead to over-reliance on a specific approach or heuristic, which can be problematic if the heuristic is flawed or ineffective.
• Lack of transparency: Heuristic problem solving may not be transparent or explainable, as the decision-making process may not be explicitly articulated or understood.
• Trial and error: This heuristic involves trying different solutions to a problem and learning from mistakes until a successful solution is found. A software developer encountering a bug in their code may try other solutions and test each one until they find the one that solves the issue.
• Working backward: This heuristic involves starting at the goal and then figuring out what steps are needed to reach that goal. For example, a project manager may begin by setting a project deadline and then work backward to determine the necessary steps and deadlines for each team member to ensure the project is completed on time.
• Breaking a problem into smaller parts: This heuristic involves breaking down a complex problem into smaller, more manageable pieces that can be tackled individually. For example, an HR manager tasked with implementing a new employee benefits program may break the project into smaller parts, such as researching options, getting quotes from vendors, and communicating the unique benefits to employees.
• Using analogies: This heuristic involves finding similarities between a current problem and a similar problem that has been solved before and using the solution to the previous issue to help solve the current one. For example, a salesperson struggling to close a deal may use an analogy to a successful sales pitch they made to help guide their approach to the current pitch.
• Simplifying the problem: This heuristic involves simplifying a complex problem by ignoring details that are not necessary for solving it. This allows the problem solver to focus on the most critical aspects of the problem. For example, a customer service representative dealing with a complex issue may simplify it by breaking it down into smaller components and addressing them individually rather than simultaneously trying to solve the entire problem.

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Heuristics: Definition, Examples, And How They Work

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On This Page:

Every day our brains must process and respond to thousands of problems, both large and small, at a moment’s notice. It might even be overwhelming to consider the sheer volume of complex problems we regularly face in need of a quick solution.

While one might wish there was time to methodically and thoughtfully evaluate the fine details of our everyday tasks, the cognitive demands of daily life often make such processing logistically impossible.

Therefore, the brain must develop reliable shortcuts to keep up with the stimulus-rich environments we inhabit. Psychologists refer to these efficient problem-solving techniques as heuristics.

Heuristics can be thought of as general cognitive frameworks humans rely on regularly to reach a solution quickly.

For example, if a student needs to decide what subject she will study at university, her intuition will likely be drawn toward the path that she envisions as most satisfying, practical, and interesting.

She may also think back on her strengths and weaknesses in secondary school or perhaps even write out a pros and cons list to facilitate her choice.

It’s important to note that these heuristics broadly apply to everyday problems, produce sound solutions, and helps simplify otherwise complicated mental tasks. These are the three defining features of a heuristic.

While the concept of heuristics dates back to Ancient Greece (the term is derived from the Greek word for “to discover”), most of the information known today on the subject comes from prominent twentieth-century social scientists.

Herbert Simon’s study of a notion he called “bounded rationality” focused on decision-making under restrictive cognitive conditions, such as limited time and information.

This concept of optimizing an inherently imperfect analysis frames the contemporary study of heuristics and leads many to credit Simon as a foundational figure in the field.

Kahneman’s Theory of Decision Making

The immense contributions of psychologist Daniel Kahneman to our understanding of cognitive problem-solving deserve special attention.

As context for his theory, Kahneman put forward the estimate that an individual makes around 35,000 decisions each day! To reach these resolutions, the mind relies on either “fast” or “slow” thinking.

The fast thinking pathway (system 1) operates mostly unconsciously and aims to reach reliable decisions with as minimal cognitive strain as possible.

While system 1 relies on broad observations and quick evaluative techniques (heuristics!), system 2 (slow thinking) requires conscious, continuous attention to carefully assess the details of a given problem and logically reach a solution.

Given the sheer volume of daily decisions, it’s no surprise that around 98% of problem-solving uses system 1.

Thus, it is crucial that the human mind develops a toolbox of effective, efficient heuristics to support this fast-thinking pathway.

Heuristics vs. Algorithms

Those who’ve studied the psychology of decision-making might notice similarities between heuristics and algorithms. However, remember that these are two distinct modes of cognition.

Heuristics are methods or strategies which often lead to problem solutions but are not guaranteed to succeed.

They can be distinguished from algorithms, which are methods or procedures that will always produce a solution sooner or later.

An algorithm is a step-by-step procedure that can be reliably used to solve a specific problem. While the concept of an algorithm is most commonly used in reference to technology and mathematics, our brains rely on algorithms every day to resolve issues (Kahneman, 2011).

The important thing to remember is that algorithms are a set of mental instructions unique to specific situations, while heuristics are general rules of thumb that can help the mind process and overcome various obstacles.

For example, if you are thoughtfully reading every line of this article, you are using an algorithm.

On the other hand, if you are quickly skimming each section for important information or perhaps focusing only on sections you don’t already understand, you are using a heuristic!

Why Heuristics Are Used

Heuristics usually occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind at the same moment

When studying heuristics, keep in mind both the benefits and unavoidable drawbacks of their application. The ubiquity of these techniques in human society makes such weaknesses especially worthy of evaluation.

More specifically, in expediting decision-making processes, heuristics also predispose us to a number of cognitive biases .

A cognitive bias is an incorrect but pervasive judgment derived from an illogical pattern of cognition. In simple terms, a cognitive bias occurs when one internalizes a subjective perception as a reliable and objective truth.

Heuristics are reliable but imperfect; In the application of broad decision-making “shortcuts” to guide one’s response to specific situations, occasional errors are both inevitable and have the potential to catalyze persistent mistakes.

For example, consider the risks of faulty applications of the representative heuristic discussed above. While the technique encourages one to assign situations into broad categories based on superficial characteristics and one’s past experiences for the sake of cognitive expediency, such thinking is also the basis of stereotypes and discrimination.

In practice, these errors result in the disproportionate favoring of one group and/or the oppression of other groups within a given society.

Indeed, the most impactful research relating to heuristics often centers on the connection between them and systematic discrimination.

The tradeoff between thoughtful rationality and cognitive efficiency encompasses both the benefits and pitfalls of heuristics and represents a foundational concept in psychological research.

When learning about heuristics, keep in mind their relevance to all areas of human interaction. After all, the study of social psychology is intrinsically interdisciplinary.

Many of the most important studies on heuristics relate to flawed decision-making processes in high-stakes fields like law, medicine, and politics.

Researchers often draw on a distinct set of already established heuristics in their analysis. While dozens of unique heuristics have been observed, brief descriptions of those most central to the field are included below:

Availability Heuristic

The availability heuristic describes the tendency to make choices based on information that comes to mind readily.

For example, children of divorced parents are more likely to have pessimistic views towards marriage as adults.

Of important note, this heuristic can also involve assigning more importance to more recently learned information, largely due to the easier recall of such information.

Representativeness Heuristic

This technique allows one to quickly assign probabilities to and predict the outcome of new scenarios using psychological prototypes derived from past experiences.

For example, juries are less likely to convict individuals who are well-groomed and wearing formal attire (under the assumption that stylish, well-kempt individuals typically do not commit crimes).

This is one of the most studied heuristics by social psychologists for its relevance to the development of stereotypes.

Scarcity Heuristic

This method of decision-making is predicated on the perception of less abundant, rarer items as inherently more valuable than more abundant items.

We rely on the scarcity heuristic when we must make a fast selection with incomplete information. For example, a student deciding between two universities may be drawn toward the option with the lower acceptance rate, assuming that this exclusivity indicates a more desirable experience.

The concept of scarcity is central to behavioral economists’ study of consumer behavior (a field that evaluates economics through the lens of human psychology).

Trial and Error

This is the most basic and perhaps frequently cited heuristic. Trial and error can be used to solve a problem that possesses a discrete number of possible solutions and involves simply attempting each possible option until the correct solution is identified.

For example, if an individual was putting together a jigsaw puzzle, he or she would try multiple pieces until locating a proper fit.

This technique is commonly taught in introductory psychology courses due to its simple representation of the central purpose of heuristics: the use of reliable problem-solving frameworks to reduce cognitive load.

Anchoring and Adjustment Heuristic

Anchoring refers to the tendency to formulate expectations relating to new scenarios relative to an already ingrained piece of information.

Put simply, this anchoring one to form reasonable estimations around uncertainties. For example, if asked to estimate the number of days in a year on Mars, many people would first call to mind the fact the Earth’s year is 365 days (the “anchor”) and adjust accordingly.

This tendency can also help explain the observation that ingrained information often hinders the learning of new information, a concept known as retroactive inhibition.

Familiarity Heuristic

This technique can be used to guide actions in cognitively demanding situations by simply reverting to previous behaviors successfully utilized under similar circumstances.

The familiarity heuristic is most useful in unfamiliar, stressful environments.

For example, a job seeker might recall behavioral standards in other high-stakes situations from her past (perhaps an important presentation at university) to guide her behavior in a job interview.

Many psychologists interpret this technique as a slightly more specific variation of the availability heuristic.

How to Make Better Decisions

Heuristics are ingrained cognitive processes utilized by all humans and can lead to various biases.

Both of these statements are established facts. However, this does not mean that the biases that heuristics produce are unavoidable. As the wide-ranging impacts of such biases on societal institutions have become a popular research topic, psychologists have emphasized techniques for reaching more sound, thoughtful and fair decisions in our daily lives.

Ironically, many of these techniques are themselves heuristics!

To focus on the key details of a given problem, one might create a mental list of explicit goals and values. To clearly identify the impacts of choice, one should imagine its impacts one year in the future and from the perspective of all parties involved.

Most importantly, one must gain a mindful understanding of the problem-solving techniques used by our minds and the common mistakes that result. Mindfulness of these flawed yet persistent pathways allows one to quickly identify and remedy the biases (or otherwise flawed thinking) they tend to create!

Further Information

• Shah, A. K., & Oppenheimer, D. M. (2008). Heuristics made easy: an effort-reduction framework. Psychological bulletin, 134(2), 207.
• Marewski, J. N., & Gigerenzer, G. (2012). Heuristic decision making in medicine. Dialogues in clinical neuroscience, 14(1), 77.
• Del Campo, C., Pauser, S., Steiner, E., & Vetschera, R. (2016). Decision making styles and the use of heuristics in decision making. Journal of Business Economics, 86(4), 389-412.

What is a heuristic in psychology?

A heuristic in psychology is a mental shortcut or rule of thumb that simplifies decision-making and problem-solving. Heuristics often speed up the process of finding a satisfactory solution, but they can also lead to cognitive biases.

Bobadilla-Suarez, S., & Love, B. C. (2017, May 29). Fast or Frugal, but Not Both: Decision Heuristics Under Time Pressure. Journal of Experimental Psychology: Learning, Memory, and Cognition .

Bowes, S. M., Ammirati, R. J., Costello, T. H., Basterfield, C., & Lilienfeld, S. O. (2020). Cognitive biases, heuristics, and logical fallacies in clinical practice: A brief field guide for practicing clinicians and supervisors. Professional Psychology: Research and Practice, 51 (5), 435–445.

Dietrich, C. (2010). “Decision Making: Factors that Influence Decision Making, Heuristics Used, and Decision Outcomes.” Inquiries Journal/Student Pulse, 2(02).

Groenewegen, A. (2021, September 1). Kahneman Fast and slow thinking: System 1 and 2 explained by Sue. SUE Behavioral Design. Retrieved March 26, 2022, from https://suebehaviouraldesign.com/kahneman-fast-slow-thinking/

Kahneman, D., Lovallo, D., & Sibony, O. (2011). Before you make that big decision .

Kahneman, D. (2011). Thinking, fast and slow . Macmillan.

Pratkanis, A. (1989). The cognitive representation of attitudes. In A. R. Pratkanis, S. J. Breckler, & A. G. Greenwald (Eds.), Attitude structure and function (pp. 71–98). Hillsdale, NJ: Erlbaum.

Simon, H.A., 1956. Rational choice and the structure of the environment. Psychological Review .

Tversky, A., & Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases. Science, 185 (4157), 1124–1131.

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What Are Heuristics?

These mental shortcuts lead to fast decisions—and biased thinking

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Steven Gans, MD is board-certified in psychiatry and is an active supervisor, teacher, and mentor at Massachusetts General Hospital.

Verywell / Cindy Chung 

• History and Origins
• Heuristics vs. Algorithms
• Heuristics and Bias

How to Make Better Decisions

If you need to make a quick decision, there's a good chance you'll rely on a heuristic to come up with a speedy solution. Heuristics are mental shortcuts that allow people to solve problems and make judgments quickly and efficiently. Common types of heuristics rely on availability, representativeness, familiarity, anchoring effects, mood, scarcity, and trial-and-error.

Think of these as mental "rule-of-thumb" strategies that shorten decision-making time. Such shortcuts allow us to function without constantly stopping to think about our next course of action.

However, heuristics have both benefits and drawbacks. These strategies can be handy in many situations but can also lead to  cognitive biases . Becoming aware of this might help you make better and more accurate decisions.

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History of the Research on Heuristics

Nobel-prize winning economist and cognitive psychologist Herbert Simon originally introduced the concept of heuristics in psychology in the 1950s. He suggested that while people strive to make rational choices, human judgment is subject to cognitive limitations. Purely rational decisions would involve weighing every alternative's potential costs and possible benefits.

However, people are limited by the amount of time they have to make a choice and the amount of information they have at their disposal. Other factors, such as overall intelligence and accuracy of perceptions, also influence the decision-making process.

In the 1970s, psychologists Amos Tversky and Daniel Kahneman presented their research on cognitive biases. They proposed that these biases influence how people think and make judgments.

Because of these limitations, we must rely on mental shortcuts to help us make sense of the world.

Simon's research demonstrated that humans were limited in their ability to make rational decisions, but it was Tversky and Kahneman's work that introduced the study of heuristics and the specific ways of thinking that people rely on to simplify the decision-making process.

How Heuristics Are Used

Heuristics play important roles in both  problem-solving  and  decision-making , as we often turn to these mental shortcuts when we need a quick solution.

Here are a few different theories from psychologists about why we rely on heuristics.

• Attribute substitution : People substitute simpler but related questions in place of more complex and difficult questions.
• Effort reduction : People use heuristics as a type of cognitive laziness to reduce the mental effort required to make choices and decisions.
• Fast and frugal : People use heuristics because they can be fast and correct in certain contexts. Some theories argue that heuristics are actually more accurate than they are biased.

In order to cope with the tremendous amount of information we encounter and to speed up the decision-making process, our brains rely on these mental strategies to simplify things so we don't have to spend endless amounts of time analyzing every detail.

You probably make hundreds or even thousands of decisions every day. What should you have for breakfast? What should you wear today? Should you drive or take the bus? Fortunately, heuristics allow you to make such decisions with relative ease and without a great deal of agonizing.

There are many heuristics examples in everyday life. When trying to decide if you should drive or ride the bus to work, for instance, you might remember that there is road construction along the bus route. You realize that this might slow the bus and cause you to be late for work. So you leave earlier and drive to work on an alternate route.

Heuristics allow you to think through the possible outcomes quickly and arrive at a solution.

Are Heuristics Good or Bad?

Heuristics aren't inherently good or bad, but there are pros and cons to using them to make decisions. While they can help us figure out a solution to a problem faster, they can also lead to inaccurate judgments about others or situations. Understanding these pros and cons may help you better use heuristics to make better decisions.

Types of Heuristics

There are many different kinds of heuristics. While each type plays a role in decision-making, they occur during different contexts. Understanding the types can help you better understand which one you are using and when.

Availability

The availability heuristic  involves making decisions based upon how easy it is to bring something to mind. When you are trying to make a decision, you might quickly remember a number of relevant examples.

Since these are more readily available in your memory, you will likely judge these outcomes as being more common or frequently occurring.

For example, imagine you are planning to fly somewhere on vacation. As you are preparing for your trip, you might start to think of a number of recent airline accidents. You might feel like air travel is too dangerous and decide to travel by car instead. Because those examples of air disasters came to mind so easily, the availability heuristic leads you to think that plane crashes are more common than they really are.

Familiarity

The familiarity heuristic refers to how people tend to have more favorable opinions of things, people, or places they've experienced before as opposed to new ones. In fact, given two options, people may choose something they're more familiar with even if the new option provides more benefits.

Representativeness

The representativeness heuristic  involves making a decision by comparing the present situation to the most representative mental prototype. When you are trying to decide if someone is trustworthy, you might compare aspects of the individual to other mental examples you hold.

A soft-spoken older woman might remind you of your grandmother, so you might immediately assume she is kind, gentle, and trustworthy. However, this is an example of a heuristic bias, as you can't know someone trustworthy based on their age alone.

The affect heuristic involves making choices that are influenced by an individual's emotions at that moment. For example, research has shown that people are more likely to see decisions as having benefits and lower risks when in a positive mood.

Negative emotions, on the other hand, lead people to focus on the potential downsides of a decision rather than the possible benefits.

The anchoring bias involves the tendency to be overly influenced by the first bit of information we hear or learn. This can make it more difficult to consider other factors and lead to poor choices. For example, anchoring bias can influence how much you are willing to pay for something, causing you to jump at the first offer without shopping around for a better deal.

Scarcity is a heuristic principle in which we view things that are scarce or less available to us as inherently more valuable. Marketers often use the scarcity heuristic to influence people to buy certain products. This is why you'll often see signs that advertise "limited time only," or that tell you to "get yours while supplies last."

Trial and Error

Trial and error is another type of heuristic in which people use a number of different strategies to solve something until they find what works. Examples of this type of heuristic are evident in everyday life.

People use trial and error when playing video games, finding the fastest driving route to work, or learning to ride a bike (or any new skill).

Difference Between Heuristics and Algorithms

Though the terms are often confused, heuristics and algorithms are two distinct terms in psychology.

Algorithms are step-by-step instructions that lead to predictable, reliable outcomes, whereas heuristics are mental shortcuts that are basically best guesses. Algorithms always lead to accurate outcomes, whereas, heuristics do not.

Examples of algorithms include instructions for how to put together a piece of furniture or a recipe for cooking a certain dish. Health professionals also create algorithms or processes to follow in order to determine what type of treatment to use on a patient.

How Heuristics Can Lead to Bias

Heuristics can certainly help us solve problems and speed up our decision-making process, but that doesn't mean they are always a good thing. They can also introduce errors, bias, and irrational decision-making. As in the examples above, heuristics can lead to inaccurate judgments about how commonly things occur and how representative certain things may be.

Just because something has worked in the past does not mean that it will work again, and relying on a heuristic can make it difficult to see alternative solutions or come up with new ideas.

Heuristics can also contribute to stereotypes and  prejudice . Because people use mental shortcuts to classify and categorize people, they often overlook more relevant information and create stereotyped categorizations that are not in tune with reality.

While heuristics can be a useful tool, there are ways you can improve your decision-making and avoid cognitive bias at the same time.

We are more likely to make an error in judgment if we are trying to make a decision quickly or are under pressure to do so. Taking a little more time to make a decision can help you see things more clearly—and make better choices.

Whenever possible, take a few deep breaths and do something to distract yourself from the decision at hand. When you return to it, you may find a fresh perspective or notice something you didn't before.

Identify the Goal

We tend to focus automatically on what works for us and make decisions that serve our best interest. But take a moment to know what you're trying to achieve. Consider some of the following questions:

• Are there other people who will be affected by this decision?
• What's best for them?
• Is there a common goal that can be achieved that will serve all parties?

Thinking through these questions can help you figure out your goals and the impact that these decisions may have.

Process Your Emotions

Fast decision-making is often influenced by emotions from past experiences that bubble to the surface. Anger, sadness, love, and other powerful feelings can sometimes lead us to decisions we might not otherwise make.

Is your decision based on facts or emotions? While emotions can be helpful, they may affect decisions in a negative way if they prevent us from seeing the full picture.

Recognize All-or-Nothing Thinking

When making a decision, it's a common tendency to believe you have to pick a single, well-defined path, and there's no going back. In reality, this often isn't the case.

Sometimes there are compromises involving two choices, or a third or fourth option that we didn't even think of at first. Try to recognize the nuances and possibilities of all choices involved, instead of using all-or-nothing thinking .

Heuristics are common and often useful. We need this type of decision-making strategy to help reduce cognitive load and speed up many of the small, everyday choices we must make as we live, work, and interact with others.

But it pays to remember that heuristics can also be flawed and lead to irrational choices if we rely too heavily on them. If you are making a big decision, give yourself a little extra time to consider your options and try to consider the situation from someone else's perspective. Thinking things through a bit instead of relying on your mental shortcuts can help ensure you're making the right choice.

Vlaev I. Local choices: Rationality and the contextuality of decision-making .  Brain Sci . 2018;8(1):8. doi:10.3390/brainsci8010008

Hjeij M, Vilks A. A brief history of heuristics: how did research on heuristics evolve? Humanit Soc Sci Commun . 2023;10(1):64. doi:10.1057/s41599-023-01542-z

Brighton H, Gigerenzer G. Homo heuristicus: Less-is-more effects in adaptive cognition .  Malays J Med Sci . 2012;19(4):6-16.

Schwartz PH. Comparative risk: Good or bad heuristic?   Am J Bioeth . 2016;16(5):20-22. doi:10.1080/15265161.2016.1159765

Schwikert SR, Curran T. Familiarity and recollection in heuristic decision making .  J Exp Psychol Gen . 2014;143(6):2341-2365. doi:10.1037/xge0000024

AlKhars M, Evangelopoulos N, Pavur R, Kulkarni S. Cognitive biases resulting from the representativeness heuristic in operations management: an experimental investigation .  Psychol Res Behav Manag . 2019;12:263-276. doi:10.2147/PRBM.S193092

Finucane M, Alhakami A, Slovic P, Johnson S. The affect heuristic in judgments of risks and benefits . J Behav Decis Mak . 2000; 13(1):1-17. doi:10.1002/(SICI)1099-0771(200001/03)13:1<1::AID-BDM333>3.0.CO;2-S

Teovanović P. Individual differences in anchoring effect: Evidence for the role of insufficient adjustment .  Eur J Psychol . 2019;15(1):8-24. doi:10.5964/ejop.v15i1.1691

Cheung TT, Kroese FM, Fennis BM, De Ridder DT. Put a limit on it: The protective effects of scarcity heuristics when self-control is low . Health Psychol Open . 2015;2(2):2055102915615046. doi:10.1177/2055102915615046

Mohr H, Zwosta K, Markovic D, Bitzer S, Wolfensteller U, Ruge H. Deterministic response strategies in a trial-and-error learning task . Inman C, ed. PLoS Comput Biol. 2018;14(11):e1006621. doi:10.1371/journal.pcbi.1006621

Grote T, Berens P. On the ethics of algorithmic decision-making in healthcare .  J Med Ethics . 2020;46(3):205-211. doi:10.1136/medethics-2019-105586

Bigler RS, Clark C. The inherence heuristic: A key theoretical addition to understanding social stereotyping and prejudice. Behav Brain Sci . 2014;37(5):483-4. doi:10.1017/S0140525X1300366X

del Campo C, Pauser S, Steiner E, et al.  Decision making styles and the use of heuristics in decision making .  J Bus Econ.  2016;86:389–412. doi:10.1007/s11573-016-0811-y

Marewski JN, Gigerenzer G. Heuristic decision making in medicine .  Dialogues Clin Neurosci . 2012;14(1):77-89. doi:10.31887/DCNS.2012.14.1/jmarewski

Zheng Y, Yang Z, Jin C, Qi Y, Liu X. The influence of emotion on fairness-related decision making: A critical review of theories and evidence .  Front Psychol . 2017;8:1592. doi:10.3389/fpsyg.2017.01592

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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Heuristic Methods: The Definition, Use Case, and Relevance for Enterprises

What is it.

Heuristic methods are problem-solving strategies that use practical, common-sense principles to address complex issues. These methods are often used in artificial intelligence to help machines make decisions and solve problems in a more human-like manner. Heuristic methods allow AI to reason and learn from past experiences, making them more efficient and effective in a variety of tasks.

In business, heuristic methods can be incredibly valuable for decision-making and problem-solving. They allow AI systems to quickly evaluate large amounts of data and make informed choices, which can lead to more optimized processes and better outcomes. For example, in marketing, AI can use heuristic methods to analyze customer behavior and make personalized recommendations. In finance, heuristic methods can be used to identify patterns and trends in market data. Overall, heuristic methods help businesses leverage the power of AI to make smarter decisions and achieve better results.

How does it work?

Heuristic methods are rules or guidelines that AI uses to make decisions, rather than following a strict set of instructions. For example, you can think of heuristic methods like a set of general guidelines that a coach might give to a sports team. Instead of telling the players exactly what to do in every situation, the coach gives them some general guidelines to follow based on their experience and knowledge of the game.

In the same way, AI uses heuristic methods to make decisions based on its experience and knowledge of the data it has been given. This allows AI to be flexible and adapt to new situations, rather than being limited to a rigid set of instructions.

For example, let’s say you run a retail business and you want to use AI to predict which products are likely to sell well in the coming months. You could use heuristic methods to analyze past sales data, customer behavior, and market trends to come up with a set of general rules that the AI can use to make predictions. This allows the AI to make informed decisions without needing to be explicitly told what to do in every situation.

I hope this helps to give you a better understanding of how AI works using heuristic methods!

• Heuristic methods can provide quick, approximate solutions to complex problems, making them useful in decision-making and problem-solving scenarios.
• They are relatively easy to implement and can be applied in a wide range of domains, from computer science to psychology to economics.
• Heuristic methods can help in generating new ideas and insights by providing a different perspective on a problem.
• They are not always guaranteed to produce the best solution, and their results may be suboptimal in some cases.
• Heuristic methods can be biased and may lead to errors or inaccuracies, especially when dealing with incomplete or uncertain information.
• There is a risk of over-reliance on heuristic methods, which may limit the exploration of alternative problem-solving approaches.

Applications and Examples

Heuristic methods are commonly used in artificial intelligence to solve complex problems or make decisions based on limited information. For example, in route planning apps, heuristic methods may be used to find the most efficient route by considering factors such as traffic conditions, distance, and historical travel data.

Another example of heuristic methods in artificial intelligence is in medical diagnosis systems. These systems may use heuristic methods to determine the likelihood of a certain disease based on a patient’s symptoms, medical history, and demographic information.

In both of these examples, heuristic methods in artificial intelligence allow for more efficient and accurate decision-making when faced with complex and uncertain situations.

History and Evolution

The term ""heuristic methods"" was coined in the early 19th century by the German cognitive psychologist, Abraham Maslow. He introduced the term to describe problem-solving strategies that are practical, intuitive, and efficient, even if not always guaranteed to produce the most optimal solution. Heuristic methods were initially used in cognitive psychology to explain how individuals make decisions in complex or uncertain situations, based on their intuition and experience.

Over time, the term ""heuristic methods"" has become a key concept in the field of artificial intelligence. In AI, heuristic methods refer to algorithms that use rules of thumb, trial and error, or domain-specific knowledge to guide the search for solutions in complex problems. The use of heuristic methods has evolved to be a crucial component in various AI applications, such as heuristic search algorithms, heuristic evaluation techniques, and heuristic optimization methods. The term's application within AI has expanded to encompass a wide range of problem-solving approaches that prioritize efficiency and speed over optimality.

Heuristic methods in artificial intelligence are crucial for businesses to understand and utilize.

These methods involve using practical and experience-based techniques to solve complex problems, making them essential for decision-making and problem-solving processes within a business. By leveraging heuristic methods, businesses can improve their operational efficiency, gain insights into customer behavior, and enhance their overall decision-making processes.

Additionally, understanding heuristic methods in AI can assist businesses in developing more effective strategies for marketing, customer engagement, and product development. With the ability to analyze large volumes of data and identify patterns, heuristic methods allow businesses to make more informed and strategic decisions, ultimately leading to improved performance and competitiveness in the market.

Overall, the importance of heuristic methods in AI cannot be understated, as they hold the potential to revolutionize the way businesses operate and compete in the modern business landscape.

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What are heuristics and how do they help us make decisions?

Heuristics are simple rules of thumb that our brains use to make decisions. When you choose a work outfit that looks professional instead of sweatpants, you’re making a decision based on past information. That's not intuition; it’s heuristics. Instead of weighing all the information available to make a data-backed choice, heuristics enable us to move quickly into action—mostly without us even realizing it. In this article, you’ll learn what heuristics are, their common types, and how we use them in different scenarios.

Green means go. Most of us accept this as common knowledge, but it’s actually an example of a micro-decision—in this case, your brain is deciding to go when you see the color green.

You make countless of these subconscious decisions every day. Many things that you might think just come naturally to you are actually caused by heuristics—mental shortcuts that allow you to quickly process information and take action. Heuristics help you make smaller, almost unnoticeable decisions using past information, without much rational input from your brain.

Heuristics are helpful for getting things done more quickly, but they can also lead to biases and irrational choices if you’re not aware of them. Luckily, you can use heuristics to your advantage once you recognize them, and make better decisions in the workplace.

What is a heuristic?

Heuristics are mental shortcuts that your brain uses to make decisions. When we make rational choices, our brains weigh all the information, pros and cons, and any relevant data. But it’s not possible to do this for every single decision we make on a day-to-day basis. For the smaller ones, your brain uses heuristics to infer information and take almost-immediate action.

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How heuristics work

For example, if you’re making a larger decision about whether to accept a new job or stay with your current one, your brain will process this information slowly. For decisions like this, you collect data by referencing sources—chatting with mentors, reading company reviews, and comparing salaries. Then, you use that information to make your decision. Meanwhile, your brain is also using heuristics to help you speed along that track. In this example, you might use something called the “availability heuristic” to reference things you’ve recently seen about the new job. The availability heuristic makes it more likely that you’ll remember a news story about the company’s higher stock prices. Without realizing it, this can make you think the new job will be more lucrative.

On the flip side, you can recognize that the new job has had some great press recently, but that might be just a great PR team at work. Instead of “buying in” to what the availability heuristic is trying to tell you—that positive news means it’s the right job—you can acknowledge that this is a bias at work. In this case, comparing compensation and work-life balance between the two companies is a much more effective way to choose which job is right for you.

History of heuristics

The term "heuristics," originating from the Greek word meaning “to discover,” has ancient roots, but much of today's understanding comes from twentieth-century social scientists. Herbert Simon's research into "bounded rationality" highlighted the use of heuristics in decision-making, particularly under constraints like limited time and information.

Daniel Kahneman was one of the first researchers to study heuristics in his behavioral economics work in the 1970’s, along with fellow psychologist Amos Tversky. They theorized that many of the decisions and judgments we make aren’t rational—meaning we don’t move through a series of decision-making steps to come to a solution. Instead, the human brain uses mental shortcuts to form seemingly irrational, “fast and frugal” decisions—quick choices that don’t require a lot of mental energy.

Kahneman’s work showed that heuristics lead to systematic errors (or biases), which act as the driving force for our decisions. He was able to apply this research to economic theory, leading to the formation of behavioral economics and a Nobel Prize for Kahneman in 2002.

In the years since, the study of heuristics has grown in popularity with economists and in cognitive psychology. Gerd Gigerenzer’s research , for example, challenges the idea that heuristics lead to errors or flawed thinking. He argues that heuristics are actually indicators that human beings are able to make decisions more effectively without following the traditional rules of logic. His research seems to indicate that heuristics lead us to the right answer most of the time.

Types of heuristics

Heuristics are everywhere, whether we notice them or not. There are hundreds of heuristics at play in the human brain, and they interact with one another constantly. To understand how these heuristics can help you, start by learning some of the more common types of heuristics.

Recognition heuristic

The recognition heuristic uses what we already know (or recognize) as a criterion for decisions. The concept is simple: When faced with two choices, you’re more likely to choose the item you recognize versus the one you don’t.

This is the very base-level concept behind branding your business, and we see it in all well-known companies. Businesses develop a brand messaging strategy in the hopes that when you’re faced with buying their product or buying someone else's, you recognize their product, have a positive association with it, and choose that one. For example, if you’re going to grab a soda and there are two different cans in the fridge, one a Coca-Cola, and the other a soda you’ve never heard of, you are more likely to choose the Coca-Cola simply because you know the name.

Familiarity heuristic

The familiarity heuristic is a mental shortcut where individuals prefer options or information that is familiar to them. This heuristic is based on the notion that familiar items are seen as safer or superior. It differs from the recognition heuristic, which relies solely on whether an item is recognized. The familiarity heuristic involves a deeper sense of comfort and understanding, as opposed to just recognizing something.

An example of this heuristic is seen in investment decisions. Investors might favor well-known companies over lesser-known ones, influenced more by brand familiarity than by an objective assessment of the investment's potential. This tendency showcases how the familiarity heuristic can lead to suboptimal choices, as it prioritizes comfort and recognition over a thorough evaluation of all available options.

Availability heuristic

The availability heuristic is a cognitive bias where people judge the frequency or likelihood of events based on how easily similar instances come to mind. This mental shortcut depends on the most immediate examples that pop into one's mind when considering a topic or decision. The ease of recalling these instances often leads to a distorted perception of their actual frequency, as recent, dramatic, or emotionally charged memories tend to be more memorable.

A notable example of the availability heuristic is the public's reaction to shark attacks. When the media reports on shark attacks, these incidents become highly memorable due to their dramatic nature, leading people to overestimate the risk of such events. This heightened perception is despite statistical evidence showing the rarity of shark attacks. The result is an exaggerated fear and a skewed perception of the actual danger of swimming in the ocean.

Representativeness heuristic

The representativeness heuristic is when we try to assign an object to a specific category or idea based on past experiences. Oftentimes, this comes up when we meet people—our first impression. We expect certain things (such as clothing and credentials) to indicate that a person behaves or lives a certain way.

Without proper awareness, this heuristic can lead to discrimination in the workplace. For example, representativeness heuristics might lead us to believe that a job candidate from an Ivy League school is more qualified than one from a state university, even if their qualifications show us otherwise. This is because we expect Ivy League graduates to act a certain way, such as by being more hard-working or intelligent. Of course, in our rational brains, we know this isn’t the case. That’s why it’s important to be aware of this heuristic, so you can use logical thinking to combat potential biases.

Anchoring and adjustment heuristic

Used in finance for economic forecasting, anchoring and adjustment is when you start with an initial piece of information (the anchor) and continue adjusting until you reach an acceptable decision. The challenge is that sometimes the anchor ends up not being a good enough value to begin with. In other words, you choose the anchor based on unknown biases and then make further decisions based on this faulty assumption.

Anchoring and adjustment are often used in pricing, especially with SaaS companies. For example, a displayed, three-tiered pricing model shows you how much you get for each price point. The layout is designed to make it look like you won’t get much for the lower price, and you don’t necessarily need the highest price, so you choose the mid-level option (the original target). The anchors are the low price (suggesting there’s not much value here) and the high price (which shows that you’re getting a "discount" if you choose another option). Thanks to those two anchors, you feel like you’re getting a lot of value, no matter what you spend.

Affect heuristic

You know the advice; think with your heart. That’s the affect heuristic in action, where you make a decision based on what you’re feeling. Emotions are important ways to understand the world around us, but using them to make decisions is irrational and can impact your work.

For example, let’s say you’re about to ask your boss for a promotion. As a product marketer, you’ve made a huge impact on the company by helping to build a community of enthusiastic, loyal customers. But the day before you have your performance review , you find out that a small project you led for a new product feature failed. You decide to skip the conversation asking for a raise and instead double down on how you can improve.

In this example, you’re using the affect heuristic to base your entire performance on the failure of one small project—even though the rest of your performance (building that profitable community) is much more impactful than a new product feature. If you weighed the options rationally, you would see that asking for a raise is still a logical choice. But instead, the fear of asking for a raise after a failure felt like too big a trade-off.

Satisficing

Satisficing is when you accept an available option that’s satisfactory (i.e., just fine) instead of trying to find the best possible solution. In other words, you’re settling. This creates a “bounded rationality,” where you’re constrained by the choices that are good-enough, instead of pushing past the limits to discover more. This isn’t always negative—for lower-impact scenarios, it might not make sense to invest time and energy into finding the optimal choice. But there are also times when this heuristic kicks in and you end up settling for less than what’s possible.

For example, let’s say you’re a project manager planning the budget for the next fiscal year. Instead of looking at previous spend and revenue, you satisfice and base the budget off projections, assuming that will be good enough. But without factoring in historical data, your budget isn’t going to be as equipped to manage hiccups or unexpected changes. In this case, you can mitigate satisficing with a logically-based data review that, while longer, will produce a more accurate and thoughtful budget plan.

Trial and error heuristic

The trial and error heuristic is a problem-solving method where solutions are found through repeated experimentation. It's used when a clear path to the solution isn't known, relying on iterative learning from failures and adjustments.

For example, a chef might experiment with various ingredient combinations and techniques to perfect a new recipe. Each attempt informs the next, demonstrating how trial and error facilitates discovery in situations without formal guidelines.

Pros and cons of heuristics

Heuristics are effective at helping you get more done quickly, but they also have downsides. Psychologists don’t necessarily agree on whether heuristics and biases are positive or negative. But the argument seems to boil down to these two pros and cons:

Heuristics pros:

Simple heuristics reduce cognitive load, allowing you to accomplish more in less time with fast and frugal decisions. For example, the satisficing heuristic helps you find a "good enough" choice. So if you’re making a complex decision between whether to cut costs or invest in employee well-being , you can use satisficing to find a solution that’s a compromise. The result might not be perfect, but it allows you to take action and get started—you can always adjust later on.

Heuristics cons:

Heuristics create biases. While these cognitive biases enable us to make rapid-fire decisions, they can also lead to rigid, unhelpful beliefs. For example, confirmation bias makes it more likely that you’ll seek out other opinions that agree with your own. This makes it harder to keep an open mind, hear from the other side, and ultimately change your mind—which doesn’t help you build the flexibility and adaptability so important for succeeding in the workplace.

Heuristics and psychology

Heuristics play a pivotal role in psychology, especially in understanding how people make decisions within their cognitive limitations. These mental shortcuts allow for quicker decisions, often necessary in a fast-paced world, but they can sometimes lead to errors in judgment.

The study of heuristics bridges various aspects of psychology, from cognitive processes to behavioral outcomes, and highlights the balance between efficient decision-making and the potential for bias.

Stereotypes and heuristic thinking

Stereotypes are a form of heuristic where individuals make assumptions based on group characteristics, a process analyzed in both English and American psychology.

While these generalizations can lead to rapid conclusions and rational decisions under certain circumstances, they can also oversimplify complex human behaviors and contribute to prejudiced attitudes. Understanding stereotypes as a heuristic offers insight into the cognitive limitations of the human mind and their impact on social perceptions and interactions.

How heuristics lead to bias

Because heuristics rely on shortcuts and stereotypes, they can often lead to bias. This is especially true in scenarios where cognitive limitations restrict the processing of all relevant information. So how do you combat bias? If you acknowledge your biases, you can usually undo them and maybe even use them to your advantage. There are ways you can hack heuristics, so that they work for you (not against you):

Be aware. Heuristics often operate like a knee-jerk reaction—they’re automatic. The more aware you are, the more you can identify and acknowledge the heuristic at play. From there, you can decide if it’s useful for the current situation, or if a logical decision-making process is best.

Flip the script. When you notice a negative bias, turn it around. For example, confirmation bias is when we look for things to be as we expect. So if we expect our boss to assign us more work than our colleagues, we might always experience our work tasks as unfair. Instead, turn this around by repeating that your boss has your team’s best interests at heart, and you know everyone is working hard. This will re-train your confirmation bias to look for all the ways that your boss is treating you just like everyone else.

Practice mindfulness. Mindfulness helps to build self-awareness, so you know when heuristics are impacting your decisions. For example, when we tap into the empathy gap heuristic, we’re unable to empathize with someone else or a specific situation. However, if we’re mindful, we can be aware of how we’re feeling before we engage. This helps us to see that the judgment stems from our own emotions and probably has nothing to do with the other person.

Examples of heuristics in business

This is all well and good in theory, but how do heuristic decision-making and thought processes show up in the real world? One reason researchers have invested so much time and energy into learning about heuristics is so that they can use them, like in these scenarios:

How heuristics are used in marketing

Effective marketing does so much for a business—it attracts new customers, makes a brand a household name, and converts interest into sales, to name a few. One way marketing teams are able to accomplish all this is by applying heuristics.

Let’s use ambiguity aversion as an example. Ambiguity aversion means you're less likely to choose an item you don’t know. Marketing teams combat this by working to become familiar to their customers. This could include the social media team engaging in a more empathetic or conversational way, or employing technology like chat-bots to show that there’s always someone available to help. Making the business feel more approachable helps the customer feel like they know the brand personally—which lessens ambiguity aversion.

How heuristics are used in business strategy

Have you ever noticed how your CEO seems to know things before they happen? Or that the CFO listens more than they speak? These are indications that they understand people in a deeper way, and are able to engage with their employees and predict outcomes because of it. C-suite level executives are often experts in behavioral science, even if they didn’t study it. They tend to get what makes people tick, and know how to communicate based on these biases. In short, they use heuristics for higher-level decision-making processes and execution. 

This includes business strategy . For example, a startup CEO might be aware of their representativeness bias towards investors—they always look for the person in the room with the  fancy suit or car. But after years in the field, they know logically that this isn’t always true—plenty of their investors have shown up in shorts and sandals. Now, because they’re aware of their bias, they can build it into their investment strategy. Instead of only attending expensive, luxury events, they also attend conferences with like-minded individuals and network among peers. This approach can lead them to a greater variety of investors and more potential opportunities.

Heuristics vs algorithms

Heuristics and algorithms are both used by the brain to reduce the mental effort of decision-making, but they operate a bit differently. Algorithms act as guidelines for specific scenarios. They have a structured process designed to solve that specific problem. Heuristics, on the other hand, are general rules of thumb that help the brain process information and may or may not reach a solution.

For example, let's say you’re cooking a well-loved family recipe. You know the steps inside and out, and you no longer need to reference the instructions. If you’re following a recipe step-by-step, you’re using an algorithm. If, however, you decide on a whim to sub in some of your fresh garden vegetables because you think it will taste better, you’re using a heuristic.

How to use heuristics to make better decisions

Heuristics can help us make decisions quickly and with less cognitive strain. While they can be efficient, they sometimes lead to errors in judgment. Understanding how to use heuristics effectively can improve decision-making, especially in complex or uncertain situations.

Take time to think

Rushing often leads to reliance on automatic heuristics, which might not always be suitable. To make better decisions, slow down your thinking process. Take a step back, breathe, and allow yourself a moment of distraction. This pause can provide a fresh perspective and help you notice details or angles you might have missed initially.

Clarify your objectives

When making a decision, it's important to understand the ultimate goal. Our automatic decision-making processes tend to favor immediate benefits, sometimes overlooking long-term impacts or the needs of others involved. Consider the broader implications of your decision. Who else is affected? Is there a common objective that benefits all parties? Such considerations can lead to more holistic and effective decisions.

Manage your emotional influences

Emotions significantly influence our decision-making, often without our awareness. Fast decisions are particularly prone to emotional biases. Acknowledge your feelings, but also separate them from the facts at hand. Are you making a decision based on solid information or emotional reactions? Distinguishing between the two can lead to more rational and balanced choices.

Beware of binary thinking

All-or-nothing thinking is a common heuristic trap, where we see decisions as black or white with no middle ground. However, real-life decisions often have multiple paths and possibilities. It's important to recognize this complexity. There might be compromises or alternative options that weren't initially considered. By acknowledging the spectrum of possibilities, you can make more nuanced and effective decisions.

Heuristic FAQs

What is heuristic thinking.

Heuristic thinking refers to a method of problem-solving, learning, or discovery that employs a practical approach—often termed a "rule of thumb"—to make decisions quickly. Heuristic thinking is a type of cognition that humans use subconsciously to make decisions and judgments with limited time.

What is a heuristic evaluation?

A heuristic evaluation is a usability inspection method used in the fields of user interface (UI) and user experience (UX) design. It involves evaluators examining the interface and judging its compliance with recognized usability principles, known as heuristics. These heuristics serve as guidelines to identify usability problems in a design, making the evaluation process more systematic and comprehensive.

What are computer heuristics?

Computer heuristics are algorithms used to solve complex problems or make decisions where an exhaustive search is impractical. In fields like artificial intelligence and cybersecurity, these heuristic methods allow for efficient problem-solving and decision-making, often based on trial and error or rule-of-thumb strategies.

What are heuristics in psychology?

In psychology, heuristics are quick mental rules for making decisions. They are important in social psychology for understanding how we think and decide. Figures like Kahneman and Tversky, particularly in their work "Judgment Under Uncertainty: Heuristics and Biases," have influenced the study of heuristics in psychology.

Learn heuristics, de-mystify your brain

Your brain doesn’t actually work in mysterious ways. In reality, researchers know why we do a lot of the things we do. Heuristics help us to understand the choices we make that don’t make much sense. Once you understand heuristics, you can also learn to use them to your advantage—both in business, and in life. 

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Using Heuristic Problem-Solving Methods for Effective Decision-Making

Problem-solving capability and effective decision making are two of the most prized capabilities of any leader. However, one cannot expect these traits to be simply present by default in an individual, as both require extensive analysis of the root cause of issues and to know what to look for when anticipating a gain. In a previous article, we brought you  5 Problem-Solving Strategies to Become a Better Problem Solver . This time we have something that can help you dig deep to resolve problems, i.e. using heuristic problem-solving methods for effective decision-making.

What are Heuristics?

Heuristics are essentially problem-solving tools that can be used for solving non-routine and challenging problems. A heuristic method is a practical approach for a short-term goal, such as solving a problem. The approach might not be perfect but can help find a quick solution to help move towards a reasonable way to resolve a problem.

Example: A computer that is to be used for an event to allow presenters to play PowerPoint presentations via a projector malfunctions due to an operating system problem. In such a case a system administrator might quickly refresh the system using a backup to make it functional for the event. Once the event concludes the system administrator can run detailed diagnostic tests to see if there are any further underlying problems that need to be resolved.

In this example, restoring the system using a backup was a short-term solution to solve the immediate problem, i.e. to make the system functional for the event that was to start in a few hours. There are a number of heuristic methods that can lead to such a decision to resolve a problem. These are explained in more detail in the sections below.

Examples of Heuristic Methods Used for Challenging and Non-Routine Problems

Heuristic methods can help ease the cognitive load by making it easy to process decisions. These include various basic methods that aren’t rooted in any theory per se but rather rely on past experiences and common sense. Using heuristics one can, therefore, resolve challenging and non-routine problems. Let’s take a look at some examples.

A Rule of Thumb

This includes using a method based on practical experience. A rule of thumb can be applied to find a short-term solution to a problem to quickly resolve an issue during a situation where one might be pressed for time.

Example: In the case of the operating system failure mentioned earlier, we assume that the PC on which PowerPoint presentations are to be run by presenters during an event is getting stuck on the start screen. Considering that the event is about to start in 2 hours, it is not practical for the system administrator to reinstall the operating system and all associated applications, hotfixes and updates, as it might take several hours. Using a rule of thumb, he might try to use various tried and tested methods, such as trying to use a system restore point to restore the PC without deleting essential files or to use a backup to restore the PC to an earlier environment.

An Educated Guess

An educated guess or guess and check can help resolve a problem by using knowledge and experience. Based on your knowledge of a subject, you can make an educated guess to resolve a problem.

Example: In the example of the malfunctioning PC, the system administrator will have to make an educated guess regarding the best possible way to resolve the problem. The educated guess, in this case, can be to restore the system to a backup instead of using system restore, both of which might take a similar amount of time; however, the former is likely to work better as a quick fix based on past experience and knowledge of the system administrator.

Trial and Error

This is another heuristic method to problem-solving where one might try various things that are expected to work until a solution is achieved.

Example: The system administrator might try various techniques to fix the PC using trial and error. He might start with checking if the system is accessible in safe mode. And if so, does removing a newly installed software or update solve the problem? If he can’t access the system at all, he might proceed with restoring it from a backup. If that too fails, he might need to quickly opt for a wipe and load installation and only install PowerPoint to ensure that at least presenters can run presentations on the PC. In this case he can perform other required software installations after the event.

An Intuitive Judgment

Intuitive judgment does not result from a rational analysis of a situation or based on reasoning. It is more of a feeling one has which may or may not lead to the desired outcome. Sometimes, intuitive judgement can help resolve problems. Perhaps the most rational way to describe an intuition is that it is some type of calculation at the subconscious level, where you can’t put your finger on the reason why you think something might be the way it is.

Example: The system administrator might have a feeling that the PC is not working because the hard drive has failed. This might be an intuitive judgment without hard evidence. He might quickly replace the hard drive to resolve the problem. Later, after he runs diagnostics on the old hard drive, he might realize that it was indeed that hard drive that was faulty and trying to fix it would have been a waste of time. In this case, he might be able to solve a problem using intuitive judgment.

Stereotyping

A stereotype is an opinion which is judgmental rather than rational. Certain types of possessions for example create a stereotype of social status. A person who wears an expensive watch might be deemed rich, although he might simply have received it as a gift from someone, instead of being rich himself.

Example: A certain company might have developed a bad reputation of developing faulty hard drives. If the systems administrator sees the name of that company on the hard drive when opening the faulty PC, he might think that the hard drive is faulty based on stereotyping and decide to replace it.

Profiling is used to systematically analyze data to understand its dynamics. Profiling as a heuristic method for problem-solving might entail analyzing data to understand and resolve a problem or to look for patterns, just like a root cause analysis .

Example: To solve the issue of the faulty PC, a system administrator might look for similar patterns which might have led to the problem. He might search online for solutions via online forums to understand what might have caused the issue. He might also look at the information associated with recently installed software and updates to see if something conflicted with the operating system. During the profiling process, he might realize that software he installed yesterday before shutting down the PC is the cause of the problem, since similar issues have been reported by other users. He might try to remove the software using Safe Mode or by removing its files by running the computer from a bootable disc drive.

Common Sense

Common sense is the use of practical judgment to understand something. The use of common sense is also a heuristic method used for problem-solving.

Example: When dealing with a faulty PC the system administrator sees smoke coming out of the PC. In this case, it is common sense that a hardware component is faulty. He shuts down the PC, removes the power cord and investigates the issue further based on common sense. This is because keeping the system linked to a power socket amidst smoke emitting from the PC can only make things worse. It is common sense to turn off everything and take the necessary precautions to investigate the issue further.

How are Heuristic Methods Used in Decision-Making?

There are a number of formal and informal models of heuristics used for decision making. Let’s take a look at a few of the formal models of heuristics used for decision making.

Formal Models of Heuristics

Fast-and-frugal tree.

A fast-and-frugal tree is a classification or decision tree. It is a graphical form that helps make decisions. For example, a fast-and-frugal tree might help doctors determine if a patient should be sent to a regular ward or for an emergency procedure. fast-and-frugal trees are methods for making decisions based on hierarchical models, where one has to make a decision based on little information.

Fluency Heuristic

In psychology, fluency heuristic implies an object that can be easily processed and deemed to have a higher value, even if it is not logical to assume this. Understanding the application of fluency heuristic can help make better decisions in a variety of fields. Fluency heuristic is more like sunk cost fallacy .

For example, a designer might design a user interface that is easier for users to process, with fewer buttons and easily labeled options. This can help them think fast, work quicker and improve productivity. Similarly, the concept might be used in marketing to sell products using effective marketing techniques. Even if two products are identical, a consumer might pick one over the other based on fluency heuristic. The consumer might deem the product to be better for his needs, even if it is the same as the other one.

Gaze Heuristic

Assume that you aim to catch a ball. Based on your judgment you would leap to catch the ball. If you were to leave yourself to instinct, you will end up at the same spot to catch the ball at a spot you would predict it to fall. This is essentially gaze heuristic. The concept of gaze heuristic is thought to be applied for simple situations and its applications are somewhat limited.

Recognition Heuristic

If there are two objects, one recognizable and the one isn’t, the person is likely to deem the former to be of greater value. A simple example of recognition heuristic is branding. People get used to brand logos, assuming them to be of high quality. This helps brands to sell multiple products using recognition heuristic. So, if you are looking to buy an air conditioner and come across two products, A and B, where A is a brand you know and B is a new company you don’t recognize, you might opt for A. Even if B is of better quality, you might simply trust A because you have been buying electronics from the brand for many years and they have been of good quality.

Satisficing

Satisficing entails looking for alternatives until an acceptable threshold can be ensured. Satisficing in decision making implies selecting an option which meets most needs or the first option which can meet a need, even if it is not the optimal solution. For example, when choosing between early retirement or continuing service for 2 or 3 more years, one might opt for early retirement assuming that it would meet the individual’s needs.

Similarity Heuristic

Similarity heuristic is judgment based on which is deemed similar, if something reminds someone of good or bad days, something similar might be considered the same. Similarity heuristics is often used by brands to remind people of something that they might have sentimental value for.

Someone might buy a limited-edition bottle of perfume that is being sold in a packaging style that was replaced 20 years ago. Assuming that sales were great in those days, the company might sell such limited-edition perfume bottles in the hope of boosting sales. Consumers might buy them simply because they remind them of the ‘good old days’, even though the product inside might not even be of the same but rather similar to what it used to be. Many consumers claim to buy these types of products claiming that it reminds them of a fond memory, such as their youth, marriage or  first job, when they used the product back in the day.

Final Words

Heuristics play a key role in decision making and affect the way we make decisions. Understanding heuristics can not only help resolve problems but also understand biases that affect effective decision making. A business decision or one that affects one’s health, life, or well-being cannot rely merely on a hunch. Understanding heuristics and applying them effectively can therefore help make the best possible decisions. Heuristic methods are not only used in different professions and personal decision making but are also used in artificial intelligence and programming.

Modern anti-virus software for instance uses heuristic methods to dig out the most elusive malware. The same rule can be essentially applied to decision making, by effectively using heuristics to resolve problems and to make decisions based on better judgment.

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Common Sense, Decision Making, Educated Guess, Heuristics, Judgment, Problem Solving, Profiling, Rule of Thumb, Stereotyping, Trial and Error Filed under Business

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Exploring Heuristic Methods For Problem Solving

Heuristic methods refer to experience-based techniques for mastering problem solving , learning , and discovery that find solutions that are good enough but may not be optimal.

Heuristics are mental shortcuts that allow people to solve problems and make judgments quickly based on intuitive judgments.

Background In Heuristic Methods In Business

Heuristic methods have long been used in business as a practical approach to making decisions and judgments efficiently.

The rationale behind using heuristics in business is that they allow managers and leaders to make timely assessments and choices without getting bogged down in a lengthy optimization process.

Some key reasons why businesses rely on heuristic methods include:

• Business problems are often complex with many variables, making strict optimization difficult. Heuristics allow for quick solutions.
• There is often uncertainty and ambiguity in business situations. Heuristics help managers make decent decisions with incomplete information.
• Businesses need to be agile and adapt quickly to changing conditions. Heuristics facilitate fast decision making.
• Finding optimal solutions can require significant time, resources, and information that businesses often don’t have. Heuristics provide good enough solutions.

Examples Of Heuristic Methods Used In Business

Here are 7 common heuristic techniques used in a business context:

• Satisficing: Managers set a minimum threshold or standard and choose the first option that meets it rather than finding the optimal solution.
• Rules of Thumb: Businesses use simple decision rules gained from experience, such as setting prices at double the production cost.
• Extrapolation: Projecting historical data into the future based on current trends, such as forecasting sales.
• Estimation: Gauging an approximate value when the precise value is unknown, like estimating project costs.
• Elimination-by-Aspects: Removing options based on a key disqualifying trait rather than systematically comparing all options.
• Recognition: Making decisions by recognizing similarities of a current situation to past experiences.
• Availability : Judging an event’s likelihood based on how readily examples come to mind. Used to assess business risks.

Challenges With Relying On Heuristics

While heuristic methods are very useful in business, overreliance on heuristics can also lead to poor decisions and cognitive biases. Some limitations to keep in mind include:

• Heuristics may lead to suboptimal solutions rather than optimal ones.
• They are prone to biases which can skew judgment.
• Overuse of heuristics can inhibit creative problem solving .
• They rely heavily on the intuition and past experience of the individual.
• Changing environments can make previously useful heuristics less relevant.

Using Heuristics Positively In Business

Despite their shortcomings, heuristics can be leveraged productively in business. Here are 10 tips:

• Clearly define the problem before applying a heuristic.
• Use heuristics as one input but don’t rely entirely on them.
• Combine heuristics with optimization models when possible.
• Leverage heuristics to direct and focus optimization techniques.
• Apply multiple heuristics and look for consensus.
• Update heuristics as the business environment evolves.
• Weigh heuristic solutions against data and metrics when available.
• Recognize the influence of biases and test assumptions.
• Consider when heuristics may lead to suboptimal results or cognitive biases.
• Ensure heuristics align with organizational values and goals.

Heuristic methods provide business leaders with practical mental shortcuts for making timely decisions with limited information.

While overreliance on heuristics can be risky, used judiciously and strategically they offer a valuable decision-making tool.

Businesses should leverage heuristics while being aware of their limitations and mitigating the risks of biases. With the right approach, they can enhance agility and performance.

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Heuristic algorithms

Author: Anmol Singh (as2753) (ChemE 6800 Fall 2020)

• 1 Introduction
• 2.1.1 Example: Scheduling Problem
• 2.2.1 Example Problem
• 3.1 Genetic Algorithm
• 3.2.1 Example: The Classical Vehicle Routing Problem
• 3.3 Simulated Annealing Algorithm
• 4 Numerical Example: Knapsack Problem
• 5 Applications
• 6 Conclusion
• 7 References

Introduction

In mathematical programming, a heuristic algorithm is a procedure that determines near-optimal solutions to an optimization problem. However, this is achieved by trading optimality, completeness, accuracy, or precision for speed. [1] Nevertheless, heuristics is a widely used technique for a variety of reasons:

• Problems that do not have an exact solution or for which the formulation is unknown
• The computation of a problem is computationally intensive
• Calculation of bounds on the optimal solution in branch and bound solution processes

Methodology

Optimization heuristics can be categorized into two broad classes depending on the way the solution domain is organized:

Construction methods (Greedy algorithms)

The greedy algorithm works in phases, where the algorithm makes the optimal choice at each step as it attempts to find the overall optimal way to solve the entire problem. [2] It is a technique used to solve the famous “traveling salesman problem” where the heuristic followed is: "At each step of the journey, visit the nearest unvisited city."

Example: Scheduling Problem

You are given a set of N schedules of lectures for a single day at a university. The schedule for a specific lecture is of the form (s time, f time) where s time represents the start time for that lecture, and similarly, the f time represents the finishing time. Given a list of N lecture schedules, we need to select a maximum set of lectures to be held out during the day such that none of the lectures overlaps with one another i.e. if lecture L i and L j are included in our selection then the start time of j ≥ finish time of i or vice versa. The most optimal solution to this would be to consider the earliest finishing time first. We would sort the intervals according to the increasing order of their finishing times and then start selecting intervals from the very beginning.

Local Search methods

The Local Search method follows an iterative approach where we start with some initial solution, explore the neighborhood of the current solution, and then replace the current solution with a better solution. [3] For this method, the “traveling salesman problem” would follow the heuristic in which a solution is a cycle containing all nodes of the graph and the target is to minimize the total length of the cycle.

Example Problem

Suppose that the problem P is to find an optimal ordering of N jobs in a manufacturing system. A solution to this problem can be described as an N-vector of job numbers, in which the position of each job in the vector defines the order in which the job will be processed. For example, [3, 4, 1, 6, 5, 2] is a possible ordering of 6 jobs, where job 3 is processed first, followed by job 4, then job 1, and so on, finishing with job 2. Define now M as the set of moves that produce new orderings by the swapping of any two jobs. For example, [3, 1, 4, 6, 5, 2] is obtained by swapping the positions of jobs 4 and 1.

Popular Heuristic Algorithms

Genetic algorithm.

The term Genetic Algorithm was first used by John Holland. [4] They are designed to mimic the Darwinian theory of evolution, which states that populations of species evolve to produce more complex organisms and fitter for survival on Earth. Genetic algorithms operate on string structures, like biological structures, which are evolving in time according to the rule of survival of the fittest by using a randomized yet structured information exchange. Thus, in every generation, a new set of strings is created, using parts of the fittest members of the old set. [5] The algorithm terminates when the satisfactory fitness level has been reached for the population or the maximum generations have been reached. The typical steps are [6] :

1.     Choose an initial population of candidate solutions

2.     Calculate the fitness, how well the solution is, of each individual

3.     Perform crossover from the population. The operation is to randomly choose some pair of individuals like parents and exchange so parts from the parents to generate new individuals

4.     Mutation is to randomly change some individuals to create other new individuals

5.     Evaluate the fitness of the offspring

6.     Select the survive individuals

7.    Proceed from 3 if the termination criteria have not been reached

Tabu Search Algorithm

Tabu search (TS) is a heuristic algorithm created by Fred Glover [7] using a gradient-descent search with memory techniques to avoid cycling for determining an optimal solution. It does so by forbidding or penalizing moves that take the solution, in the next iteration, to points in the solution space previously visited. The algorithm spends some memory to keep a Tabu list of forbidden moves, which are the moves of the previous iterations or moves that might be considered unwanted. A general algorithm is as follows [8] :

1.     Select an initial solution s 0 ∈ S . Initialize the Tabu List L 0 = ∅ and select a list tabu size. Establish k = 0.

2.     Determine the neighborhood feasibility N ( s k ) that excludes inferior members of the tabu list L k .

3.     Select the next movement s k + 1 from N ( S k ) or L k if there is a better solution and update L k + 1

4.     Stop if a condition of termination is reached, else, k = k + 1 and return to 1

Example: The Classical Vehicle Routing Problem

Vehicle Routing Problems have very important applications in distribution management and have become some of the most studied problems in the combinatorial optimization literature. These include several Tabu Search implementations that currently rank among the most effective. The Classical Vehicle Routing Problem (CVRP) is the basic variant in that class of problems. It can formally be defined as follows. Let G = ( V, A ) be a graph where V is the vertex set and A is the arc set. One of the vertices represents the depot at which a fleet of identical vehicles of capacity Q is based, and the other vertices customers that need to be serviced. With each customer vertex v i are associated a demand q i and a service time t i . With each arc (v i , v j ) of A are associated a cost c ij and a travel time t ij . [9] The CVRP consists of finding a set of routes such that:

1.     Each route begins and ends at the depot

2.     Each customer is visited exactly once by exactly one route

3.     The total demand of the customers assigned to each route does not exceed Q

4.     The total duration of each route (including travel and service times) does not exceed a specified value L

5.     The total cost of the routes is minimized

A feasible solution for the problem thus consists of a partition of the customers into m groups, each of total demand no larger than Q , that are sequenced to yield routes (starting and ending at the depot) of duration no larger than L .

Simulated Annealing Algorithm

The Simulated Annealing Algorithm was developed by Kirkpatrick et. al. in 1983 [10] and is based on the analogy of ideal crystals in thermodynamics. The annealing process in metallurgy can make particles arrange themselves in the position with minima potential as the temperature is slowly decreased. The Simulation Annealing algorithm mimics this mechanism and uses the objective function of an optimization problem instead of the energy of a material to arrive at a solution. A general algorithm is as follows [11]  :

1.    Fix initial temperature ( T 0 )

2.    Generate starting point x 0 (this is the best point X * at present)

3.    Generate randomly point X S (neighboring point)

4.    Accept X S as X * (currently best solution) if an acceptance criterion is met. This must be such a condition that the probability of accepting a worse point is greater than zero, particularly at higher temperatures

5.    If an equilibrium condition is satisfied, go to (6), otherwise jump back to (3).

6.    If termination conditions are not met, decrease the temperature according to a certain cooling scheme and jump back to (1). If the termination conditions are satisfied, stop calculations accepting the current best value X * as the final (‘optimal’) solution.

Numerical Example: Knapsack Problem

One of the most common applications of the heuristic algorithm is the Knapsack Problem, in which a given set of items (each with a mass and a value) are grouped to have a maximum value while being under a certain mass limit. It uses the Greedy Approximation Algorithm to sort the items based on their value per unit mass and then includes the items with the highest value per unit mass if there is still space remaining.

The following table specifies the weights and values per unit of five different products held in storage. The quantity of each product is unlimited. A plane with a weight capacity of 13 is to be used, for one trip only, to transport the products. We would like to know how many units of each product should be loaded onto the plane to maximize the value of goods shipped.

(a) Stages:

We view each type of product as a stage, so there are 5 stages. We can also add a sixth stage representing the endpoint after deciding

(b) States:

We can view the remaining capacity as states, so there are 14 states in each stage: 0,1, 2, 3, …13

(c) Possible decisions at each stage:

Suppose we are in state s in stage n (n < 6), hence there are s capacity remaining. Then the possible number of items we can pack is:

j = 0, 1, …[s/w n ]

For each such action j, we can have an arc going from the state s in stage n to the state n – j*w n in stage n + 1. For each arc in the graph, there is a corresponding benefit j*v n . We are trying to find a maximum benefit path from state 13 in stage 1, to stage 6.

(d) Optimization function:

Let f n (s) be the value of the maximum benefit possible with items of type n or greater using total capacity at most s

(e) Boundary conditions:

The sixth stage should have all zeros, that is, f 6 (s) = 0 for each s = 0,1, … 13

(f) Recurrence relation:

f n (s) = max {j*v n + f n+1 (s – j*w n )}, j = 0, 1, …, [s/w n ]

(g) Compute:

The solution will not show all the computations steps. Instead, only a few cases are given below to illustrate the idea.

• For stage 5, f 5 (s) = max j=0, 1, …[s/1] {j*0.5 + 0} = 0.5s because given the all zero states in stage 6, the maximum possible value is to use up all the remaining s capacity.
• For stage 4, state 7,

f 4 (7) = max j=0,1, …, [7/w4] = {j*v 4 + f 5 (7 - w 4* j)}

= max {0 + 3.5; 2 + 2; 4 + 0.5}

Using the recurrence relation above, we get the following table:

Optimal solution: The maximum benefit possible is 13.5. Tracing forward to get the optimal solution: the optimal decision corresponding to the entry 13.5 for f 1 (1) is 1, therefore we should pack 1 unit of type 1. After that we have 6 capacity remaining, so look at f 2 (6) which is 4.5, corresponding to the optimal decision of packing 1 unit of type 2. After this, we have 6-5 = 1 capacity remaining, and f 3 (1) = f 4 (1) = 0, which means we are not able to pack any type 3 or type 4. Hence we go to stage 5 and find that f 5 (1) = 1, so we should pack 1 unit of type 5. This gives the entire optimal solution as can be seen in the table below:

Applications

Heuristic algorithms have become an important technique in solving current real-world problems. Its applications can range from optimizing the power flow in modern power systems [12] to groundwater pumping simulation models [13] . Heuristic optimization techniques are increasingly applied in environmental engineering applications as well such as the design of a multilayer sorptive barrier system for landfill liner. [14] Heuristic algorithms have also been applied in the fields of bioinformatics, computational biology, and systems biology. [15]

Heuristic algorithms are not a panacea, but they are handy tools to be used when the use of exact methods cannot be implemented. Heuristics can provide flexible techniques to solve hard problems with the advantage of simple implementation and low computational cost. Over the years, we have seen a progression in heuristics with the development of hybrid systems that combine selected features from various types of heuristic algorithms such as tabu search, simulated annealing, and genetic or evolutionary computing. Future research will continue to expand the capabilities of existing heuristics to solve complex real-world problems.

• ↑ Eiselt, Horst A et al. Integer Programming and Network Models. Springer, 2011.
• ↑ Introduction to Algorithms (Cormen, Leiserson, Rivest, and Stein) 2001, Chapter 16 "Greedy Algorithms".
• ↑ J.H. Holland (1975) Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, Michigan; re-issued by MIT Press (1992).
• ↑ Optimal design of heat exchanger networks, Editor(s): Wilfried Roetzel, Xing Luo, Dezhen Chen, Design and Operation of Heat Exchangers and their Networks, Academic Press, 2020, Pages 231-317, ISBN 9780128178942, https://doi.org/10.1016/B978-0-12-817894-2.00006-6 .
• ↑ Wang FS., Chen LH. (2013) Genetic Algorithms. In: Dubitzky W., Wolkenhauer O., Cho KH., Yokota H. (eds) Encyclopedia of Systems Biology. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9863-7_412
• ↑ Fred Glover (1986). "Future Paths for Integer Programming and Links to Artificial Intelligence". Computers and Operations Research. 13 (5): 533–549, https://doi.org/10.1016/0305-0548(86)90048-1
• ↑ Optimization of Preventive Maintenance Program for Imaging Equipment in Hospitals, Editor(s): Zdravko Kravanja, Miloš Bogataj, Computer-Aided Chemical Engineering, Elsevier, Volume 38, 2016, Pages 1833-1838, ISSN 1570-7946, ISBN 9780444634283, https://doi.org/10.1016/B978-0-444-63428-3.50310-6 .
• ↑ Glover, Fred, and Gary A Kochenberger. Handbook Of Metaheuristics. Kluwer Academic Publishers, 2003.
• ↑ Kirkpatrick, S., Gelatt, C., & Vecchi, M. (1983). Optimization by Simulated Annealing. Science, 220 (4598), 671-680. Retrieved November 25, 2020, from http://www.jstor.org/stable/1690046
• ↑ Brief review of static optimization methods, Editor(s): Stanisław Sieniutycz, Jacek Jeżowski, Energy Optimization in Process Systems and Fuel Cells (Third Edition), Elsevier, 2018, Pages 1-41, ISBN 9780081025574, https://doi.org/10.1016/B978-0-08-102557-4.00001-3 .
• ↑ NIU, M., WAN, C. & Xu, Z. A review on applications of heuristic optimization algorithms for optimal power flow in modern power systems. J. Mod. Power Syst. Clean Energy 2, 289–297 (2014), https://doi.org/10.1007/s40565-014-0089-4
• ↑ J. L. Wang, Y. H. Lin and M. D. Lin, "Application of heuristic algorithms on groundwater pumping source identification problems," 2015 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), Singapore, 2015, pp. 858-862, https://doi.org/10.1109/IEEM.2015.7385770 .
• ↑ Matott, L. Shawn, et al. “Application of Heuristic Optimization Techniques and Algorithm Tuning to Multilayered Sorptive Barrier Design.” Environmental Science & Technology, vol. 40, no. 20, 2006, pp. 6354–6360., https://doi.org/10.1021/es052560+ .
• ↑ Larranaga P, Calvo B, Santana R, Bielza C, Galdiano J, Inza I, Lozano JA, Armananzas R, Santafe G, Perez A, Robles V (2006) Machine learning in bioinformatics. Brief Bioinform 7(1):86–112

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8.2 Problem-Solving: Heuristics and Algorithms

Learning objectives.

• Describe the differences between heuristics and algorithms in information processing.

When faced with a problem to solve, should you go with intuition or with more measured, logical reasoning? Obviously, we use both of these approaches. Some of the decisions we make are rapid, emotional, and automatic. Daniel Kahneman (2011) calls this “fast” thinking. By definition, fast thinking saves time. For example, you may quickly decide to buy something because it is on sale; your fast brain has perceived a bargain, and you go for it quickly. On the other hand, “slow” thinking requires more effort; applying this in the same scenario might cause us not to buy the item because we have reasoned that we don’t really need it, that it is still too expensive, and so on. Using slow and fast thinking does not guarantee good decision-making if they are employed at the wrong time. Sometimes it is not clear which is called for, because many decisions have a level of uncertainty built into them. In this section, we will explore some of the applications of these tendencies to think fast or slow.

We will look further into our thought processes, more specifically, into some of the problem-solving strategies that we use. Heuristics are information-processing strategies that are useful in many cases but may lead to errors when misapplied. A heuristic is a principle with broad application, essentially an educated guess about something. We use heuristics all the time, for example, when deciding what groceries to buy from the supermarket, when looking for a library book, when choosing the best route to drive through town to avoid traffic congestion, and so on. Heuristics can be thought of as aids to decision making; they allow us to reach a solution without a lot of cognitive effort or time.

The benefit of heuristics in helping us reach decisions fairly easily is also the potential downfall: the solution provided by the use of heuristics is not necessarily the best one. Let’s consider some of the most frequently applied, and misapplied, heuristics in the table below.

In many cases, we base our judgments on information that seems to represent, or match, what we expect will happen, while ignoring other potentially more relevant statistical information. When we do so, we are using the representativeness heuristic . Consider, for instance, the data presented in the table below. Let’s say that you went to a hospital, and you checked the records of the babies that were born on that given day. Which pattern of births do you think you are most likely to find?

Most people think that list B is more likely, probably because list B looks more random, and matches — or is “representative of” — our ideas about randomness, but statisticians know that any pattern of four girls and four boys is mathematically equally likely. Whether a boy or girl is born first has no bearing on what sex will be born second; these are independent events, each with a 50:50 chance of being a boy or a girl. The problem is that we have a schema of what randomness should be like, which does not always match what is mathematically the case. Similarly, people who see a flipped coin come up “heads” five times in a row will frequently predict, and perhaps even wager money, that “tails” will be next. This behaviour is known as the gambler’s fallacy . Mathematically, the gambler’s fallacy is an error: the likelihood of any single coin flip being “tails” is always 50%, regardless of how many times it has come up “heads” in the past.

The representativeness heuristic may explain why we judge people on the basis of appearance. Suppose you meet your new next-door neighbour, who drives a loud motorcycle, has many tattoos, wears leather, and has long hair. Later, you try to guess their occupation. What comes to mind most readily? Are they a teacher? Insurance salesman? IT specialist? Librarian? Drug dealer? The representativeness heuristic will lead you to compare your neighbour to the prototypes you have for these occupations and choose the one that they seem to represent the best. Thus, your judgment is affected by how much your neibour seems to resemble each of these groups. Sometimes these judgments are accurate, but they often fail because they do not account for base rates , which is the actual frequency with which these groups exist. In this case, the group with the lowest base rate is probably drug dealer.

Our judgments can also be influenced by how easy it is to retrieve a memory. The tendency to make judgments of the frequency or likelihood that an event occurs on the basis of the ease with which it can be retrieved from memory is known as the availability heuristic (MacLeod & Campbell, 1992; Tversky & Kahneman, 1973). Imagine, for instance, that I asked you to indicate whether there are more words in the English language that begin with the letter “R” or that have the letter “R” as the third letter. You would probably answer this question by trying to think of words that have each of the characteristics, thinking of all the words you know that begin with “R” and all that have “R” in the third position. Because it is much easier to retrieve words by their first letter than by their third, we may incorrectly guess that there are more words that begin with “R,” even though there are in fact more words that have “R” as the third letter.

The availability heuristic may explain why we tend to overestimate the likelihood of crimes or disasters; those that are reported widely in the news are more readily imaginable, and therefore, we tend to overestimate how often they occur. Things that we find easy to imagine, or to remember from watching the news, are estimated to occur frequently. Anything that gets a lot of news coverage is easy to imagine. Availability bias does not just affect our thinking. It can change behaviour. For example, homicides are usually widely reported in the news, leading people to make inaccurate assumptions about the frequency of murder. In Canada, the murder rate has dropped steadily since the 1970s (Statistics Canada, 2018), but this information tends not to be reported, leading people to overestimate the probability of being affected by violent crime. In another example, doctors who recently treated patients suffering from a particular condition were more likely to diagnose the condition in subsequent patients because they overestimated the prevalence of the condition (Poses & Anthony, 1991).

The anchoring and adjustment heuristic is another example of how fast thinking can lead to a decision that might not be optimal. Anchoring and adjustment is easily seen when we are faced with buying something that does not have a fixed price. For example, if you are interested in a used car, and the asking price is $10,000, what price do you think you might offer? Using $10,000 as an anchor, you are likely to adjust your offer from there, and perhaps offer $9000 or $9500. Never mind that $10,000 may not be a reasonable anchoring price. Anchoring and adjustment does not just happen when we’re buying something. It can also be used in any situation that calls for judgment under uncertainty, such as sentencing decisions in criminal cases (Bennett, 2014), and it applies to groups as well as individuals (Rutledge, 1993).

In contrast to heuristics, which can be thought of as problem-solving strategies based on educated guesses, algorithms are problem-solving strategies that use rules. Algorithms are generally a logical set of steps that, if applied correctly, should be accurate. For example, you could make a cake using heuristics — relying on your previous baking experience and guessing at the number and amount of ingredients, baking time, and so on — or using an algorithm. The latter would require a recipe which would provide step-by-step instructions; the recipe is the algorithm. Unless you are an extremely accomplished baker, the algorithm should provide you with a better cake than using heuristics would. While heuristics offer a solution that might be correct, a correctly applied algorithm is guaranteed to provide a correct solution. Of course, not all problems can be solved by algorithms.

As with heuristics, the use of algorithmic processing interacts with behaviour and emotion. Understanding what strategy might provide the best solution requires knowledge and experience. As we will see in the next section, we are prone to a number of cognitive biases that persist despite knowledge and experience.

Key Takeaways

• We use a variety of shortcuts in our information processing, such as the representativeness, availability, and anchoring and adjustment heuristics. These help us to make fast judgments but may lead to errors.
• Algorithms are problem-solving strategies that are based on rules rather than guesses. Algorithms, if applied correctly, are far less likely to result in errors or incorrect solutions than heuristics. Algorithms are based on logic.

Bennett, M. W. (2014). Confronting cognitive ‘anchoring effect’ and ‘blind spot’ biases in federal sentencing: A modest solution for reforming and fundamental flaw. Journal of Criminal Law and Criminology , 104 (3), 489-534.

Kahneman, D. (2011). Thinking, fast and slow. New York, NY: Farrar, Straus and Giroux.

MacLeod, C., & Campbell, L. (1992). Memory accessibility and probability judgments: An experimental evaluation of the availability heuristic.  Journal of Personality and Social Psychology, 63 (6), 890–902.

Poses, R. M., & Anthony, M. (1991). Availability, wishful thinking, and physicians’ diagnostic judgments for patients with suspected bacteremia.  Medical Decision Making,  11 , 159-68.

Rutledge, R. W. (1993). The effects of group decisions and group-shifts on use of the anchoring and adjustment heuristic. Social Behavior and Personality, 21 (3), 215-226.

Statistics Canada. (2018). Ho micide in Canada, 2017 . Retrieved from https://www150.statcan.gc.ca/n1/en/daily-quotidien/181121/dq181121a-eng.pdf

Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability.  Cognitive Psychology, 5 , 207–232.

Psychology - 1st Canadian Edition Copyright © 2020 by Sally Walters is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Reviewed by Psychology Today Staff

A heuristic is a mental shortcut that allows an individual to make a decision, pass judgment, or solve a problem quickly and with minimal mental effort. While heuristics can reduce the burden of decision-making and free up limited cognitive resources, they can also be costly when they lead individuals to miss critical information or act on unjust biases.

• Understanding Heuristics
• Different Heuristics
• Problems with Heuristics

As humans move throughout the world, they must process large amounts of information and make many choices with limited amounts of time. When information is missing, or an immediate decision is necessary, heuristics act as “rules of thumb” that guide behavior down the most efficient pathway.

Heuristics are not unique to humans; animals use heuristics that, though less complex, also serve to simplify decision-making and reduce cognitive load.

Generally, yes. Navigating day-to-day life requires everyone to make countless small decisions within a limited timeframe. Heuristics can help individuals save time and mental energy, freeing up cognitive resources for more complex planning and problem-solving endeavors.

The human brain and all its processes—including heuristics— developed over millions of years of evolution . Since mental shortcuts save both cognitive energy and time, they likely provided an advantage to those who relied on them.

Heuristics that were helpful to early humans may not be universally beneficial today . The familiarity heuristic, for example—in which the familiar is preferred over the unknown—could steer early humans toward foods or people that were safe, but may trigger anxiety or unfair biases in modern times.

The study of heuristics was developed by renowned psychologists Daniel Kahneman and Amos Tversky. Starting in the 1970s, Kahneman and Tversky identified several different kinds of heuristics, most notably the availability heuristic and the anchoring heuristic.

Since then, researchers have continued their work and identified many different kinds of heuristics, including:

Familiarity heuristic

Fundamental attribution error

Representativeness heuristic

Satisficing

The anchoring heuristic, or anchoring bias , occurs when someone relies more heavily on the first piece of information learned when making a choice, even if it's not the most relevant. In such cases, anchoring is likely to steer individuals wrong .

The availability heuristic describes the mental shortcut in which someone estimates whether something is likely to occur based on how readily examples come to mind . People tend to overestimate the probability of plane crashes, homicides, and shark attacks, for instance, because examples of such events are easily remembered.

People who make use of the representativeness heuristic categorize objects (or other people) based on how similar they are to known entities —assuming someone described as "quiet" is more likely to be a librarian than a politician, for instance. 

Satisficing is a decision-making strategy in which the first option that satisfies certain criteria is selected , even if other, better options may exist.

Heuristics, while useful, are imperfect; if relied on too heavily, they can result in incorrect judgments or cognitive biases. Some are more likely to steer people wrong than others.

Assuming, for example, that child abductions are common because they’re frequently reported on the news—an example of the availability heuristic—may trigger unnecessary fear or overprotective parenting practices. Understanding commonly unhelpful heuristics, and identifying situations where they could affect behavior, may help individuals avoid such mental pitfalls.

Sometimes called the attribution effect or correspondence bias, the term describes a tendency to attribute others’ behavior primarily to internal factors—like personality or character— while attributing one’s own behavior more to external or situational factors .

If one person steps on the foot of another in a crowded elevator, the victim may attribute it to carelessness. If, on the other hand, they themselves step on another’s foot, they may be more likely to attribute the mistake to being jostled by someone else .

Listen to your gut, but don’t rely on it . Think through major problems methodically—by making a list of pros and cons, for instance, or consulting with people you trust. Make extra time to think through tasks where snap decisions could cause significant problems, such as catching an important flight.

Your plans should not be set based on the wisdom shared by successful people. They should be based on your context, your strengths, and your creative inspiration from that wisdom.

Discover how the anchoring effect, a subtle cognitive bias, shapes our decisions across life's domains.

Artificial intelligence already plays a role in deciding who’s getting hired. The way to improve AI is very similar to how we fight human biases.

Think you are avoiding the motherhood penalty by not having children? Think again. Simply being a woman of childbearing age can trigger discrimination.

Psychological experiments on human judgment under uncertainty showed that people often stray from presumptions about rational economic agents.

Psychology, like other disciplines, uses the scientific method to acquire knowledge and uncover truths—but we still ask experts for information and rely on intuition. Here's why.

We all experience these 3 cognitive blind spots at work, frequently unaware of their costs in terms of productivity and misunderstanding. Try these strategies to work around them.

How do we make sense of new experiences? Ultimately, it's about how we categorize them—which we often do by "lumping" or "splitting" them.

Have you ever fallen for fake news? This toolkit can help you easily evaluate whether a claim is real or phony.

An insidious form of prejudice occurs when a more powerful group ignores groups with less power and keeps them out of the minds of society.

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What Are Heuristics?

Understanding heuristics.

• Pros and Cons
• Examples in Behavioral Economics

Heuristics and Psychology

The bottom line.

• Investing Basics

Heuristics: Definition, Pros & Cons, and Examples

James Chen, CMT is an expert trader, investment adviser, and global market strategist.

Heuristics are mental shortcuts that help people make quick decisions. They are rules or methods that help people use reason and past experience to solve problems efficiently. Commonly used to simplify problems and avoid cognitive overload, heuristics are part of how the human brain evolved and is wired, allowing individuals to quickly reach reasonable conclusions or solutions to complex problems. These solutions may not be optimal ones but are often sufficient given limited timeframes and calculative capacity.

These cognitive shortcuts feature prominently in behavioral economics .

Key Takeaways

• Heuristics are mental shortcuts for solving problems in a quick way that delivers a result that is sufficient enough to be useful given time constraints.
• Investors and financial professionals use a heuristic approach to speed up analysis and investment decisions.
• Heuristics can lead to poor decision-making based on a limited data set, but the speed of decisions can sometimes make up for the disadvantages.
• Behavioral economics has focused on heuristics as one limitation of human beings behaving like rational actors.
• Availability, anchoring, confirmation bias, and the hot hand fallacy are some examples of heuristics people use in their economic lives.

Investopedia / Danie Drankwalter

People employ heuristics naturally due to the evolution of the human brain. The brain can only process so much information at once and therefore must employ various shortcuts or practical rules of thumb . We would not get very far if we had to stop to think about every little detail or collect every piece of available information and integrate it into an analysis.

Heuristics therefore facilitate timely decisions that may not be the absolute best ones but are appropriate enough. Individuals are constantly using this sort of intelligent guesswork, trial and error, process of elimination, and past experience to solve problems or chart a course of action. In a world that is increasingly complex and overloaded with big data, heuristic methods make decision-making simpler and faster through shortcuts and good-enough calculations.

First identified in economics by the political scientist and organizational scholar Herbert Simon in his work on bounded rationality, heuristics have now become a cornerstone of behavioral economics.

Rather than subscribing to the idea that economic behavior was rational and based upon all available information to secure the best possible outcome for an individual ("optimizing"), Simon believed decision-making was about achieving outcomes that were "good enough" for the individual based on their limited information and balancing the interests of others. Simon called this " satisficing ," a portmanteau of the words "satisfy" and "suffice."

Advantages and Disadvantages of Using Heuristics

The main advantage to using heuristics is that they allow people to make good enough decisions without having all of the information and without having to undertake complex calculations.

Because humans cannot possibly obtain or process all the information needed to make fully rational decisions, they instead seek to use the information they do have to produce a satisfactory result, or one that is good enough. Heuristics allow people to go beyond their cognitive limits.

Heuristics are also advantageous when speed or timeliness matters—for example, deciding to enter a trade or making a snap judgment about some important decision. Heuristics are thus handy when there is no time to carefully weigh all options and their merits.

Disadvantages

There are also drawbacks to using heuristics. While they may be quick and dirty, they will likely not produce the optimal decision and can also be wrong entirely. Quick decisions without all the information can lead to errors in judgment, and miscalculations can lead to mistakes.

Moreover, heuristics leave us prone to biases that tend to lead us toward irrational economic behavior and sway our understanding of the world. Such heuristics have been identified and cataloged by the field of behavioral economics.

Quick & easy

Allows decision-making that goes beyond our cognitive capacity

Allows for snap judgments when time is limited

Often inaccurate

Can lead to systemic biases or errors in judgment

Example of Heuristics in Behavioral Economics

Representativeness.

A popular shortcut method in problem-solving identified in behavioral economics is called representativeness heuristics. Representativeness uses mental shortcuts to make decisions based on past events or traits that are representative of or similar to the current situation.

Say, for example, Fast Food ABC expanded its operations to India and its stock price soared. An analyst noted that India is a profitable venture for all fast-food chains. Therefore, when Fast Food XYZ announced its plan to explore the Indian market the following year, the analyst wasted no time in giving XYZ a "buy" recommendation.

Although their shortcut approach saved reviewing data for both companies, it may not have been the best decision. Fast Food XYZ may have food that is not appealing to Indian consumers, which research would have revealed.

Anchoring and Adjustment

Anchoring and adjustment is another prevalent heuristic approach. With anchoring and adjustment, a person begins with a specific target number or value—called the anchor—and subsequently adjusts that number until an acceptable value is reached over time. The major problem with this method is that if the value of the initial anchor is not the true value, then all subsequent adjustments will be systematically biased toward the anchor and away from the true value.

An example of anchoring and adjustment is a car salesman beginning negotiations with a very high price (that is arguably well above the  fair value ). Because the high price is an anchor, the final price will tend to be higher than if the car salesman had offered a fair or low price to start.

Availability (Recency) Heuristic

The availability (or recency) heuristic is an issue where people give too much weight to the probability of an event happening again if it recently has occurred. For instance, if a shark attack is reported in the news, those headlines make the event salient and can lead people to stay away from the water, even though shark attacks remain very rare.

Another example is the case of the " hot hand ," or the sense that following a string of successes, an individual is likely to continue being successful. Whether at the casino, in the markets, or playing basketball, the hot hand has been debunked. A string of recent good luck does not alter the overall probability of events occurring.

Confirmation Bias

Confirmation bias is a well-documented heuristic whereby people give more weight to information that fits with their existing worldviews or beliefs. At the same time, information that contradicts these beliefs is discounted or rejected.

Investors should be aware of their own tendency toward confirmation bias so that they can overcome poor decision-making, missing chances, and avoid falling prey to bubbles . Seeking out contrarian views and avoiding affirmative questions are two ways to counteract confirmation bias.

Hindsight Bias

Hindsight is always 20/20. However, the hindsight bias leads us to forget that we made incorrect predictions or estimates prior to them occurring. Rather, we become convinced that we had accurately predicted an event before it occurred, even when we did not. This can lead to overconfidence for making future predictions, or regret for not taking past opportunities.

Stereotypes

Stereotypes are a kind of heuristic that allows us to form opinions or judgments about people whom we have never met. In particular, stereotyping takes group-level characteristics about certain social groups—often ones that are racist, sexist, or otherwise discriminatory—and casts those characteristics onto all of the members in that group, regardless of their individual personalities, beliefs, skills, or behaviors.

By imposing oversimplified beliefs onto people, we can quickly judge potential interactions with them or individual outcomes of those people. However, these judgments are often plain wrong, derogatory, and perpetuate social divisions and exclusions.

Heuristics were first identified and taken seriously by scholars in the middle of the 20th century with the work of Herbert Simon, who asked why individuals and firms don't act like rational actors in the real world, even with market pressures punishing irrational decisions. Simon found that corporate managers do not usually optimize but instead rely on a set of heuristics or shortcuts to get the job done in a way that is good enough (to "satisfice").

Later, in the 1970s and '80s, psychologists Amos Tversky and Daniel Kahneman working at the Hebrew University in Jerusalem, built off of Herbert Simon's work and developed what is known as Prospect Theory . A cornerstone of behavioral economics, Prospect Theory catalogs several heuristics used subconsciously by people as they make financial evaluations.

One major finding is that people are loss-averse —that losses loom larger than gains (i.e., the pain of losing $50 is far more than the pleasure of receiving $50). Here, people adopt a heuristic to avoid realizing losses, sometimes spurring them to take excessive risks in order to do so—but often leading to even larger losses.

More recently, behavioral economists have tried to develop policy measures or "nudges" to help correct people's irrational use of heuristics in order to help them achieve more optimal outcomes—for instance, by having people enroll in a retirement savings plan by default instead of having to opt in.

What Are the Types of Heuristics?

To date, several heuristics have been identified by behavioral economics—or else developed to aid people in making otherwise complex decisions. In behavioral economics, representativeness, anchoring and adjustment, and availability (recency) are among the most widely cited. Heuristics may be categorized in many ways, such as cognitive versus emotional biases or errors in judgment versus errors in calculation.

What Is Heuristic Thinking?

Heuristic thinking uses mental shortcuts—often unconsciously—to quickly and efficiently make otherwise complex decisions or judgments. These can be in the form of a "rule of thumb" (e.g., saving 5% of your income in order to have a comfortable retirement) or cognitive processes that we are largely unaware of like the availability bias.

What Is Another Word for Heuristic?

Heuristic may also go by the following terms: rule of thumb; mental shortcut; educated guess; or satisfice.

How Does a Heuristic Differ From an Algorithm?

An algorithm is a step-by-step set of instructions that are followed to achieve some goal or outcome, often optimizing that outcome. They are formalized and can be expressed as a formula or "recipe." As such, they are reproducible in the sense that an algorithm will always provide the same output, given the same input.

A heuristic amounts to an educated guess or gut feeling. Rather than following a set of rules or instructions, a heuristic is a mental shortcut. Moreover, it often produces sub-optimal and even irrational outcomes that may differ even when given the same input.

What Are Computer Heuristics?

In computer science, a heuristic refers to a method of solving a problem that proves to be quicker or more efficient than traditional methods. This may involve using approximations rather than precise calculations or techniques that circumvent otherwise computationally intensive routines.

Heuristics are practical rules of thumb that manifest as mental shortcuts in judgment and decision-making. Without heuristics, our brains would not be able to function given the complexity of the world, the amount of data to process, and the calculative abilities required to form an optimal decision. Instead, heuristics allow us to make quick, good-enough choices.

However, these choices may also be subject to inaccuracies and systemic biases, such as those identified by behavioral economics.

Simon, Herbert. " Herbert Simon, Innovation, and Heuristics ." Mind & Society, vol. 17, 2019, pp. 97-109.

Kahneman, Daniel, and Tversky, Amos. " Prospect Theory: An Analysis of Decision Under Risk ." The Econometric Society, vol. 47, no. 2, 1979, pp. 263-292.

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• Published: 17 February 2023

A brief history of heuristics: how did research on heuristics evolve?

• Mohamad Hjeij   ORCID: orcid.org/0000-0003-4231-1395 1 &
• Arnis Vilks 1  

Humanities and Social Sciences Communications volume  10 , Article number:  64 ( 2023 ) Cite this article

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Heuristics are often characterized as rules of thumb that can be used to speed up the process of decision-making. They have been examined across a wide range of fields, including economics, psychology, and computer science. However, scholars still struggle to find substantial common ground. This study provides a historical review of heuristics as a research topic before and after the emergence of the subjective expected utility (SEU) theory, emphasising the evolutionary perspective that considers heuristics as resulting from the development of the brain. We find it useful to distinguish between deliberate and automatic uses of heuristics, but point out that they can be used consciously and subconsciously. While we can trace the idea of heuristics through many centuries and fields of application, we focus on the evolution of the modern notion of heuristics through three waves of research, starting with Herbert Simon in the 1950s, who introduced the notion of bounded rationality and suggested the use of heuristics in artificial intelligence, thereby paving the way for all later research on heuristics. A breakthrough came with Daniel Kahneman and Amos Tversky in the 1970s, who analysed the biases arising from using heuristics. The resulting research programme became the subject of criticism by Gerd Gigerenzer in the 1990s, who argues that an ‘adaptive toolbox’ consisting of ‘fast-and-frugal’ heuristics can yield ‘ecologically rational’ decisions.

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Introduction.

Over the past 50 years, the notion of ‘heuristics’ has considerably gained attention in fields as diverse as psychology, cognitive science, decision theory, computer science, and management scholarship. While for 1970, the Scopus database finds a meagre 20 published articles with the word ‘heuristic’ in their title, the number has increased to no less than 3783 in 2021 (Scopus, 2022 ).

We take this to be evidence that many researchers in the aforementioned fields find the literature that refers to heuristics stimulating and that it gives rise to questions that deserve further enquiry. While there are some review articles on the topic of heuristics (Gigerenzer and Gaissmaier, 2011 ; Groner et al., 1983 ; Hertwig and Pachur, 2015 ; Semaan et al., 2020 ), a somewhat comprehensive and non-partisan historical review seems to be missing.

While interest in heuristics is growing, the very notion of heuristics remains elusive to the point that, e.g., Shah and Oppenheimer ( 2008 ) begin their paper with the statement: ‘The word “heuristic” has lost its meaning.’ Even if one leaves aside characterizations such as ‘rule of thumb’ or ‘mental shortcut’ and considers what Kahneman ( 2011 ) calls ‘the technical definition of heuristic,’ namely ‘a simple procedure that helps find adequate, though often imperfect, answers to difficult questions,’ one is immediately left wondering how simple it has to be, what an adequate, but the imperfect answer is, and how difficult the questions need to be, in order to classify a procedure as a heuristic. Shah and Oppenheimer conclude that ‘the term heuristic is vague enough to describe anything’.

However, one feature does distinguish heuristics from certain other, typically more elaborate procedures: heuristics are problem-solving methods that do not guarantee an optimal solution. The use of heuristics is, therefore, inevitable where no method to find an optimal solution exists or is known to the problem-solver, in particular where the problem and/or the optimality criterion is ill-defined. However, the use of heuristics may be advantageous even where the problem to be solved is well-defined and methods do exist which would guarantee an optimal solution. This is because definitions of optimality typically ignore constraints on the process of solving the problem and the costs of that process. Compared to infallible but elaborate methods, heuristics may prove to be quicker or more efficient.

Nevertheless, the range of what has been called heuristics is very broad. Application of a heuristic may require intuition, guessing, exploration, or experience; some heuristics are rather elaborate, others are truly shortcuts, some are described in somewhat loose terms, and others are well-defined algorithms.

One procedure of decision-making that is commonly not regarded as a heuristic is the application of the full-blown theory of subjective expected utility (SEU) in the tradition of Ramsey ( 1926 ), von Neumann and Morgenstern ( 1944 ), and Savage ( 1954 ). This theory is arguably spelling out what an ideally rational decision would be, but was already seen by Savage (p. 16) to be applicable only in what he called a ‘small world’. Quite a few approaches that have been called heuristics have been explicitly motivated by SEU imposing demands on the decision-maker, which are utterly impractical (cf., e.g., Klein, 2001 , for a discussion). As a second defining feature of the heuristics we want to consider, therefore, we take them to be procedures of decision-making that differ from the ‘gold standard’ of SEU by being practically applicable in at least a number of interesting cases. Along with SEU, we also leave aside the rules of deductive logic, such as Aristotelian syllogisms, modus ponens, modus tollens, etc. While these can also be seen as rules of decision-making, and the universal validity of some of them is not quite uncontroversial (see, e.g., Priest, 2008 , for an introduction to non-classical logic), they are widely regarded as ‘infallible’. By stark contrast, it seems characteristic for heuristics that their application may fail to yield a ‘best’ or ‘correct’ result.

By taking heuristics to be practically applicable, but fallible, procedures for problem-solving, we will also neglect the literature that focuses on the adjective ‘heuristic’ instead of on the noun. When, e.g., Suppes ( 1983 ) characterizes axiomatic analyses as ‘heuristic’, he is not suggesting any rule, but he is saying that heuristic axioms ‘seem intuitively to organize and facilitate our thinking about the subject’ (p. 82), and proceeds to give examples of both heuristic and nonheuristic axioms. It may of course be said that many fundamental equations in science, such as Newton’s force = mass*acceleration, have some heuristic value in the sense indicated by Suppes, but the research we will review is not about the property of being heuristic.

Given that heuristics can be assessed against the benchmark of SEU, one may distinguish broadly between heuristics suggested pre-SEU, i.e., before the middle of the 20th century, and the later research on heuristics that had to face the challenge of an existing theory of allegedly rational decision-making. We will review the former in the section “Deliberate heuristics—the art of invention” below, and devote sections “Herbert Simon: rationality is bounded”, “Heuristics in computer science” and “Daniel Kahneman and Amos Tversky: heuristics and biases” to the latter.

To cover the paradigmatic cases of what has been termed ‘heuristics’ in the literature, we have to take ‘problem-solving’ in a broad sense that includes decision-making and judgement, but also automatic, instinctive behaviour. We, therefore, feel that an account of research on heuristics should also review the main views on how observable behaviour patterns in humans—or maybe animals in general—can be explained. This we do in the section “Automatic heuristics: learnt or innate?”.

While our brief history cannot aim for completeness, we selected the scholars to be included based on their influence and contributions to different fields of research related to heuristics. Our focus, however, will be on the more recent research that may be said to begin with Herbert Simon.

That problem-solving according to SEU will, in general, be impractical, was clearly recognized by Herbert Simon, whose notion of bounded rationality we look at in the section “Herbert Simon: rationality is bounded”. In the section “Heuristics in computer science”, we also consider heuristics in computer science, where the motivation to use heuristics is closely related to Simon’s reasoning. In the section “Daniel Kahneman and Amos Tversky: heuristics and biases”, we turn to the heuristics identified and analysed by Kahneman and Tversky; while their assessment was primarily that the use of those heuristics often does not conform to rational decision-making, the approach by Gigerenzer and his collaborators, reviewed in the section “Gerd Gigerenzer: fast-and-frugal heuristics” below, takes a much more affirmative view on the use of heuristics. Section “Critiques” explains the limitations and critiques of the corresponding ideas. The final section “Conclusion” contains the conclusion, discussion, and avenues for future research.

The evolutionary perspective

While we focus on the history of research on heuristics, it is clear that animal behaviour patterns evolved and were shaped by evolutionary forces long before the human species emerged. Thus ‘heuristics’ in the mere sense of behaviour patterns have been used long before humans engaged in any kind of conscious reflection on decision-making, let alone systematic research. However, evolution endowed humans with brains that allow them to make decisions in ways that are quite different from animal behaviour patterns. According to Gibbons ( 2007 ), the peculiar evolution of the human brain started thousands of years ago when the ancient human discovered fire and started cooking food, which reduced the amount of energy the body needed for digestion. This paved the way for a smaller intestinal tract and implied that the excess calories led to the development of larger tissues and eventually a larger brain. Through this organ, intelligence increased exponentially, resulting in advanced communication that allowed Homo sapiens to collaborate and form relationships that other primates at the time could not match. According to Dunbar ( 1998 ), it was in the time between 400,000 and 100,000 years ago that abilities to hunt more effectively took humans from the middle of the food chain right to the top.

It does not seem to be known when and how exactly the human brain developed the ability to reflect on decisions made consciously, but it is now widely recognized that in addition to the fast, automatic, and typically nonconscious type of decision-making that is similar to animal behaviour, humans also employ another, rather a different type of decision-making that can be characterized as slow, conscious, controlled, and reflective. The former type is known as ‘System 1’ or ‘the old mind’, and the latter as ‘System 2’ or ‘the new mind’ (Evans, 2010 ; Kahneman, 2011 ), and both systems have clearly evolved side by side throughout the evolution of the human brain. According to Gigerenzer ( 2021 ), humans as well as other organisms evolved to acquire what he calls ‘embodied heuristics’ that can be both innate or learnt rules of thumb, which in turn supply the agility to respond to the lack of information by fast judgement. The ‘embodied heuristics’ use the mental capacity that includes the motor and sensory abilities that start to develop from the moment of birth.

While a detailed discussion of the ‘dual-process theories’ of the mind is beyond the scope of this paper, we find it helpful to point out that one may distinguish between ‘System 1 heuristics’ and ‘System 2 heuristics’ (Kahneman 2011 , p. 98). While some ‘rules of decision-making’ may be hard-wired into the human species by its genes and physiology, others are complicated enough that their application typically requires reflection and conscious mental effort. Upon reflection, however, the two systems are not as separate as they may seem. For example, participants in the Mental Calculation World Cup perform mathematical tasks instantly, whereas ordinary people would need a pen and paper or a calculator. Today, many people cannot multiply large numbers or calculate a square root using only a pen and paper but can easily do this using the calculator app on their smartphone. Thus, what can be done by spontaneous effortless calculation by some, may for others require the application of a more or less complicated theory.

Nevertheless, one can loosely characterize the heuristics that have been explained and recommended for more or less well-specified purposes over the course of history as System 2 or deliberate heuristics.

Deliberate heuristics—the art of invention

Throughout history, scholars have investigated methods to solve complex tasks. In this section, we review those attempts to formulate ‘operant and voluntary’ heuristics to solve demanding problems—in particular, to generate new insights or do research in more or less specified fields. Most of the heuristics in this section have been suggested before the emergence of the SEU theory and the associated modern definition of rationality, and none of them deals with the kind of decision problems that are assumed as ‘given’ in the SEU model. The reader will notice that some historical heuristics were suggested for problems that, today, may seem too general to be solved. However, through the development of such attempts, later scholars were inspired to develop a more concrete understanding of the notion of heuristics.

The Greek origin

The term heuristic originates from the Greek verb heurísko , which means to discover or find out. The Greek word heúrēka , allegedly exclaimed by Archimedes when discovering how to measure the volume of a random object through water, derives from the same verb and can be translated as I found it! (Pinheiro and McNeill, 2014 ). Heuristics can thus be said to be etymologically related to the discipline of discovery, the branch of knowledge based on investigative procedures, and are naturally associated with trial techniques, including what-if scenarios and simple trial and error.

While the term heurísko does not seem to be used in this context by Aristotle, his notion of induction ( epagôgê ) can be seen as a method to find, but not prove, true general statements and thus as a heuristic. At any rate, Aristotle considered inductive reasoning as leading to insights and as distinct from logically valid syllogisms (Smith, 2020 ).

Pappus (4th century)

While a brief, somewhat cryptic, mention of analysis and synthesis appears in Book 13 of some, but not all, editions of Euclid’s Elements, a clearer explanation of the two methods was given in the 4th century by the Greek mathematician and astronomer Pappus of Alexandria (cf. Heath, 1926 ; Polya, 1945 ; Groner et al., 1983 ). While synthesis is what today would be called deduction from known truths, analysis is a method that can be used to try and find proof. Two slightly different explanations are given by Pappus. They boil down to this: in order to find proof for a statement A, one can deduce another statement B from A, continue by deducing yet another statement C from B, and so on, until one comes upon a statement T that is known to be true. If all the inferences are convertible, the converse deductions evidently constitute a proof of A from T. While Pappus did not mention the condition that the inferences must be convertible, his second explanation of analysis makes it clear that one must be looking for deductions from A which are both necessary and sufficient for A. In Polya’s paraphrase of Pappus’ text: ‘We enquire from what antecedent the desired result could be derived; then we enquire again what could be the antecedent of that antecedent, and so on, until passing from antecedent to antecedent, we come eventually upon something already known or admittedly true.’ Analysis thus described is hardly a ‘shortcut’ or ‘rule of thumb’, but quite clearly it is a heuristic: it may help to find a proof of A, but it may also fail to do so…

Al-Khawarizmi (9th century)

In the 9th century, the Persian thinker Mohamad Al-Khawarizmi, who resided in Baghdad’s centre of knowledge or the House of Wisdom , used stepwise methods for problem-solving. Thus, after his name and findings, the algorithm concept was derived (Boyer, 1991 ). Although a heuristic orientation has sometimes been contrasted with an algorithmic one (Groner and Groner, 1991 ), it is worth noting that an algorithm may well serve as a heuristic—certainly in the sense of a shortcut, and also in the sense of a fallible method. After all, an algorithm may fail to produce a satisfactory result. We will return to this issue in the section “Heuristics in computer science” below.

Zairja (10th century)

Heuristic methods were created by medieval polymaths in their attempts to find solutions for the complex problems they faced—science not yet being divorced from what today would appear as theology or astrology. Perhaps the first tangible example of a heuristic based on a mechanical device was using an ancient tool called a zairja , which Arab astrologers employed before the 11th century (Ritchey, 2022 ). It was designed to reconfigure notions into ideas through randomization and resonance and thus to produce answers to questions mechanically (Link, 2010 ). The word zairja may have originated from the Persian combination zaicha-daira , which means horoscope-circle. According to Ibn Khaldoun, ‘zairja is the technique of finding out answers from questions by means of connections existing between the letters of the expressions used in the question; they imagine that these connections can form the basis for knowing the future happenings they want to know’ (Khaldun, 1967 ).

Ramon Llull (1305)

The Majorcan philosopher Ramon Llull (or Raimundus Lullus), who was exposed to the Arabic culture, used the zairja as a starting point for his ars inveniendi veritatem that was meant to complement the ars demonstrandi of medieval Scholastic logic and on which he worked from around 1270–1305 (Link, 2010 ; Llull, 1308 ; Ritchey, 2022 ) when he finished his Ars Generalis Ultima (or Ars Magna ). Llull transformed the astrological and combinatorial components of the zairja into a religious system that took the fundamental ideas of the three Abrahamic faiths of Islam, Christianity, and Judaism and analysed them through symbolic and numeric reasoning. Llull tried to broaden his theory across all fields of knowledge and combine all sciences into a single science that would address all human problems. His thoughts impacted great thinkers, such as Leibniz, and even the modern theory of computation (Fidora and Sierra, 2011 ). Llull’s approach may be considered a clear example of heuristic methods applied to complicated and even theological questions (Hertwig and Pachur, 2015 ).

Joachim Jungius (1622)

Arguably, the German mathematician and philosopher Joachim Jungius was the first to use the terminology heuretica in a call to establish a research society in 1622. Jungius distinguished between three degrees or levels of learning and cognition: empirical, epistemic, and heuristic. Those who have reached the empirical level believe that what they have learned is true because it corresponds to experience. Those who have reached the epistemic level know how to derive their knowledge from principles with rigorous evidence. But those who have reached the highest level, the heuristic level, have a method of solving unsolved problems, finding new theorems, and introducing new methods into science (Ritter et al., 2017 ).

René Descartes (1637)

In 1637, the French philosopher René Descartes published his Discourse on Method (one of the first major works not written in Latin). Descartes argued that humans could utilize mathematical reasoning as a vehicle for progress in knowledge. He proposed four simple steps to follow in problem-solving. First, to accept as true only what is indubitable. Next, divide the problem into as many smaller subproblems as possible and helpful. After that, to conduct one’s thoughts in an orderly fashion, beginning with the simplest and gradually ascending to the most complex. And finally, to make enumerations so complete that one is assured of having omitted nothing (Descartes, 1998 ). In reference to his other methods, Descartes ( 1908 ) started working on the proper heuristic rules to transform every problem, when possible, into algebraic equations, thus creating a mathesis universalis or universal science. In his unfinished ‘Rules for the Direction of the Mind’ or Regulae ad directionem ingenii , Descartes suggested 21 heuristic rules (of planned 36) for scientific research like simplifying the problem, rewriting the problem in geometrical shape, and identifying the knowns and the unknowns. Although Leibniz criticized the rules of Descartes for being too general (Leibniz, 1880 ), this treatise outlined the basis for later work on complex problems in several disciplines.

Gottfried Wilhelm Leibniz (1666)

Influenced by the ideas of Llull, Jungius, and Descartes, the Prussian–German polymath Gottfried Wilhelm Leibniz suggested an original approach to problem-solving in his Dissertatio de Arte Combinatoria , published in Leipzig in 1666. His aim was to create a new universal language into which all problems could be translated and a standard solving procedure that could be applied regardless of the type of the problem. Leibniz also defined an ars inveniendi as a method for finding new truths, distinguishing it from an ars iudicandi , a method to evaluate the validity of alleged truths. Later, in 1673, he invented the calculating machine that could execute all four arithmetic operations and thus find ‘new’ arithmetic truths (Pombo, 2002 ).

Bernard Bolzano ( 1837 )

In 1837, the Czech mathematician and philosopher Bernard Bolzano published his four-volume Wissenschaftslehre (Theory of Science). The fourth part of his theory he called ‘Erfindungskunst’ or the art of invention, mentions in the introductory section 322 that ‘heuristic’ is just the Greek translation. Bolzano explains that the rules he is going to state are not at all entirely new, but instead have always been used ‘by the talented’—although mostly not consciously. He then explains 13 general and 33 special rules one should follow when trying to find new truths. Among the general rules are, e.g., that one should first decide on the question one wants to answer, and the kind of answer one is looking for (section 325), or that one should choose suitable symbols to represent one’s ideas (section 334). Unlike the general rules, the special ones are meant to be helpful for special mental tasks only. E.g., in order to solve the task of finding the reason for any given truth, Bolzano advises first to analyse or dissect the truth into its parts and then use those to form truths which are simpler than the given one (section 378). Another example is Bolzano’s special rule 28, explained in section 386, which is meant to help identify the intention behind a given action. To do so, Bolzano advises exploring the agent’s beliefs about the effects of his action at the time he decided to act, and explains that this will require investigating the agent’s knowledge, his degree of attention and deliberation, any erroneous beliefs the agent may have had, and ‘many other circumstances’. Bolzano continues to point out that any effect the agent may have expected to result from his action will not be an intended one if he considered it neither as an obligation nor as advantageous. While Bolzano’s rules can hardly be considered as ‘shortcuts’, he mentions again and again that they may fail to solve the task at hand adequately (cf. Hertwig and Pachur, 2015 ; Siitonen, 2014 ).

Frank Ramsey ( 1926 )

In Ramsey’s pathbreaking paper on ‘Truth and Probability’ which laid the foundation of subjective probability theory, a final section that has received little attention in the literature is devoted to inductive logic. While he does not use the word ‘heuristic’, he characterizes induction as a ‘habit of the mind,’ explaining that he uses ‘habit in the most general possible sense to mean simply rule or the law of behaviour, including instinct,’ but also including ‘acquired rules.’ Ramsey gives the following pragmatic justification for being convinced by induction: ‘our conviction is reasonable because the world is so constituted that inductive arguments lead on the whole to true opinions,’ and states more generally that ‘we judge mental habits by whether they work, i.e., whether the opinions they lead to are for the most part true, or more often true than those which alternative habits would lead to’ (Ramsey, 1926 ). In modern terminology, Ramsey was pointing out that mental habits—such as inductive inference—may be more or less ‘ecologically rational’.

Karl Duncker ( 1935 )

Karl Duncker was a pioneer in the experimental investigation of human problem-solving. In his 1935 book Zur Psychologie des produktiven Denkens , he discussed both heuristics that help to solve problems, but also hindrances that may block the solution of a problem—and reported on a number of experimental findings. Among the heuristics was a situational analysis with the aim of uncovering the reasons for the gap between the status quo and the problem-solvers goal, analysis of the goal itself, and of sacrifices the problem-solver is willing to make, of prerequisites for the solution, and several others. Among the hindrances to problem-solving was what Duncker called functional fixedness, illustrated by the famous candle problem, in which he asked the participants to fix a candle to the wall and light it without allowing the wax to drip. The available tools were a candle, matches, and a box filled with thumbtacks. The solution was to empty the box of thumbtacks, fix the empty box to the wall using the thumbtacks, put the candle in the box, and finally light the candle. Participants who were given the empty box as a separate item could solve this problem, while those given the box filled with thumbtacks struggled to find a solution. Through this experiment, Duncker illustrated an inability to think outside the box and the difficulty in using a device in a way that is different from the usual one (Glaveanu, 2019 ). Duncker emphasized that success in problem-solving depends on a complementary combination of both the internal mind and the external problem structure (cf. Groner et al., 1983 ).

George Polya ( 1945 )

The Hungarian mathematician George Polya can be aptly called the father of problem-solving in modern mathematics and education. In his 1945 book, How to Solve it , Polya writes that ‘heuristic…or ‘ ars inveniendi ’ was the name of a certain branch of study…often outlined, seldom presented in detail, and as good as forgotten today’ and he attempts to ‘revive heuristic in a modern and modest form’. According to his four principles of mathematical problem-solving, it is first necessary to understand the problem, then plan the execution, carry out the plan, and finally, reflect and search for improvement opportunities. Among the more detailed suggestions for problem-solving explained by Polya are to ask questions such as ‘can you find the solution to a similar problem?’, to use inductive reasoning and analogy, or to choose a suitable notation. Procedures inspired by Polya’s ( 1945 ) book and several later ones (e.g., Induction and Analogy in Mathematics of 1954 ) also informed the field of artificial intelligence (AI) (Hertwig and Pachur, 2015 ).

Johannes Müller (1968)

In 1968, the German scientist Johannes Müller introduced the concept of systematic heuristics while working on his postdoctoral thesis at the Chemnitz University of Technology. Systematic heuristics is a framework for improving the efficiency of intellectual work using problem-solving processes in the fields of science and technology.

The main idea of systematic heuristics is to solve repeated problems with previously validated solutions. These methods are called programmes and are gathered in a library that can be accessed by the main programme, which receives the requirements, prepares the execution plan, determines the required procedures, executes the plan, and finally evaluates the results. Müller’s team was dismissed for ideological reasons, and his programme was terminated after a few years, but his findings went on to be successfully applied in many projects across different industries (Banse and Friedrich, 2000 ).

Imre Lakatos ( 1970 )

In his ‘Methodology of Scientific Research Programmes’ that turned out to be a major contribution to the Popper–Kuhn controversy about the rationality of non-falsifiable paradigms in the natural sciences, Lakatos introduced the interesting distinction between a ‘negative heuristic’ that is given by the ‘hard core’ of a research programme and the ‘positive heuristic’ of the ‘protective belt’. While the latter suggests ways to develop the research programme further and to predict new facts, the ‘hard core’ of the research programme is treated as irrefutable ‘by the methodological decision of its protagonists: anomalies must lead to changes only in the ‘protective’ belt’ of auxiliary hypotheses. The Lakatosian notion of a negative heuristic seems to have received little attention outside of the Philosophy of Science community but may be important elsewhere: when there are too many ways to solve a complicated problem, excluding some of them from consideration may be helpful.

Gerhard Kleining ( 1982 )

The German sociologist Gerhard Kleining suggested a qualitative heuristic as the appropriate research method for qualitative social science. It is based on four principles: (1) open-mindedness of the scientist who should be ready to revise his preconceptions about the topic of study, (2) openness of the topic of study, which is initially defined only provisionally and allowed to be modified in course of the research, (3) maximal variation of the research perspective, and (4) identification of similarities within the data (Kleining, 1982 , 1995 ).

Automatic heuristics: learnt or innate?

Unlike the deliberate, and in some cases quite elaborate, heuristics reviewed above, at least some System 1 heuristics are often applied automatically, without any kind of deliberation or conscious reflection on the task that needs to be performed or the question that needs to be answered. One may view them as mere patterns of behaviour, and as such their scientific examination has been a long cumulative process through different disciplines, even though explicit reference to heuristics was not often made.

Traditionally, examining the behaviour patterns of any living creature, any study concerning thoughts, feelings, or cognitive abilities was regarded as the task of biologists. However, the birth of psychology as a separate discipline paved the way for an alternative outlook. Evolutionary psychology views human behaviour as being shaped through time and experience to promote survival throughout the long history of human struggle with nature. With many factors to consider, scholars have been interested in the evolution of the human brain, patterns of behaviour, and problem-solving (Buss and Kenrick, 1998 ).

Charles Darwin (1873)

Charles Darwin himself maybe qualifies for the title of first evolutionary psychologist, as his perceptions laid the foundations for this field that would continue to grow over a century later (Ghiselin, 1973 ).

In 1873, Darwin claimed that the brain’s articulations regarding expressions and emotions have probably developed similarly to its physical traits (Baumeister and Vohs, 2007 ). He acknowledged that personal demonstrations or expressions have a high capacity for interaction with different peers from the same species. For example, an aggressive look flags an eagerness to battle yet leaves the recipient with the option of retreating without either party being harmed. Additionally, Darwin, as well as his predecessor Lamarck, constantly emphasized the role of environmental factors in ‘the struggle for existence’ that could shape the organism’s traits in response to changes in their corresponding environments (Sen, 2020 ). The famous example of giraffes that grew long necks in response to trees growing taller is an illustration of a major environmental effect. Similarly, cognitive skills, including heuristics, must have also been shaped by the environments to evolve and keep humans surviving and reproducing.

Darwin’s ideas impacted the early advancement of brain science, psychology, and all related disciplines, including the topic of cognitive heuristics (Smulders, 2009 ).

William James (1890)

A few years later, in 1890, the father of American psychology, William James, introduced the notion of evolutionary psychology in his 1200-page text The Principles of Psychology , which later became a reference on the subject and helped establish psychology as a science. In its core content, James reasoned that many actions of the human being demonstrate the activity of instincts, which are the evolutionary embedded inclinations to react to specific incentives in adaptive manners. With this idea, James added an important building block to the foundation of heuristics as a scientific topic.

A simple example of such hard-wired behaviour patterns would be a sneeze, the preprogrammed reaction of convulsive nasal expulsion of air from the lungs through the nose and mouth to remove irritants (Baumeister and Vohs, 2007 ).

Ivan Pavlov (1897)

Triggered by scientific curiosity or the instinct for research, as he called it, the first Russian Nobel laureate, Ivan Pavlov, introduced classical conditioning, which occurs when a stimulus is used that has a predictive relationship with a reinforcer, resulting in a change in response to the stimulus (Schreurs, 1989 ). This learning process was demonstrated through experiments conducted with dogs. In the experiments, a bell (a neutral stimulus) was paired with food (a potent stimulus), resulting ultimately in the dogs salivating at the ringing of the bell—a conditioned response. Pavlov’s experiments remain paradigmatic cases of the emergence of behaviour patterns through association learning.

William McDougall (1909)

At the start of the 20th century, the Anglo-American psychologist William McDougall was one of the first to write about the instinct theory of motivation. McDougall argued that instincts trigger many critical social practices. He viewed instincts as extremely sophisticated faculties in which specific provocations such as social impediments can drive a person’s state of mind in a particular direction, for example, towards a state of hatred, envy, or anger, which in turn may increase the probability of specific practices such as hostility or violence (McDougall, 2015 ).

However, in the early 1920s, McDougall’s perspective about human behaviour being driven by instincts faded remarkably as scientists supporting the concept of behaviourism started to get more attention with original ideas (Buss and Kenrick, 1998 ).

John B. Watson (1913)

The pioneer of the psychological school of behaviourism, John B. Watson, who conducted the controversial ‘Little Albert’ experiment by imposing a phobia on a child to evidence classical conditioning in humans (Harris, 1979 ), argued against the ideas of McDougall, even within public debates (Stephenson, 2003 ). Unlike McDougall, Watson considered the brain an empty page ( tabula rasa as described by Aristotle). According to him. all personality traits and behaviours directly result from the accumulated experience that starts from birth. Thus, the story of the human mind is a continuous writing process featured by surrounding events and factors. This perception was supported in the following years of the 20th century by anthropologists who revealed many very different social standards in different societies, and numerous social researchers argued that the wide variety of cross-cultural differences should lead to the conclusion that there is no mental content built-in from birth, and that all knowledge, therefore, comes from individual experience or perception (Farr, 1996 ). In stark contrast to McDougall, Watson suggested that human intuitions and behaviour patterns are the product of a learning process that starts blank.

B. F. Skinner (1938)

Inspired by the work of Pavlov, the American psychologist B.F. Skinner took the classical conditioning approach to a more advanced level by modifying a key aspect of the process. According to Skinner, human behaviour is dependent on the outcome of past activities. If the outcome is bad, the action will probably not be repeated; however, if the outcome is good, the likelihood of the activity being repeated is relatively high. Skinner called this process reinforcement learning (Schacter et al., 2011 ). Based on reinforcement learning, Skinner also introduced the concept of operant conditioning, a type of associative learning process through which the strength of a behaviour is adjusted by reinforcement or punishment. Considering, for example, a parent’s response to a child’s behaviour, the probability of the child repeating an action will be highly dependent on the parent’s reaction (Zilio, 2013 ). Effectively, Skinner argues that the intuitive System 1 may get edited and that a heuristical cue may become more or less ‘hard-wired’ in the subject’s brain as a stimulus leading to an automatic response.

The DNA and its environment (1953 onwards)

Today, there seems to be wide agreement that behaviour patterns in humans and other species are to some extent ‘in the DNA’, the structure of which was discovered by Francis Crick and James Watson in 1953, but that they also to some extent depend on ‘the environment’—including the social environment in which the agent lives and has problems to solve. Today, it seems safe to say, therefore, that the methods of problem-solving that humans apply are neither completely innate nor completely the result of environmental stimuli—but rather the product of the complex interaction between genes and the environment (Lerner, 1978 ).

Herbert Simon: rationality is bounded

Herbert Simon is well known for his contributions to several fields, including economics, psychology, computer science, and management. Simon proposed a remarkable theory that led him to be awarded the Nobel Prize for Economics in 1978.

Bounded rationality and satisficing

In the mid-1950s, Simon published A Behavioural Model of Rational Choice, which focused on bounded rationality: the idea that people must make decisions with limited time, mental resources, and information (Simon, 1955 ). He clearly states the triangle of limitations in every decision-making process—the availability of information, time, and cognitive ability (Bazerman and Moore, 1994 ). The ideas of Simon are considered an inspiring foundation for many technologies in use today.

Instead of conforming to the idea that economic behaviour can be seen as rational and dependent on all accessible data (i.e., as optimization), Simon suggested that the dynamics of decision-making were essentially ‘satisficing,’ a notion synthesized from ‘satisfy’ and ‘suffice’ (Byron, 1998 ). During the 1940s, scholars noticed the frequent failure of two assumptions required for ‘rational’ decision-making. The first is that data is never enough and may be far from perfect, while people dependably make decisions based on incomplete data. Second, people do not assess every feasible option before settling on a decision. This conduct is highly correlated with the cost of data collection since data turns out to be progressively harder and costlier to accumulate. Rather than trying to find the ideal option, people choose the first acceptable or satisfactory option they find. Simon described this procedure as satisficing and concluded that the human brain in the decision-making process would, at best, exhibit restricted abilities (Barros, 2010 ).

Since people can neither obtain nor process all the data needed to make a completely rational decision, they use the limited data they possess to determine an outcome that is ‘good enough’—a procedure later refined into the take-the-best heuristic. Simon’s view that people are bounded by their cognitive limits is usually known as the theory of bounded rationality (cf. Gigerenzer and Selten, 2001 ).

Herbert Simon and AI

With the cooperation of Allen Newell of the RAND Corporation, Simon attempted to create a computer simulator for human decision-making. In 1956, they created a ‘thinking’ machine called the ‘Logic Theorist’. This early smart device was a computer programme with the ability to prove theorems in symbolic logic. It was perhaps the first man-made programme that simulated some human reasoning abilities to solve actual problems (Gugerty, 2006 ). After a few years, Simon, Newell, and J.C. Shaw proposed the General Problem Solver or GPS, the first AI-based programme ever invented. They actually aimed to create a single programme that could solve all problems with the same unified algorithm. However, while the GPS was efficient with sufficiently well-structured problems like the Towers of Hanoi (a puzzle with 3 rods and different-sized disks to be moved), it could not solve real-life scenarios with all their complexities (A. Newell et al., 1959 ).

By 1965, Simon was confident that ‘machines will be capable of doing any work a man can do’ (Vardi, 2012 ). Therefore, Simon dedicated most of the remainder of his career to the advancement of machine intelligence. The results of his experiments showed that, like humans, certain computer programmes make decisions using trial-and-error and shortcut methods (Frantz, 2003 ). Quite explicitly, Simon and Newell ( 1958 , p. 7) referred to heuristics being used by both humans and intelligent machines: ‘Digital computers can perform certain heuristic problem-solving tasks for which no algorithms are available… In doing so, they use processes that are closely parallel to human problem-solving processes’.

Additionally, the importance of the environment was also clearly observed in Newell and Simon’s ( 1972 ) work:

‘Just as scissors cannot cut paper without two blades, a theory of thinking and problem-solving cannot predict behaviour unless it encompasses both an analysis of the structure of task environments and an analysis of the limits of rational adaptation to task requirements’ (p. 55).

Accordingly, the term ‘task environment’ describes the formal structure of the universe of choices and results for a specific problem. At the same time, Newell and Simon do not treat the agent and the environment as two isolated entities, but rather as highly related. Consequently, they tend to believe that agents with different cognitive abilities and choice repertoires will inhabit different task environments even though their physical surroundings and intentions might be the same (Agre and Horswill, 1997 ).

Heuristics in computer science

Computer science as a discipline may have the biggest share of deliberately applied heuristics. As heuristic problem-solving has often been contrasted with algorithmic problem-solving—even by Simon and Newell ( 1958 )—it is worth recalling that the very notion of ‘algorithm’ was clarified only in the first half of the 20th century, when Alan Turing ( 1937 ) defined what was later named ‘Turing-machine’. Basically, he defined ‘mechanical’ computation as a computation that can be done by a—stylized—machine. ‘Mechanical’ being what is also known today as algorithmic, one can say that any procedure that can be performed by a digital computer is algorithmic. Nevertheless, many of them are also heuristics because an algorithm may fail to produce an optimal solution to the problem it is meant to solve. This may be so either because the problem is ill-defined or because the computations required to produce the optimal solution may not be feasible with the available resources. If the problem is ill-defined—as it often is, e.g., in natural language processing—the algorithm that does the processing has to rely on a well-defined model that does not capture the vagueness and ambiguities of the real-life problem—a problem typically stated in natural language. If the problem is well-defined, but finding the optimal solution is not feasible, algorithms that would find it may exist ‘in principle’, but require too much time or memory to be practically implemented.

In fact, there is today a rich theory of complexity classes that distinguishes between types of (well-defined) problems according to how fast the time or memory space required to find the optimal solution increases with increasing problem size. E.g., for problem types of the complexity class P, any deterministic algorithm that produces the optimal solution has a running time bounded by a polynomial function of the input size, whereas, for problems of complexity class EXPTIME, the running time is bounded by an exponential function of the input size. In the jargon of computer science, problems of the latter class are considered intractable, although the input size has to become sufficiently large before the computation of the optimal solution becomes practically infeasible (cf. Harel, 2000 ; Hopcroft et al., 2007 ). Research indicates that the computational complexity of problems can also reduce the quality of human decision-making (Bossaerts and Murawski, 2017 ).

Shortest path algorithms

A classic optimization problem that may serve to illustrate the issues of optimal solution, complexity, and heuristics goes by the name of the travelling salesman problem (TSP), which was first introduced in 1930. In this problem, several cities with given distances between each two are considered, and the goal is to find the shortest possible path through all cities and return to the starting point. For a small input size, i.e., for a small number of cities, the ‘brute-force’ algorithm is easy to use: write down all the possible paths through all the cities, calculate their lengths, and choose the shortest. However, the number of steps that are required by this procedure quickly increases with the number of cities. The TSP is today known to belong to the complexity class NP which is in between P and EXPTIME Footnote 1 ). To solve the TSP, Jon Bentley ( 1982 ) proposed the greedy (or nearest-neighbour) algorithm that will yield an acceptable result, but not necessarily the optimal one, within a relatively short time. This approach always picks the nearest neighbour as the next city to visit without regard to possible later non-optimal steps. Hence, it is considered a good-enough solution with fast results. Bentley argued that there may be better solutions, but that it approximates the optimal solution. Many other heuristic algorithms have been explored later on. There is no assurance that the solution found by a heuristic algorithm will be an ideal answer for the given problem, but it is acceptable and adequate (Pearl, 1984 ).

Heuristic algorithms of the shortest path are utilized nowadays by GPS frameworks and self-driving vehicles to choose the best route from any point of departure to any destination (for example, A* Search Algorithm). Further developed algorithms can also consider additional elements, including traffic, speed limits, and quality of roads, they may yield the shortest routes in terms of distance and the fastest ones in terms of driving time.

Computer chess

While the TSP consists of a whole set of problems which differ by the number of cities and the distances between them, determining the optimal strategy for chess is just one problem of a given size. The rules of chess make it a finite game, and Ernst Zermelo proved in 1913 that it is ‘determined’: if it were played between perfectly rational players, it would always end with the same outcome: either White always wins, or Black always wins, or it always ends with a draw (Zermelo, 1913 ). Up to the present day, it is not known which of the three is true, which points to the fact that a brute-force algorithm that would go through all possible plays of chess is practically infeasible: it would have to explore too many potential moves, and the required memory would quickly run out of space (Schaeffer et al., 2007 ). Inevitably, a chess-playing machine has to use algorithms that are ‘shortcuts’—which can be more or less intelligent.

While Simon and Newell had predicted in 1958 that within ten years the world chess champion would be a computer, it took until 1997, when a chess-playing machine developed by IBM under the name Deep Blue defeated grandmaster Garry Kasparov. Although able to analyse millions of possibilities due to their computing powers, today’s chess-playing machines apply a heuristic approach to eliminate unlikely moves and focus on those with a high probability of defeating their opponent (Newborn, 1997 ).

Machine learning

One of the main features of machine learning is the ability of the model to predict a future outcome based on past data points. Machine learning algorithms build a knowledge base similar to human experience from previous experiences in the dataset provided. From this knowledge base, the model can derive educated guesses.

A good demonstration of this is the card game Top Trumps in which the model can learn to play and keep improving to dominate the game. It does so by undertaking a learning path through a sequence of steps in which it picks two random cards from the deck and then analyses and compares them with random criteria. According to the winning result, the model iteratively updates its knowledge base in the same manner as a human, following the rule that ‘practice makes perfect.’ Hence the model will play, collect statistics, update, and iterate while becoming more accurate with each increment (Volz et al., 2016 ).

Natural language processing

In the world of language understanding, current technologies are far from perfect. However, models are becoming more reliable by the minute. When analysing and dissecting a search phrase entered into the Google search engine, a background model tries to make sense of the search criteria. Stemming words, context analysis, the affiliation of phrases, previous searches, and autocorrect/autocomplete can be applied in a heuristic algorithm to display the most relevant result in less than a second. Heuristic methods can be utilized when creating certain algorithms to understand what the user is trying to express when searching for a phrase. For example, using word affiliation, an algorithm tries to narrow down the meaning of words as much as possible toward the user’s intention, particularly when a word has more than one meaning but changes with the context. Therefore, a search for apple pie allows the algorithm to deduce that the user is highly interested in recipes and not in the technology company (Sullivan, 2002 ).

Search and big data

Search is a good example to appreciate the value of time, as one of the most important criteria is retrieving acceptable results in an acceptable timeframe. In a full search algorithm, especially in large datasets, retrieving optimal results can take a massive amount of time, making it necessary to apply heuristic search.

Heuristic search is a type of search algorithm that is used to find solutions to problems in a faster way than an exhaustive search. It uses specific criteria to guide the search process and focuses on more favourable areas of the search space. This can greatly reduce the number of nodes required to find a solution, especially for large or complex search trees.

Heuristic search algorithms work by evaluating the possible paths or states in a search tree and selecting the better ones to explore further. They use a heuristic function, which is a measure of how close a given state is to the goal state, to guide the search. This allows the algorithm to prioritize certain paths or states over others and avoid exploring areas of the search space that are unlikely to lead to a solution. The reached solution is not necessarily the best, however, a ‘good enough’ one is found within a ‘fast enough’ time. This technique is an example of a trade-off between optimality and speed (Russell et al., 2010 ).

Today, there is a rich literature on heuristic methods in computer science (Martí et al., 2018 ). As the problem to be solved may be the choice of a suitable heuristic algorithm, there are also meta-heuristics that have been explored (Glover and Kochenberger, 2003 ), and even hyper-heuristics which may serve to find or generate a suitable meta-heuristic (Burke et al., 2003 ). As Sörensen et al. ( 2018 ) point out, the term ‘metaheuristic’ may refer either to an ‘algorithmic framework that provides a set of guidelines or strategies to develop heuristic optimization algorithms’—or to a specific algorithm that is based on such a framework. E.g., a metaheuristic to find a suitable search algorithm may be inspired by the framework of biological evolution and use its ideas of mutation, reproduction and selection to produce a particular search algorithm. While this algorithm will still be a heuristic one, the fact that it has been generated by an evolutionary process indicates its superiority over alternatives that have been eliminated in the course of that process (cf. Vikhar, 2016 ).

Daniel Kahneman and Amos Tversky: heuristics and biases

Inspired by the concepts of Herbert Simon, psychologists Daniel Kahneman and Amos Tversky initiated the heuristics and biases research programme in the early 1970s, which emphasized how individuals make judgements and the conditions under which those judgements may be inaccurate (Kahneman and Klein, 2009 ).

In addition, Kahneman and Tversky emphasized information processing to elaborate on how real people with limitations can decide, choose, or estimate (Kahneman, 2011 ).

The remarkable article Judgement under Uncertainty: Heuristics and Biases , published in 1974, is considered the turning key that opened the door wide to research on this topic, although it was and still is considered controversial (Kahneman, 2011 ). In their research, Kahneman and Tversky identified three types of heuristics by which probabilities are often assessed: availability, representativeness, and anchoring and adjustment. In passing, Kahneman and Tversky mention that other heuristics are used to form non-probabilistic judgements; for example, the distance of an object may be assessed according to the clarity with which it is seen. Other researchers subsequently introduced different types of heuristics. However, availability, representativeness, and anchoring are still considered fundamental heuristics for judgements under uncertainty.

Availability

According to the psychological definition, availability or accessibility is the ease with which a specific thought comes to mind or can be inferred. Many people use this type of heuristic when judging the probability of an event that may have happened or will happen in the future. Hence, people tend to overestimate the likelihood of a rare event if it easily comes to mind because it is frequently mentioned in daily discussions (Kahneman, 2011 ). For instance, individuals overestimate their probability of being victims of a terrorist attack while the real probability is negligible. However, since terrorist attacks are highly available in the media, the feeling of a personal threat from such an attack will also be highly available during our daily life (Kahneman, 2011 ).

This concept is also present in business, as we remember the successful start-ups whose founders quit college for their dreams, such as Steve Jobs and Mark Zuckerberg, and ignore the thousands of ideas, start-ups, and founders that failed. This is because successful companies are considered a hot topic and receive broad coverage in the media, while failures do not. Similarly, broad media coverage is known to create top-of-mind awareness (TOMA) (Farris et al., 2010 ). Moreover, the availability type of heuristics was offered as a clarification for fanciful connections or irrelevant correlations in which individuals wrongly judge two events to be related to each other when they are not. Tversky and Kahneman clarified that individuals judge relationships based on the ease of envisioning the two events together (Tversky and Kahneman, 1973 ).

Representativeness

The representativeness heuristic is applied when individuals assess the probability that an object belongs to a particular class or category based on how much it resembles the typical case or prototype representing this category (Tversky and Kahneman, 1974 ). Conceptually, this heuristic can be decomposed into three parts. The first one is that the ideal case or prototype of the category is considered representative of the group. The second part judges the similarity between the object and the representative prototype. The third part is that a high degree of similarity indicates a high probability that the object belongs to the category, and a low degree of similarity indicates a low probability.

While the heuristic is often applied automatically within an instant and may be compelling in many cases, Tversky and Kahneman point out that the third part of the heuristic will often lead to serious errors or, at any rate, biases.

In particular, the representativeness heuristic can give rise to what is known as the base rate fallacy. As an example, Tversky and Kahneman consider an individual named Steve, who is described as shy, withdrawn, and somewhat pedantic, and report that people who have to assess, based on this description, whether Steve is more likely to be a librarian or a farmer, invariably consider it more likely that he is a librarian—ignoring the fact that there are many more farmers than librarians, the fact that an estimate of the probability that Steve is a librarian or a farmer, respectively, must take into account.

Another example is that a taxicab was engaged in an accident. The data indicates that 85% of the taxicabs are green and 15% blue. An eyewitness claims that the involved cab was blue. The court then evaluates the witness for reliability because he is 80% accurate and 20% inaccurate. So now, what would be the probability of the involved cab being blue, given that the witness identified it as blue as well?

To evaluate this case correctly, people should consider the base rate, 15% of the cabs being blue, and the witness accuracy rate, 80%. Of course, if the number of cabs is equally split between colours, then the only factor in deciding is the reliability of the witness, which is an 80% probability.

However, regardless of the colours’ distribution, most participants would select 80% to respond to this enquiry. Even participants who wanted to take the base rate into account estimated a probability of more than 50%, while the right answer is 41% using the Bayesian inference (Kahneman, 2011 ).

In relation to the representativeness heuristic, Kahnemann ( 2011 ) illustrated the ‘conjunction fallacy’ in the following example: based only on a detailed description of a character named Linda, doctoral students in the decision science programme of the Stanford Graduate School of Business, all of whom had taken several advanced courses in probability, statistics, and decision theory, were asked to rank various other descriptions of Linda according to their probability. Even Kahneman and Tversky were surprised to find that 85% of the students ranked Linda as a bank teller active in the feminist movement as more likely than Linda as a bank teller.

From these and many other examples, one must conclude that even sophisticated humans use the representativeness heuristic to make probability judgements without referring to what they know about probability.

Representativeness is used to make probability judgements and judgements about causality. The similarity of A and B neither indicates that A causes B nor that B causes A. Nevertheless, if A precedes B and is similar to B, it is often judged to be B’s cause.

Adjustment and anchoring

Based on Tversky and Kahneman’s interpretations, the anchor is the first available number introduced in a question forming the centre of a circle whose radius (up or down) is an acceptable range within which lies the best answer (Baron, 2000 ). This is used and tested in several academic and real-world scenarios and in business negotiations where parties anchor their prices to formulate the range of acceptance through which they can close the deal, deriving the ceiling and floor from the anchor. The impact is more dominant when parties lack time to analyse actions thoroughly.

Significantly, even if the anchor is way beyond logical boundaries, it can still bias the estimated numbers by all parties without them even realizing that it does (Englich et al., 2006 ).

In one of their experiments, Tversky and Kahneman ( 1974 ) asked participants to quickly calculate the product of numbers from 1 to 8 and others to do so from 8 to 1. Since the time was limited to 5 min, they needed to make a guess. The group that started from 1 had an average of 512, while the group that started from 8 had an average of 2250. The right answer was 40,320.

Perhaps this is one of the most unclear cognitive heuristics introduced by Kahneman and Tversky that can be interchangeably considered as a bias instead of a heuristic. The problem is that the mind tends to fixate on the anchor and adjust according to it, whether it was introduced implicitly or explicitly. Some scholars even believe that such bias/heuristic is unavoidable. For instance, in one study, participants were asked if they believed that Mahatma Gandhi died before or after nine years old versus before or after 140 years old. Unquestionably, these anchors were considered unrealistic by the audience. However, when the participants were later asked to give their estimate of Gandhi’s age of death, the group which was anchored to 9 years old speculated the average age to be 50, while the group anchored to the highest value estimated the age of death to be as high as 67 (Strack and Mussweiler, 1997 ).

Gerd Gigerenzer: fast-and-frugal heuristics

The German psychologist Gerd Gigerenzer is one of the most influential figures in the field of decision-making, with a particular emphasis on the use of heuristics. He has built much of his research on the theories of Herbert Simon and considers that Simon’s theory of bounded rationality was unfinished (Gigerenzer, 2015 ). As for Kahneman and Tversky’s work, Gigerenzer has a different approach and challenges their ideas with various arguments, facts, and numbers.

Gigerenzer explores how people make sense of their reality with constrained time and data. Since the world around us is highly uncertain, complex, and volatile, he suggests that probability theory cannot stand as the ultimate concept and is incapable of interpreting everything, particularly when probabilities are unknown. Instead, people tend to use the effortless approach of heuristics. Gigerenzer introduced the concept of the adaptive toolbox, which is a collection of mental shortcuts that a person or group of people can choose from to solve a current problem (Gigerenzer, 2000 ). A heuristic is considered ecologically rational if adjusted to the surrounding ecosystem (Gigerenzer, 2015 ).

A daring argument of Gigerenzer, which very much opposes the heuristics and biases approach of Kahneman and Tversky, is that heuristics cannot be considered irrational or inferior to a solution by optimization or probability calculation. He explicitly argues that heuristics are not gambling shortcuts that are faster but riskier (Gigerenzer, 2008 ), but points to several situations where less is more, meaning that results from frugal heuristics, which neglect some data, were nevertheless more accurate than results achieved by seemingly more elaborate multiple regression or Bayesian methods that try to incorporate all relevant data. While researchers consider this counterintuitive since a basic rule in research seems to be that more data is always better than less, Gigerenzer points out that the less-is-more effect (abbreviated as LIME) could be confirmed by computer simulations. Without denying that in some situations, the effect of using heuristics may be biased (Gigerenzer and Todd, 1999 ), Gigerenzer emphasizes that fast-and-frugal heuristics are basic, task-oriented choice systems that are a part of the decision-maker’s toolbox, the available collection of cognitive techniques for decision-making (Goldstein and Gigerenzer, 2002 ).

Heuristics are considered economical because they are easy to execute, seek limited data, and do not include many calculations. Contrary to most traditional decision-making models followed in the social and behavioural sciences, models of fast-and-frugal heuristics portray not just the result of the process but also the process itself. They comprise three simple building blocks: the search rule that specifies how information is searched for, the stopping rule that specifies when the information search will be stopped, and finally, the decision rule that specifies how the processed information is integrated into a decision (Goldstein and Gigerenzer, 2002 ).

Rather than characterizing heuristics as rules of thumb or mental shortcuts that can cause biases and must therefore be regarded as irrational, Gigerenzer and his co-workers emphasize that fast-and-frugal heuristics are often ecologically rational, even if the conjunction of them may not even be logically consistent (Gigerenzer and Todd, 1999 ).

According to Goldstein and Gigerenzer ( 2002 ), a decision maker’s pool of mental techniques may contain logic and probability theory, but it also embraces a set of simple heuristics. It is compared to a toolbox because just as a wood saw is perfect for cutting wood but useless for cutting glass or hammering a nail into a wall, the ingredients of the adaptive toolbox are intended to tackle specific scenarios.

For instance, there are specific heuristics for choice tasks, estimation tasks, and categorization tasks. In what follows, we will discuss two well-known examples of fast-and-frugal heuristics: the recognition heuristic (RH), which utilizes the absence of data, and the take-the-best heuristic (TTB), which purposely disregards the data.

Both examples of heuristics can be connected to decision assignments and to circumstances in which a decision-maker needs to decide which of two options has a higher reward on a quantitative scale.

Ideal scenarios would be deducing which one of two stock shares will have a better income in the next month, which of two cars is more convenient for a family, or who is a better candidate for a particular job (Goldstein and Gigerenzer, 2002 ).

The recognition heuristic

The recognition heuristic has been examined broadly with the famous experiment to determine which of the two cities has a higher population. This experiment was conducted in 2002, and the participants were undergraduate students: one group in the USA and one in Germany. The question was as follows: which has more occupants—San Diego or San Antonio? Given the cultural difference between the student groups and the level of information regarding American cities, it could be expected that American students would have a higher accuracy rate than their German peers. However, most German students did not even know that San Antonio is an American city (Goldstein and Gigerenzer, 2002 ). Surprisingly, the examiners, Goldstein and Gigerenzer, found the opposite of what was expected. 100% of the German students got the correct answer, while the American students achieved an accuracy rate of around 66%. Remarkably, the German students who had never known about San Antonio had more correct answers. Their lack of knowledge empowered them to utilize the recognition heuristic, which states that if one of two objects is recognized and the other is not, then infer that the recognized object has the higher value concerning the relevant criterion. The American students could not use the recognition heuristic because they were familiar with both cities. Ironically, they knew too much.

The recognition heuristic is an incredible asset. In many cases, it is used for swift decisions since recognition is usually systematic and not arbitrary. Useful applications may be cities’ populations, players’ performance in major leagues, or writers’ level of productivity. However, this heuristic will be less efficient in more difficult scenarios than a city’s population, such as the age of the city’s mayor or its sea-level altitude (Gigerenzer and Todd, 1999 ).

Take-the-best heuristic

When the recognition heuristic is not efficient because the decision-maker has enough information about both options, another important heuristic can be used that relies on hints or cues to arrive at a decision. The take-the-best (TTB) heuristic is a heuristic that relies only on specific cues or signals and does not require any complex calculations. In practice, it often boils down to a one-reason decision rule, a type of heuristic where judgements are based on a single good reason only, ignoring other cues (Gigerenzer and Gaissmaier, 2011 ). According to the TTB heuristic, a decision-maker evaluates the case by selecting the attributes which are important to him and sorts these cues by importance to create a hierarchy for the decision to be taken. Then alternatives are compared according to the first, i.e., the most important, cue; if an alternative is the best according to the first cue, the decision is taken. Otherwise, the decision-maker moves to the next layer and checks that level of cues. In other words, the decision is based on the most important attribute that allows one to discriminate between the alternatives (Gigerenzer and Goldstein, 1996 ). Although this lexicographic preference ordering is well known from traditional economic theory, it appears there mainly to provide a counterexample to the existence of a real-valued utility function (Debreu, 1959 ). Surprisingly, however, it seems to be used in many critical situations. For example, in many airports, the customs officials may decide if a traveller is chosen for a further check by looking only at the most important attributes, such as the city of departure, nationality, or luggage weight (Pachur and Marinello, 2013 ). Moreover, in 2012, a study explored voters’ views of how US presidential competitors would deal with the single issue that voters viewed as most significant, for example, the state of the economy or foreign policy. A model dependent on this attribute picked the winner in most cases (Graefe and Armstrong, 2012 ).

However, the TTB heuristic has a stopping rule applied when the search reaches a discriminating cue. So, if the most important signal discriminates, there is no need to continue searching for other cues, and only one signal is considered. Otherwise, the next most important signal will be considered. If no discriminating signal is found, the heuristic will need to make a random guess (Gigerenzer and Gaissmaier, 2011 ).

Empirical evidence on fast-and-frugal heuristics

More studies have been conducted on fast-and-frugal heuristics using analytical methods and simulations to investigate when and why heuristics yield accurate results on the one hand, and on the other hand, using experiments and observational methods to find out whether and when people use fast-and-frugal heuristics (Luan et al., 2019 ). Structured examinations and benchmarking with standard models, for example, regression or Bayesian models, have shown that the accuracy of fast-and-frugal heuristics relies upon the structure of the information environment (e.g., the distribution of signal validities, the interrelation between signals, etc.). In numerous situations, fast-and-frugal heuristics can perform well, particularly in generalized contexts, when making predictions for new cases that have not been previously experienced. Empirical examinations show that people utilize fast-and-frugal heuristics under a time constraint when data is hard to obtain or must be retrieved from memory. Remarkably, some studies have inspected how individuals adjust to various situations by learning. Rieskamp and Otto ( 2006 ) found that individuals seemingly learn to choose the heuristic that has the best performance in a specific domain. Nevertheless, Reimer and Katsikopoulos ( 2004 ) found that individuals apply fast-and-frugal heuristics when making inferences in groups.

While interest in heuristics has been increasing, some of the literature has been mostly critical. In particular, the heuristics and biases programme introduced by Kahneman and Tversky has been the target of more than one critique (Reisberg, 2013 ).

The arguments are mainly in two directions. The first is that the main focus is on the coherence standards such as rationality and that the detection of biases ignores the context-environmental factors where the judgements occur (B.R. Newell, 2013 ). The second is that notions such as availability or representativeness are vague and undefined, and state little regarding the procedures’ hidden judgements (Gigerenzer, 1996 ). For example, it has been argued that the replies in the acclaimed Linda-the-bank-teller experiment could be considered sensible instead of biased if one uses conversational or colloquial standards instead of formal probability theory (Hilton, 1995 ).

The argument of having a vague explanation for certain phenomena can be illustrated when considering the following two scenarios. People tend to believe that an opposite outcome will be achieved after having a stream of the same outcome (e.g., people tend to believe that ‘heads’ should be the next outcome in a coin-flipping game with many consecutive ‘tails’). This is called the gambler fallacy (Barron and Leider, 2010 ). By contrast, the hot-hand fallacy (Gilovich et al., 1985 ) argues that people tend to believe that a stream of the same outcome will continue when there is a lucky day (e.g., a player is taking a shot in a sport such as a basketball after a series of successful attempts). Ayton and Fisher ( 2004 ) argued that, although these two practices are quite opposite, they have both been classified under the heuristic of representativeness. In the two cases, a flawed idea of random events drives observers to anticipate that a certain stream of results is representative of the whole procedure. In the first scenario of coin flipping, people tend to believe that a long stream of tails should not occur; hence the head is predicted. While in the case of the sports player, the stream of the same outcome is expected to continue (Gilovich et al., 1985 ). Therefore, representativeness cannot be diagnosed without considering in advance the expected results. Also, the heuristic does not clarify why people have the urge to believe that a stream of random events should have a representative, while in real life, it does not (Ayton and Fischer, 2004 ).

Nevertheless, the most common critique of Kahneman and Tversky is the idea that ‘we cannot be that dumb’. It states that the heuristics and biases programme is overly pessimistic when assessing the average human decision-making. Also, humans collectively have accumulated many achievements and discoveries throughout human history that would not have been possible if their ability to adequate decision-making had been so limited (Gilovich and Griffin, 2002 ).

Similarly, the probabilistic mental models (PMM) theory of human inference inspired by Simon and pioneered by Gigerenzer has also been exposed to criticism (B.R. Newell et al., 2003 ). Indeed, the enticing character of heuristics that they are both easy to apply and efficient has made them famous within different domains. However, it has also made them vulnerable to replications or variations of the experiments that challenge the original results. For example, Daniel Oppenheimer ( 2003 ) argues that the recognition heuristic (RH) could not yield satisfactory results after replicating the experiment of city populations. He claims that the participants’ judgements failed to obey the RH not just when there were cues other and stronger than mere recognition but also in circumstances where recognition would have been the best cue available. In any case, one could claim that there are numerous methods in the adaptive toolbox and that under certain conditions, people may prefer to use heuristics other than the RH. However, this statement is also questionable since many heuristics that are thought to exist in the adaptive toolbox acknowledge the RH as an initial step (Gigerenzer and Todd, 1999 ). Hence, if individuals are not using the RH, they cannot use many of the other heuristics in the adaptive toolbox (Oppenheimer, 2003 ). Likewise, Newell et al. ( 2003 ) question whether the fast-and-frugal heuristics accurately explain actual human behaviour. In two experiments, they challenged the take-the-best (TTB) heuristic, as it is considered a building block in the PMM framework. The outcomes of these experiments, together with others, such as those of Jones et al. ( 2000 ) and Bröder ( 2000 ), show that the TTB heuristic is not a reliable approach even within circumstances favouring its use. In a somewhat heated debate published in the Psychological Review 1996, Gigerenzer’s criticism of Kahneman and Tversky that many of the so-called biases ‘disappear’ if frequencies rather than probabilities are assumed, was countered by Kahneman and Tversky ( 1996 ) by means of a detailed re-examination of the conjunction fallacy (or Linda Problem). Gigerenzer ( 1996 ) remained unconvinced, and was in turn, blamed by Kahneman and Tversky ( 1996 , p. 591) for just reiterating ‘his objections … without answering our main arguments’.

Our historical review has revealed a number of issues that have received little attention in the literature.

Deliberate vs. automatic heuristics

We have differentiated between deliberate and automatic heuristics, which often seem to be confused in the literature. While it is a widely shared view today that the human brain often relies heavily on the fast and effortless ‘System 1’ in decision-making, but can also use the more demanding tools of ‘System 2’, and it has been acknowledged, e.g. by Kahneman ( 2011 , p. 98), that some heuristics belong to System 1 and others to System 2, the two systems are not as clearly distinct as it may seem. In fact, the very wide range of what one may call ‘heuristics’ shows that there is a whole spectrum of fallible decision-making procedures—ranging from the probably innate problem-solving strategy of the baby that cries whenever it is hungry or has some other problem, to the most elaborate and sophisticated procedures of, e.g., Polya, Bolzano, or contemporary chess-engines. One may be tempted to characterize instinctive procedures as subconscious and sophisticated ones as conscious, but a deliberate heuristic can very well become a subconsciously applied ‘habit of the mind’ or learnt routine with experience and repetition. Vice versa, automatic, subconscious heuristics can well be raised to consciousness and be applied deliberately. E.g., the ‘inductive inference’ from tasty strawberries to the assumption that all red berries are sweet and edible may be quite automatic and subconscious in little children, but the philosophical literature on induction shows that it can be elaborated into something quite conscious. However, while the notion of consciousness may be crucial for an adequate understanding of heuristics in human cognition, for the time being, it seems to remain a philosophical mystery (Harley, 2021 ; Searle, 1997 ), and once programmed, sophisticated heuristic algorithms can be executed by automata.

The deliberate heuristics that we reviewed also illustrate that some of them can hardly be called ‘simple’, ‘shortcuts’, or ‘rules of thumb’. E.g., the heuristics of Descartes, Bolzano, or Polya each consist of a structured set of suggestions, and, e.g., ‘to devise a plan’ for a mathematical proof is certainly not a shortcut. Llull ( 1308 , p. 329), to take another example, wrote of his ‘ars magna’ that ‘the best kind of intellect can learn it in two months: one month for theory and another month for practice’.

Heuristics vs. algorithms

Our review of heuristics also allowed us to clarify the distinction between heuristics and algorithms. As evidenced by our glimpse at computer science, there are procedures that are quite obviously both an algorithm and a heuristic. Within computer science, they are in fact quite common. Algorithms of the heuristic type may be required for certain problems even though an algorithm that finds the optimal solution exists ‘in principle’—as in the case of determining the optimal strategy in chess, where the brute-force-method to enumerate all possible plays of chess is just not practically feasible. In other cases, heuristic algorithms are used because an exhaustive search, while practically feasible, would be too costly or time-consuming. Clearly, for many problems, there are also problem-solving algorithms which always do produce the optimal solution in a reasonable time frame. Given our definition of a heuristic as a fallible method, algorithms of this kind are counterexamples to the complaint that the notion has become so wide that ‘any procedure can be called a heuristic’. However, as we have seen, there are also heuristic procedures that are non-algorithmic. These may be necessary either because the problem to be solved is not sufficiently well-defined to allow for an algorithm, or because an algorithm that would solve the problem at hand, is not known or does not exist. Kleining’s qualitative heuristics is an example of non-algorithmic heuristics necessitated by the ill-defined problems of research in the social sciences, while Polya’s heuristic for solving mathematical problems is an example of the latter: an algorithm that would allow one to decide if a given mathematical conjecture is a theorem or not does not exist (cf. Davis, 1965 ).

Pre-SEU vs. post-SEU heuristics

As we noted in the introduction, the emergence of the SEU theory can be regarded as a kind of watershed for the research on heuristics, as it came to be regarded as the standard definition of rational choice. Post-SEU, fallible methods of decision-making would have to face comparison with this standard. Gigerenzer’s almost belligerent criticism of SEU shows that even today it seems difficult to discuss the pros and cons of heuristics unless one relates them to the backdrop of SEU. However, his criticism of SEU is mostly en passant and seems to assume that the SEU model requires ‘known probabilities’ (e.g., Gigerenzer, 2021 ), ignoring the fact that it is, in general, subjective probabilities, as derived from the agent’s preferences among lotteries, that the model relies on (cf. e.g., Jeffrey, 1967 or Gilboa, 2011 ). In fact, when applied to an ill-defined decision problem in, e.g., management, the SEU theory may well be regarded as a heuristic—it asks you to consider the possible consequences of the relevant set of actions, your preferences among those consequences, and the likelihood of those consequences. To the extent that one may get all of these elements wrong, SEU is a fallible method of decision-making. To be sure, it is not a fast and effortless heuristic, but our historical review of pre-SEU heuristics has illustrated that heuristics may be quite elaborate and require considerable effort and attention.

It is quite true, of course, that the SEU heuristic will hardly be helpful in problem-solving that is not ‘just’ decision-making. If, e.g., the problem to be solved is to find a proof for a mathematical conjecture, the set of possible actions will in general be too vast to be practically contemplated, let alone evaluated according to preferences and probabilities.

Positive vs. negative heuristics

To the extent that the study of heuristics aims at understanding how decisions are actually made, it is not only positive heuristics that need to be considered. It will also be required to investigate the conditions that may prevent the agent from adopting certain courses of action. As we saw, Lakatos used the notion of negative heuristics quite explicitly to characterize research programmes, but we also briefly review Duncker’s notion of ‘functional fixedness’ as an example of a hindrance to adequate problem-solving. A systematic study of such negative heuristics seems to be missing in the literature and we believe that it may be a helpful complement to the study of positive heuristics which has dominated the literature that we reviewed.

To the extent that heuristics are studied with the normative aim of identifying effective heuristics, it may also be useful to consider approaches that should not be taken. ‘Do not try to optimize!’ might be a negative heuristic favoured by the fast-and-frugal school of thought.

Heuristics as the product of evolution

Clearly, heuristics have always existed throughout the development of human knowledge due to the ‘old mind’s’ evolutionary roots and the frequent necessity to apply fast and sufficiently reliable behaviour patterns. However, unlike the behaviour patterns in the other animals, the methods used by humans in problem-solving are sufficiently diverse that the dual-process theory was suggested to provide some structure to the rich ‘toolbox’ humans can and do apply. As all our human DNA is the product of evolution, it is not only the intuitive inclinations to react to certain stimuli in a particular way that must be seen as the product of evolution, but also our ability to abstain from following our gut feelings when there is reason to do so, to reflect and analyse the situation before we embark on a particular course of action. Quite frequently, we experience a tension between our intuitive inclinations and our analytic mind’s judgement, but both of them are somehow the product of evolution, our biography, and the environment. Thus, to point out that gut feelings are an evolved capacity of the brain does in no way provide an argument that would support their superiority over the reflective mind.

Moreover, compared to the speed of problem change in our human lifetimes, biological evolution is very slow. The evolved capacities of the human brain may have been well-adapted to the survival needs of our ancestors some 300,000 years ago, but there is little reason to believe that they are uniformly well-adapted to human problem-solving in the 21st century.

Resource-bounded and ecological rationality

Throughout our review, the reader will have noticed that many heuristics have been suggested for specific problem areas. The methods of the ancient Greeks were mainly centred around solving geometrical problems. Llull was primarily concerned with theological questions, Descartes and Leibniz pursued ‘mechanical’ solutions to philosophical issues, Polya suggested heuristics for Mathematics, Müller for engineering, and Kleining for social science research. This already suggests that heuristics suitable for one type of problem need not be suitable for a different type. Likewise, the automatic heuristics that both the Kahneman-Tversky and the Gigerenzer schools focused on, are triggered by particular tasks. Simon’s observation that the success of a given heuristic will depend on the environment in which it is employed, is undoubtedly an important one that has motivated Gigerenzer’s notion of ecological rationality and is strikingly absent from the SEU model. If ‘environment’ is taken in a broad sense that includes the available resources, the cost of time and effort, the notion seems to cover what has been called resource-rational behaviour (e.g., Bhui et al., 2021 ).

Avenues of further research

A comprehensive study describing the current status of the research on heuristics and their relation to SEU seems to be missing and is beyond the scope of our brief historical review. Insights into their interrelationship can be expected from recent attempts at formal modelling of human cognition that take the issues of limited computational resources and context-dependence of decision-making seriously. E.g., Lieder and Griffiths ( 2020 ) do this from a Bayesian perspective, while Busemeyer et al. ( 2011 ) and Pothos and Busemeyer ( 2022 ) use a generalization of standard Kolmogorov probability theory that is also the basis of quantum mechanics and quantum computation. While it may seem at first glance that such modelling assumes even more computational power than the standard SEU model of decision-making, the computational power is not assumed on the part of the human decision-maker. Rather, the claim is that the decision-maker behaves as if s/he would solve an optimization problem under additional constraints, e.g., on computational resources. The ‘as if’ methodology that is employed here is well-known to economists (Friedman, 1953 ; Mäki, 1998 ) and also to mathematical biologists who have used Bayesian models to explain animal behaviour (McNamara et al., 2006 ; Oaten, 1977 ; Pérez-Escudero and de Polavieja, 2011 ). Evolutionary arguments might be invoked to support this methodology if a survival disadvantage can be shown to result from behaviour patterns that are not Bayesian optimal, but we are not aware of research that would substantiate such arguments. However, attempting to do so by embedding formal models of cognition in models of evolutionary game theory may be a promising avenue for further research.

NP stands for ‘nondeterministic polynomial-time’, which indicates that the optimal solution can be found by a nondeterministic Turing-machine in a running time that is bounded by a polynomial function of the input size. In fact, the TSP is ‘NP-hard’ which means that it is ‘at least as hard as the hardest problems in the category of NP problems’.

Agre P, Horswill I (1997) Lifeworld analysis. J Artif Intell Res 6:111–145

Article   Google Scholar  

Ayton P, Fischer I (2004) The hot hand fallacy and the gambler’s fallacy. Two faces of subjective randomness. Memory Cogn 32:8

Banse G, Friedrich K (2000) Konstruieren zwischen Kunst und Wissenschaft. Edition Sigma, Idee‐Entwurf‐Gestaltung, Berlin

Google Scholar  

Baron J (2000) Thinking and deciding. Cambridge University Press

Barron G, Leider S (2010) The role of experience in the Gambler’s Fallacy. J Behav Decision Mak 23:1

Barros G (2010) Herbert A Simon and the concept of rationality: boundaries and procedures. Brazilian. J Political Econ 30:3

Baumeister RF, Vohs KD (2007) Encyclopedia of social psychology, vol 1. SAGE

Bazerman MH, Moore DA (1994) Judgment in managerial decision making. Wiley, New York

Bentley JL (1982) Writing efficient programs Prentice-Hall software series. Prentice-Hall

Bhui R, Lai L, Gershman S (2021) Resource-rational decision making. Curr Opin Behav Sci 41:15–21. https://doi.org/10.1016/j.cobeha.2021.02.015

Bolzano B (1837) Wissenschaftslehre. Seidelsche Buchhandlung, Sulzbach

Bossaerts P, Murawski C (2017) Computational complexity and human decision-making. Trends Cogn Sci 21(12):917–929

Article   PubMed   Google Scholar  

Boyer CB (1991) The Arabic Hegemony. A History of Mathematics. Wiley, New York

Bröder A (2000) Assessing the empirical validity of the “Take-the-best” heuristic as a model of human probabilistic inference. J Exp Psychol Learn Mem Cogn 26:5

Burke E, Kendall G, Newall J, Hart E, Ross P, Schulenburg S (2003) Hyper-heuristics: an emerging direction in modern search technology. In: Glover F, Kochenberger GA (eds) Handbook of metaheuristics. International series in operations research & management science, vol 57. Springer, Boston, MA

Busemeyer JR, Pothos EM, Franco R, Trueblood JS (2011) A quantum theoretical explanation for probability judgment errors. Psychol Rev 118(2):193

Buss DM, Kenrick DT (1998) Evolutionary social psychology. In: D T Gilbert, S T Fiske, G Lindzey (eds.), The handbook of social psychology. McGraw-Hill, p. 982–1026

Byron M (1998) Satisficing and optimality. Ethics 109:1

Davis M (ed) (1965) The undecidable. Basic papers on undecidable propositions, unsolvable problems and computable functions. Raven Press, New York

MATH   Google Scholar  

Debreu G (1959) Theory of value: an axiomatic analysis of economic equilibrium. Yale University Press

Descartes R (1908) Rules for the Direction of the Mind. In: Oeuvres de Descartes, vol 10. In: Adam C, Tannery P (eds). J Vrin, Paris

Descartes R (1998) Discourse on the method for conducting one’s reason well and for seeking the truth in the sciences (1637) (trans and ed: Cress D). Hackett, Indianapolis

Dunbar RIM (1998) Grooming, gossip, and the evolution of language. Harvard University Press

Duncker K (1935) Zur Psychologie des produktiven Denkens. Springer

Englich B, Mussweiler T, Strack F (2006) Playing dice with criminal sentences: the influence of irrelevant anchors on experts’ judicial decision making. Personal Soc Psychol Bull 32:2

Evans JSB (2010) Thinking twice: two minds in one brain. Oxford University Press

Farr RM (1996) The roots of modern social psychology, 1872–1954. Blackwell Publishing

Farris PW, Bendle N, Pfeifer P, Reibstein D (2010) Marketing metrics: the definitive guide to measuring marketing performance. Pearson Education

Fidora A, Sierra C (2011) Ramon Llull, from the Ars Magna to artificial intelligence. Artificial Intelligence Research Institute, Barcelona

Frantz R (2003) Herbert Simon Artificial intelligence as a framework for understanding intuition. J Econ Psychol 24:2. https://doi.org/10.1016/S0167-4870(02)00207-6

Friedman M (1953) The methodology of positive economics. In: Friedman M (ed) Essays in positive economics. University of Chicago Press

Ghiselin MT (1973) Darwin and evolutionary psychology. Science (New York, NY) 179:4077

Gibbons A (2007) Paleoanthropology. Food for thought. Science (New York, NY) 316:5831

Gigerenzer G (1996) On narrow norms and vague heuristics: a reply to Kahneman and Tversky. 1939–1471

Gigerenzer G (2000) Adaptive thinking: rationality in the real world. Oxford University Press, USA

Gigerenzer G (2008) Why heuristics work. Perspect Psychol Sci 3:1

Gigerenzer G (2015) Simply rational: decision making in the real world. Evol Cogn

Gigerenzer G (2021) Embodied heuristics. Front Psychol https://doi.org/10.3389/fpsyg.2021.711289

Gigerenzer G, Gaissmaier W (2011) Heuristic decision making. Annual Review of Psychology 62, p 451–482

Gigerenzer G, Goldstein DG (1996) Reasoning the fast and frugal way: models of bounded rationality. Psychol Rev 103:4

Gigerenzer G, Selten R (eds) (2001) Bounded rationality: the adaptive toolbox. MIT Press

Gigerenzer G, Todd PM (1999) Simple heuristics that make us smart. Oxford University Press, USA

Gilboa I (2011) Making better decisions. Decision theory in practice. Wiley-Blackwell

Gilovich T, Griffin D (2002) Introduction—heuristics and biases: then and now in heuristics and biases: the psychology of intuitive judgment (8). Cambridge University Press

Gilovich T, Vallone R, Tversky A (1985) The hot hand in basketball: on the misperception of random sequences. Cogn Psychol 17:3

Glaveanu VP (2019) The creativity reader. Oxford University Press

Glover F, Kochenberger GA (eds) (2003) Handbook of metaheuristics. International series in operations research & management science, vol 57. Springer, Boston, MA

Goldstein DG, Gigerenzer G (2002) Models of ecological rationality: the recognition heuristic. Psychol Rev 109:1

Graefe A, Armstrong JS (2012) Predicting elections from the most important issue: a test of the take-the-best heuristic. J Behav Decision Mak 25:1

Groner M, Groner R, Bischof WF (1983) Approaches to heuristics: a historical review. In: Groner R, Groner M, Bischof WF (eds) Methods of heuristics. Erlbaum

Groner R, Groner M (1991) Heuristische versus algorithmische Orientierung als Dimension des individuellen kognitiven Stils. In: Grawe K, Semmer N, Hänni R (Hrsg) Üher die richtige Art, Psychologie zu betreiben. Hogrefe, Göttingen

Gugerty L (2006) Newell and Simon’s logic theorist: historical background and impact on cognitive modelling. In: Proceedings of the human factors and ergonomics society annual meeting. Symposium conducted at the meeting of SAGE Publications. Sage, Los Angeles, CA

Harel D (2000) Computers Ltd: what they really can’t do. Oxford University Press

Harley TA (2021) The science of consciousness: waking, sleeping and dreaming. Cambridge University Press

Harris B (1979) Whatever happened to little Albert? Am Psychol 34:2

Heath TL (1926) The thirteen books of Euclid’s elements. Introduction to vol I, 2nd edn. Cambridge University Press

Hertwig R, Pachur T (2015) Heuristics, history of. In: International encyclopedia of the social behavioural sciences. Elsevier, pp. 829–835

Hilton DJ (1995) The social context of reasoning: conversational inference and rational judgment. Psychol Bull 118:2

Hopcroft JE, Motwani R, Ullman JD (2007) Introduction to Automata Theory, languages, and computation. Addison Wesley, Boston/San Francisco/New York

Jeffrey R (1967) The logic of decision, 2nd edn. McGraw-Hill

Jones S, Juslin P, Olsson H, Winman A (2000) Algorithm, heuristic or exemplar: Process and representation in multiple-cue judgment. In: Proceedings of the 22nd annual conference of the Cognitive Science Society. Symposium conducted at the meeting of Erlbaum, Hillsdale, NJ

Kahneman D (2011) Thinking, fast and slow. Farar, Straus and Giroux

Kahneman D, Klein G (2009) Conditions for intuitive expertise: a failure to disagree. Am Psychol 64:6

Kahneman D, Tversky A (1996) On the reality of cognitive illusions. In: Psychological Review, 103(3), p 582–591

Khaldun I (1967) The Muqaddimah. An introduction to history (trans: Arabic by Rosenthal F). Abridged and edited by Dawood NJ. Princeton University Press

Klein G (2001) The fiction of optimization. In: Gigerenzer G, Selten R (eds) Bounded Rationality: The Adaptive Toolbox. MIT Press Editors

Kleining G (1982) Umriss zu einer Methodologie qualitativer Sozialforschung. Kölner Z Soziol Sozialpsychol 34:2

Kleining G (1995) Von der Hermeneutik zur qualitativen Heuristik. Beltz

Lakatos I (1970) Falsification and the methodology of scientific research programmes. In: Lakatos I, Musgrave A (eds) Criticism and the growth of knowledge. Cambridge University Press

Leibniz GW (1880) Die Philosophischen Schriften von GW Leibniz IV, hrsg von CI Gerhardt

Lerner RM (1978) Nature Nurture and Dynamic Interactionism. Human Development 21(1):1–20. https://doi.org/10.1159/000271572

Lieder F, Griffiths TL (2020) Resource-rational analysis: understanding human cognition as the optimal use of limited computational resources. Behavioral and Brain Sciences. Vol 43, e1. Cambridge University Press

Link D (2010) Scrambling TRUTH: rotating letters as a material form of thought. Variantology 4, p. 215–266

Llull R (1308) Ars Generalis Ultima (trans: Dambergs Y), Yanis Dambergs, https://lullianarts.narpan.net/

Luan S, Reb J, Gigerenzer G (2019) Ecological rationality: fast-and-frugal heuristics for managerial decision-making under uncertainty. Acad Manag J 62:6

Mäki U (1998) As if. In: Davis J, Hands DW, Mäki U (ed) The handbook of economic methodology. Edward Elgar Publishing

Martí R, Pardalos P, Resende M (eds) (2018) Handbook of heuristics. Springer, Cham

McDougall W (2015) An introduction to social psychology. Psychology Press

McNamara JM, Green RF, Olsson O (2006) Bayes’ theorem and its applications in animal behaviour. Oikos 112(2):243–251. http://www.jstor.org/stable/3548663

Newborn M (1997) Kasparov versus Deep Blue: computer chess comes of age. Springer

Newell A, Shaw JC, Simon HA (1959) Report on a general problem-solving program. In: R. Oldenbourg (ed) IFIP congress. UNESCO, Paris

Newell A, Simon HA (1972) Human problem solving. Prentice-Hall, Englewood Cliffs, NJ

Newell BR (2013) Judgment under uncertainty. In: Reisberg D (ed) The Oxford handbook of cognitive psychology. Oxford University Press

Newell BR, Weston NJ, Shanks DR (2003) Empirical tests of a fast-and-frugal heuristic: not everyone “takes the best”. Organ Behav Hum Decision Processes 91:1

Oaten A (1977) Optimal foraging in patches: a case for stochasticity. Theor Popul Biol 12(3):263–285

Article   MathSciNet   CAS   PubMed   MATH   Google Scholar  

Oppenheimer DM (2003) Not so fast! (and not so frugal!): rethinking the recognition heuristic. Cognition 90:1

Pachur T, Marinello G (2013) Expert intuitions: how to model the decision strategies of airport customs officers? Acta Psychol 144:1

Pearl J (1984) Heuristics: intelligent search strategies for computer problem solving. Addison-Wesley Longman Publishing Co, Inc

Pérez-Escudero A, de Polavieja G (2011) Collective animal behaviour from Bayesian estimation and probability matching. Nature Precedings

Pinheiro CAR, McNeill F (2014) Heuristics in analytics: a practical perspective of what influences our analytical world. Wiley Online Library

Polya G (1945) How to solve it. Princeton University Press

Polya G (1954) Induction and analogy in mathematics. Princeton University Press

Pombo O (2002) Leibniz and the encyclopaedic project. In: Actas do Congresso Internacional Ciência, Tecnologia Y Bien Comun: La atualidad de Leibniz

Pothos EM, Busemeyer JR (2022) Quantum cognition. Annu Rev Psychol 73:749–778

Priest G (2008) An introduction to non-classical logic: from if to is. Cambridge University Press

Book   MATH   Google Scholar  

Ramsey FP (1926) Truth and probability. In: Braithwaite RB (ed) The foundations of mathematics and other logical essays. McMaster University Archive for the History of Economic Thought. https://EconPapers.repec.org/RePEc:hay:hetcha:ramsey1926

Reimer T, Katsikopoulos K (2004) The use of recognition in group decision-making. Cogn Sci 28:6

Reisberg D (ed) (2013) The Oxford handbook of cognitive psychology. Oxford University Press

Rieskamp J, Otto PE (2006) SSL: a theory of how people learn to select strategies. J Exp Psychol Gen 135:2

Ritchey T (2022) Ramon Llull and the combinatorial art. https://www.swemorph.com/amg/pdf/ars-morph-1-draft-ch-4.pdf

Ritter J, Gründer K, Gabriel G, Schepers H (2017) Historisches Wörterbuch der Philosophie online. Schwabe Verlag

Russell SJ, Norvig P, Davis E (2010) Artificial intelligence: a modern approach, 3rd edn. Prentice-Hall series in artificial intelligence. Prentice-Hall

Savage LJ (ed) (1954) The foundations of statistics. Courier Corporation

Schacter D, Gilbert D, Wegner D (2011) Psychology, 2nd edn. Worth

Schaeffer J, Burch N, Bjornsson Y, Kishimoto A, Muller M, Lake R, Lu P, Sutphen S (2007) Checkers is solved. Science 317(5844):1518–1522

Article   ADS   MathSciNet   CAS   PubMed   MATH   Google Scholar  

Schreurs BG (1989) Classical conditioning of model systems: a behavioural review. Psychobiology 17:2

Scopus (2022) Search “heuristics”. https://www.scopus.com/standard/marketing.uri (TITLE-ABS-KEY(heuristic) AND (LIMIT-TO (SUBJAREA,"DECI") OR LIMIT-TO (SUBJAREA,"SOCI") OR LIMIT-TO (SUBJAREA,"BUSI"))) Accessed on 16 Apr 2022

Searle JR (1997) The mystery of consciousness. Granta Books

Semaan G, Coelho J, Silva E, Fadel A, Ochi L, Maculan N (2020) A brief history of heuristics: from Bounded Rationality to Intractability. IEEE Latin Am Trans 18(11):1975–1986. https://latamt.ieeer9.org/index.php/transactions/article/view/3970/682

Sen S (2020) The environment in evolution: Darwinism and Lamarckism revisited. Harvest Volume 1(2):84–88. https://doi.org/10.2139/ssrn.3537393

Shah AK, Oppenheimer DM (2008) Heuristics made easy: an effort-reduction framework. Psychol Bull 134:2

Siitonen A (2014) Bolzano on finding out intentions behind actions. In: From the ALWS archives: a selection of papers from the International Wittgenstein Symposia in Kirchberg am Wechsel

Simon HA (1955) A behavioural model of rational choice. Q J Econ 69:1

Simon HA, Newell A (1958) Heuristic problem solving: the next advance in operations research. Oper Res 6(1):1–10. http://www.jstor.org/stable/167397

Article   MATH   Google Scholar  

Smith R (2020) Aristotle’s logic. In: Zalta EN (ed) The Stanford encyclopedia of philosophy, 2020th edn. Metaphysics Research Lab, Stanford University

Smulders TV (2009) Darwin 200: special feature on brain evolution. Biology Letters 5(1), p. 105–107

Sörensen K, Sevaux M, Glover F (2018) A history of metaheuristics. In: Martí R, Pardalos P, Resende M (eds) Handbook of heuristics. Springer, Cham

Stephenson N (2003) Theoretical psychology: critical contributions. Captus Press

Strack F, Mussweiler T (1997) Explaining the enigmatic anchoring effect: mechanisms of selective accessibility. J Person Soc Psychol 73:3

Sullivan D (2002) How search engines work. SEARCH ENGINE WATCH, at http://www.searchenginewatch.com/webmasters/work.Html (Last Updated June 26, 2001) (on File with the New York University Journal of Legislation and Public Policy). http://www.searchenginewatch.com

Suppes P (1983) Heuristics and the axiomatic method. In: Groner R et al (ed) Methods of Heuristics. Routledge

Turing A (1937) On computable numbers, with an application to the entscheidungsproblem. Proc Lond Math Soc s2-42(1):230–265

Article   MathSciNet   MATH   Google Scholar  

Tversky A, Kahneman D (1973) Availability: a heuristic for judging frequency and probability. Cogn Psychol 5:2

Tversky A, Kahneman D (1974) Judgment under uncertainty: heuristics and biases. Science (New York, NY) 185::4157

Vardi MY (2012) Artificial intelligence: past and future. Commun ACM 55:1

Vikhar PA (2016) Evolutionary algorithms: a critical review and its future prospects. Paper presented at the international conference on global trends in signal processing, information computing and communication (ICGTSPICC). IEEE, pp. 261–265

Volz V, Rudolph G, Naujoks B (2016) Demonstrating the feasibility of automatic game balancing. Paper presented at the proceedings of the Genetic and Evolutionary Computation Conference, pp. 269–276

von Neumann J, Morgenstern O (1944) Theory of games and economic behaviour. Princeton University Press, Princeton, p. 1947

Zermelo E (1913) Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels. In: Proceedings of the fifth international congress of mathematicians. Symposium conducted at the meeting of Cambridge University Press, Cambridge. Cambridge University Press, Cambridge

Zilio D (2013) Filling the gaps: skinner on the role of neuroscience in the explanation of behavior. Behavior and Philosophy, 41, p. 33–59

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Hjeij, M., Vilks, A. A brief history of heuristics: how did research on heuristics evolve?. Humanit Soc Sci Commun 10 , 64 (2023). https://doi.org/10.1057/s41599-023-01542-z

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Heuristic Approaches to Problem Solving

“A heuristic technique, often called simply a heuristic, is any approach to problem solving, learning, or discovery that employs a practical method not guaranteed to be optimal or perfect, but sufficient for the immediate goals. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision. Examples of this method include using a rule of thumb, an educated guess, an intuitive judgement, guesstimate, stereotyping, profiling, or common sense.” (Source: Wikipedia )

“In computer science, a heuristic is a technique designed for solving a problem more quickly when classic methods are too slow, or for finding an approximate solution when classic methods fail to find any exact solution. This is achieved by trading optimality, completeness, accuracy, or precision for speed. In a way, it can be considered a shortcut.” (Source: Wikipedia )

The objective of a heuristic algorithm is to apply a rule of thumb approach to produce a solution in a reasonable time frame that is good enough for solving the problem at hand. There is no guarantee that the solution found will be the most accurate or optimal solution for the given problem. We often refer the solution as “good enough” in most cases.

Heuristic Algorithms? Heuristic Algorithms can be found in:

Let’s investigate a few basic examples where a heuristic algorithm can be used:

Based on this approach, can you think of how a similar approach could be used for an algorithm to play:

• Othello (a.k.a. Reversi Game)
• A Battleship game?
• Rock/Paper/Scissors?

It is hence essential to use a heuristic approach to quickly discard some moves which would most likely lead to a defeat while focusing on moves that would seem to be a good step towards a win!

Let’s consider the above scenario when investigating all the possible moves for this white pawn. Can the computer make a quick decision as to what would most likely be the best option?

Alternatively, a machine learning algorithm could play the game and record and update statistics after playing each card to progressively learn which criteria is more likely to win the round for each card in the deck. You can investigate how machine learning can be used in a game of Top Trumps by reading this blog post. Heuristic methods can be used when developing algorithms which try to understand what the user is saying, or asking for. For instance, by looking for words associations, an algorithm can narrow down the meaning of words especially when a word can have two different meanings:

e.g. When using Google search a user types: “Raspeberry Pi Hardware” We can deduct that in this case Raspberry has nothing to do with the piece of fruit, so there is no need to give results on healthy eating, cooking recipes or grocery stores…

However if the user searches for “Raspeberry Pie ingredients” , we can deduct that the user is searching for a recipe and is less likely to be interested in programming blogs or computer hardware online shops. Short Path Algorithms used by GPS systems and self-driving cars also use a heuristic approach to decide on the best route to go from A to Z. This is for instance the case for the A* Search algorithm which takes into consideration the distance as the crow flies between two nodes to decide which paths to explore first and hence more effectively find the shortest path between two nodes.

You can compare two different algorithms used to find the shortest route from two nodes of a graph:

• Dijkstra’s Shortest Path Algorithm (Without using a heuristic approach)
• A* Search Algorithm (Using a heuristic approach)

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Heuristics and Problem Solving

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• pp 1421–1424
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• Erik De Corte 2 ,
• Lieven Verschaffel 2 &
• Wim Van Dooren 2  

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Definitions

In a general sense heuristics are guidelines or methods for problem solving. Therefore, we will first define problem solving before presenting a specific definition of heuristics.

Problem Solving

In contrast to a routine task, a problem is a situation in which a person is trying to attain a goal but does not dispose of a ready-made solution or solution method. Problem solving involves then “cognitive processing directed at transforming the given situation into a goal situation when no obvious method of solution is available” (Mayer and Wittrock 2006 , p. 287). An implication is that a task can be a problem for one person, but not for someone else. For instance, the task “divide 120 marbles equally among 8 children” may be a problem for beginning elementary school children, but not for people who master the algorithm for long division, or know how to use a calculator.

The term “heuristic” originates from the Greek word heuriskein which means “to find.” Heuristics ...

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De Corte, E., Verschaffel, L., & Op’t Eynde, P. (2000). Self-regulation: a characteristic and a goal of mathematics education. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 687–726). San Diego, CA: Academic.

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De Corte, E., Verschaffel, L., & Masui, C. (2004). The CLIA-model: a framework for designing powerful learning environments for thinking and problem solving. European Journal of Psychology of Education, 19 , 365–384.

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Dignath, C., & Büttner, G. (2008). Components of fostering self-regulated learning among students. a meta-analysis on intervention studies at primary and secondary school level. Metacognition and Learning, 3 , 231–264.

Groner, R., Groner, M., & Bischof, W. F. (Eds.). (1983). Methods of heuristics . Hillsdale, NJ: Erlbaum.

Mayer, R. E., & Wittrock, M. C. (2006). Problem solving. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (pp. 287–303). New York: Macmillan.

Polya, G. (1945). How to solve it . Princeton, NJ: Princeton University Press.

Schoenfeld, A. H. (1985). Mathematical problem solving . New York: Academic.

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Dr. Erik De Corte, Prof. Dr. Lieven Verschaffel & Wim Van Dooren

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De Corte, E., Verschaffel, L., Van Dooren, W. (2012). Heuristics and Problem Solving. In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_420

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Problem-solving techniques that result in a quick and practical solution

What are Heuristics?

Heuristics are problem-solving techniques that result in a quick and practical solution. In contrast to business decisions that involve extensive analysis, heuristics are used in situations where a short-term solution is required.

Although heuristics may not result in the most optimal and ideal solution, it allows companies to speed up their decision-making process and achieve an adequate solution for the short term.

In situations where perfect solutions may be improbable, heuristics can be used to achieve imperfect but satisfactory decisions. Heuristics can also include mental shortcuts that help speed up the decision-making process.

• Heuristics are problem-solving techniques that result in a quick and practical solution.
• In situations where perfect solutions may be improbable, heuristics can be used to achieve imperfect but satisfactory decisions.
• Most heuristic methods involve using mental shortcuts to make decisions based on prior experiences.

Understanding Heuristics

When facing complex situations with limited time and resources, heuristics can help companies make quick decisions by using shortcuts and approximated calculations. Most heuristic methods involve using mental shortcuts to make decisions based on prior experiences.

Some of the most common fundamental heuristic methods include trial and error, historical data analysis, guesswork, and the process of elimination. Such methods typically involve easily accessible information that is not specific to the problem but is broadly applicable. It provides an opportunity to make imperfect decisions that can adequately address the problem in the short term.

Depending on the context, there may be several different heuristic methods, which correlate to the scope of the problem. They can include affect, representative, and availability heuristics.

Types of Heuristics

Affect Heuristics

Affect heuristics are based on positive and negative feelings that are associated with a certain stimulus. It typically involves quick, reactionary feelings that are based on prior beliefs. The theory of affect heuristics is that one’s emotional response to a stimulus can affect an individual’s decisions.

When people face little time to reflect and evaluate a situation carefully, they may base their decision on their immediate emotional reactions. Rather than conducting a cost-benefit analysis, affect heuristics focus on eliciting an automatic, reactionary response.

For example, it’s been shown that advertisements can influence consumers’ emotions and therefore affect their purchasing decisions. One of the most common examples is advertisements for products such as fast food. When fast-food companies run ads, they hope to elicit a positive emotional response that encourages you to view their products positively.

If individuals were to analyze the risks and benefits of consuming fast food carefully, they might decide that it is an unhealthy option. However, people rarely take the time to evaluate everything they see and often base their decisions on their automatic, emotional response. Fast-food ads rely on such a type of affect heuristic to generate a positive emotional response, which results in sales.

Availability Heuristics

Availability heuristics are judgments people make regarding the likelihood of an event based on information that comes to mind quickly. When people make decisions, they typically rely on prior knowledge of an event. As a result, we tend to overestimate the likelihood of an event occurring simply because it comes to mind quickly. Such mental shortcuts allow us to make decisions quickly, but they can also be inaccurate.

One example of the availability heuristic is stock prices, especially for newly public companies. Many investors tend to invest in new IPOs in the hopes that the stock price will increase significantly in the next few years. Rather than analyzing the company’s fundamentals, the investors remember IPOs that have become tremendously successful, such as Amazon or Apple.

Although it has been shown that most IPOs underperform, investors tend to overestimate the chances of landing a successful IPO based on prior examples that come to mind. It demonstrates a clear example of availability heuristics.

Representative Heuristics

Representative heuristics occur when we evaluate the probability of an event based on its similarity to another event. In general, people tend to overestimate the likelihood of an event occurring based on their perceived similarity with another event. When it happens, we tend to ignore the base rate, which is the actual probability of an event occurring, independent of its similarity to other events.

An example of the representative heuristic is product packaging, as consumers tend to associate quality products with their external packaging. If a generic brand packages its products in a way that resembles a well-known, high-quality product, then consumers will associate the generic product as having the same quality as the branded product.

Instead of evaluating the quality of the products, consumers are correlating the quality of the products based on the similarity in packaging.

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What is the difference between a heuristic and an algorithm?

• nomenclature

• 3 see en.wikipedia.org/wiki/Heuristic_algorithm –  Nick Dandoulakis Commented Feb 25, 2010 at 13:29
• 1 If you look at a heuristic algorithm as a sort of tree structure, I guess you could call it as a special purpose algorithm. –  James P. Commented Feb 25, 2010 at 13:35
• A heuristic is an algorithm that doesn't (provably) work. –  JeffE Commented Dec 4, 2016 at 21:43

12 Answers 12

An algorithm is the description of an automated solution to a problem . What the algorithm does is precisely defined. The solution could or could not be the best possible one but you know from the start what kind of result you will get. You implement the algorithm using some programming language to get (a part of) a program .

Now, some problems are hard and you may not be able to get an acceptable solution in an acceptable time. In such cases you often can get a not too bad solution much faster, by applying some arbitrary choices (educated guesses): that's a heuristic .

A heuristic is still a kind of an algorithm, but one that will not explore all possible states of the problem, or will begin by exploring the most likely ones.

Typical examples are from games. When writing a chess game program you could imagine trying every possible move at some depth level and applying some evaluation function to the board. A heuristic would exclude full branches that begin with obviously bad moves.

In some cases you're not searching for the best solution, but for any solution fitting some constraint. A good heuristic would help to find a solution in a short time, but may also fail to find any if the only solutions are in the states it chose not to try.

• 3 Another common use for heuristics is in virus detection, where you might not be sure a virus is there, but you can look for specific key attributes of a virus. –  TWA Commented Mar 17, 2010 at 15:59
• Heah thats true and for cracking programms –  streetparade Commented Mar 17, 2010 at 16:06
• 1 @kriss, So.. a heuristic is a kind of algorithm. –  Pacerier Commented Jun 2, 2016 at 22:30
• 1 @Pacerier: yes. It's an algorithm helping to navigate in the solution space of a particular problem. You can also see it as a strategy to modify an algorithm to make it practical (a meta-algorithm). It's still an algorithm, all methods are, and a Heuristic is definitely a method. –  kriss Commented Jun 3, 2016 at 9:30
• An algorithm is typically deterministic and proven to yield an optimal result
• A heuristic has no proof of correctness, often involves random elements, and may not yield optimal results.

Many problems for which no efficient algorithm to find an optimal solution is known have heuristic approaches that yield near-optimal results very quickly.

There are some overlaps: "genetic algorithms" is an accepted term, but strictly speaking, those are heuristics, not algorithms.

• 3 I would not say that an algorithm is proven to yield an optimal result: it depends on the algorithm with respect to which problem. –  nbro Commented Dec 31, 2016 at 20:33
• 1 Yielding an optimal result is not the essential quality of algorithms, it is preciseness i.e. the exact result whereas heuristic provides you with approximate results. –  Marina Dunst Commented Mar 18, 2017 at 11:05

Heuristic, in a nutshell is an "Educated guess". Wikipedia explains it nicely. At the end, a "general acceptance" method is taken as an optimal solution to the specified problem.

Heuristic is an adjective for experience-based techniques that help in problem solving, learning and discovery. A heuristic method is used to rapidly come to a solution that is hoped to be close to the best possible answer, or 'optimal solution'. Heuristics are "rules of thumb", educated guesses, intuitive judgments or simply common sense. A heuristic is a general way of solving a problem. Heuristics as a noun is another name for heuristic methods. In more precise terms, heuristics stand for strategies using readily accessible, though loosely applicable, information to control problem solving in human beings and machines.

While an algorithm is a method containing finite set of instructions used to solving a problem. The method has been proven mathematically or scientifically to work for the problem. There are formal methods and proofs.

Heuristic algorithm is an algorithm that is able to produce an acceptable solution to a problem in many practical scenarios, in the fashion of a general heuristic, but for which there is no formal proof of its correctness.

An algorithm is a self-contained step-by-step set of operations to be performed 4 , typically interpreted as a finite sequence of (computer or human) instructions to determine a solution to a problem such as: is there a path from A to B, or what is the smallest path between A and B. In the latter case, you could also be satisfied with a 'reasonably close' alternative solution.

There are certain categories of algorithms, of which the heuristic algorithm is one. Depending on the (proven) properties of the algorithm in this case, it falls into one of these three categories (note 1):

• Exact : the solution is proven to be an optimal (or exact solution) to the input problem
• Approximation : the deviation of the solution value is proven to be never further away from the optimal value than some pre-defined bound (for example, never more than 50% larger than the optimal value)
• Heuristic : the algorithm has not been proven to be optimal, nor within a pre-defined bound of the optimal solution

Notice that an approximation algorithm is also a heuristic, but with the stronger property that there is a proven bound to the solution (value) it outputs.

For some problems, noone has ever found an 'efficient' algorithm to compute the optimal solutions (note 2). One of those problems is the well-known Traveling Salesman Problem. Christophides' algorithm for the Traveling Salesman Problem, for example, used to be called a heuristic , as it was not proven that it was within 50% of the optimal solution. Since it has been proven, however, Christophides' algorithm is more accurately referred to as an approximation algorithm.

Due to restrictions on what computers can do, it is not always possible to efficiently find the best solution possible. If there is enough structure in a problem, there may be an efficient way to traverse the solution space, even though the solution space is huge (i.e. in the shortest path problem).

Heuristics are typically applied to improve the running time of algorithms, by adding 'expert information' or 'educated guesses' to guide the search direction. In practice, a heuristic may also be a sub-routine for an optimal algorithm, to determine where to look first .

(note 1) : Additionally, algorithms are characterised by whether they include random or non-deterministic elements. An algorithm that always executes the same way and produces the same answer, is called deterministic.

(note 2) : This is called the P vs NP problem, and problems that are classified as NP-complete and NP-hard are unlikely to have an 'efficient' algorithm. Note; as @Kriss mentioned in the comments, there are even 'worse' types of problems, which may need exponential time or space to compute.

There are several answers that answer part of the question. I deemed them less complete and not accurate enough, and decided not to edit the accepted answer made by @Kriss

• I believe your definition of the word algorithm is too restrictive. Does the use of the word sequence implies non-parallell ? Parallell algorithms are fine and even usual nowaday. What about solving a problem using a neural network ? Or a constraint propagation tool ? Algorithms ? Meta-algorithms ? –  kriss Commented Apr 19, 2016 at 22:05
• The reader get the feeling NP problems are the worse there is. That's untrue. There are truly hard problems needing truly bad algorithms like exponential ones or worse. NP are special because if we have a solution it is easy and fast to check it, while it is very hard to find it if we don't already have it. It's easy to check that we have correct instructions to get out of a labyrinth, it's much harder to find the exit. Thus NP are both easy and hard if we could try all possible solutions at the same time (non deterministically) solving it would be very simple... but we can't. –  kriss Commented Apr 19, 2016 at 22:15
• Thanks for the feedback! I've updated the phrasing slightly, and approached it differently. In my view, constraint propagation is a technique to approach something, but is not yet an algorithm that describes how to step-wise come to the solution described in constraint propagation. You are ofcourse correct about the classes of expspace and 'worse', I've added a note on that too. BTW: please write NP-Complete and/or NP-Hard fully, as the subset of NP also contains 'efficiently' solvable problems, which are not (conjectured to be) the same class. –  Joost Commented Apr 20, 2016 at 7:21
• Of course you are right I should have written NP-Complete. My bad. –  kriss Commented Apr 20, 2016 at 9:03
• It's way better than what one of my colleagues names it: NP-ness (which sounds just awful and kinda gross...) –  Joost Commented Apr 21, 2016 at 11:21

Actually I don't think that there is a lot in common between them. Some algorithm use heuristics in their logic (often to make fewer calculations or get faster results). Usually heuristics are used in the so called greedy algorithms.

Heuristics is some "knowledge" that we assume is good to use in order to get the best choice in our algorithm (when a choice should be taken). For example ... a heuristics in chess could be (always take the opponents' queen if you can, since you know this is the stronger figure). Heuristics do not guarantee you that will lead you to the correct answer, but (if the assumptions is correct) often get answer which are close to the best in much shorter time.

An Algorithm is a clearly defined set of instructions to solve a problem, Heuristics involve utilising an approach of learning and discovery to reach a solution.

So, if you know how to solve a problem then use an algorithm. If you need to develop a solution then it's heuristics.

• This should be the accepted answer. Should be stressed that both the programmer and the (complex) algorithm can use the heuristics approach. –  G M Commented Apr 27, 2022 at 7:12

Heuristics are algorithms, so in that sense there is none, however, heuristics take a 'guess' approach to problem solving, yielding a 'good enough' answer, rather than finding a 'best possible' solution.

A good example is where you have a very hard (read NP-complete) problem you want a solution for but don't have the time to arrive to it, so have to use a good enough solution based on a heuristic algorithm, such as finding a solution to a travelling salesman problem using a genetic algorithm.

Algorithm is a sequence of some operations that given an input computes something (a function) and outputs a result.

Algorithm may yield an exact or approximate values.

It also may compute a random value that is with high probability close to the exact value.

A heuristic algorithm uses some insight on input values and computes not exact value (but may be close to optimal). In some special cases, heuristic can find exact solution.

A heuristic is usually an optimization or a strategy that usually provides a good enough answer, but not always and rarely the best answer. For example, if you were to solve the traveling salesman problem with brute force, discarding a partial solution once its cost exceeds that of the current best solution is a heuristic: sometimes it helps, other times it doesn't, and it definitely doesn't improve the theoretical (big-oh notation) run time of the algorithm

I think Heuristic is more of a constraint used in Learning Based Model in Artificial Intelligent since the future solution states are difficult to predict.

But then my doubt after reading above answers is "How would Heuristic can be successfully applied using Stochastic Optimization Techniques? or can they function as full fledged algorithms when used with Stochastic Optimization?"

http://en.wikipedia.org/wiki/Stochastic_optimization

• oops!! spelling mistake it should be "Artificial Intelligence" –  A_tanA Commented Jan 26, 2011 at 18:06

One of the best explanations I have read comes from the great book Code Complete , which I now quote:

A heuristic is a technique that helps you look for an answer. Its results are subject to chance because a heuristic tells you only how to look, not what to find. It doesn’t tell you how to get directly from point A to point B; it might not even know where point A and point B are. In effect, a heuristic is an algorithm in a clown suit. It’s less predict- able, it’s more fun, and it comes without a 30-day, money-back guarantee. Here is an algorithm for driving to someone’s house: Take Highway 167 south to Puy-allup. Take the South Hill Mall exit and drive 4.5 miles up the hill. Turn right at the light by the grocery store, and then take the first left. Turn into the driveway of the large tan house on the left, at 714 North Cedar. Here’s a heuristic for getting to someone’s house: Find the last letter we mailed you. Drive to the town in the return address. When you get to town, ask someone where our house is. Everyone knows us—someone will be glad to help you. If you can’t find anyone, call us from a public phone, and we’ll come get you. The difference between an algorithm and a heuristic is subtle, and the two terms over-lap somewhat. For the purposes of this book, the main difference between the two is the level of indirection from the solution. An algorithm gives you the instructions directly. A heuristic tells you how to discover the instructions for yourself, or at least where to look for them.

• Stating that there exists a difference between an algorithm and a heuristic is like stating that there is a difference between a bird and a chicken. Heuristics are a type of algorithm. –  Joost Commented Jan 21, 2016 at 8:08

They find a solution suboptimally without any guarantee as to the quality of solution found, it is obvious that it makes sense to the development of heuristics only polynomial. The application of these methods is suitable to solve real world problems or large problems so awkward from the computational point of view that for them there is not even an algorithm capable of finding an approximate solution in polynomial time.

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Heuristic Function In AI

Heuristic functions play a critical role in artificial intelligence (AI), particularly in search algorithms used for problem-solving. These functions estimate the cost to reach the goal from a given state, helping to make informed decisions that optimize the search process.

In this article, we will explore what heuristic functions are, their role in search algorithms, various types of heuristic search algorithms, and their applications in AI.

Table of Content

What are Heuristic Functions?

Search algorithm, heuristic search algorithm in ai, a* algorithm, greedy best-first search, hill-climbing algorithm, role of heuristic functions in ai, common problem types for heuristic functions, path finding with heuristic functions, step 1: define the a* algorithm, step 2: define the visualization function, step 3: define the grid and start/goal positions, step 4: run the a* algorithm and visualize the path, complete code, applications of heuristic functions in ai.

Heuristic functions are strategies or methods that guide the search process in AI algorithms by providing estimates of the most promising path to a solution. They are often used in scenarios where finding an exact solution is computationally infeasible. Instead, heuristics provide a practical approach by narrowing down the search space, leading to faster and more efficient problem-solving.

Heuristic functions transform complex problems into more manageable subproblems by providing estimates that guide the search process. This approach is particularly effective in AI planning, where the goal is to sequence actions that lead to a desired outcome.

Search algorithms are fundamental to AI, enabling systems to navigate through problem spaces to find solutions. These algorithms can be classified into uninformed (blind) and informed (heuristic) searches. Uninformed search algorithms, such as breadth-first and depth-first search, do not have additional information about the goal state beyond the problem definition. In contrast, informed search algorithms use heuristic functions to estimate the cost of reaching the goal, significantly improving search efficiency.

Heuristic search algorithms leverage heuristic functions to make more intelligent decisions during the search process. Some common heuristic search algorithms include:

The A* algorithm is one of the most widely used heuristic search algorithms. It uses both the actual cost from the start node to the current node (g(n)) and the estimated cost from the current node to the goal (h(n)). The total estimated cost (f(n)) is the sum of these two values:

[Tex]f(n) = g(n) +h(n)[/Tex]

The Greedy Best-First Search algorithm selects the path that appears to be the most promising based on the heuristic function alone. It prioritizes nodes with the lowest heuristic cost (h(n)), but it does not necessarily guarantee the shortest path to the goal.

The Hill-Climbing algorithm is a local search algorithm that continuously moves towards the neighbor with the lowest heuristic cost. It resembles climbing uphill towards the goal but can get stuck in local optima.

Heuristic functions are essential in AI for several reasons:

• Efficiency: They reduce the search space, leading to faster solution times.
• Guidance: They provide a sense of direction in large problem spaces, avoiding unnecessary exploration.
• Practicality: They offer practical solutions in situations where exact methods are computationally prohibitive.

Heuristic functions are particularly useful in various problem types, including:

• Pathfinding Problems: Pathfinding problems, such as navigating a maze or finding the shortest route on a map, benefit greatly from heuristic functions that estimate the distance to the goal.
• Constraint Satisfaction Problems: In constraint satisfaction problems, such as scheduling and puzzle-solving, heuristics help in selecting the most promising variables and values to explore.
• Optimization Problems: Optimization problems, like the traveling salesman problem, use heuristics to find near-optimal solutions within a reasonable time frame.

This step involves defining the A* algorithm, which finds the shortest path from the start to the goal using a heuristic function. The heuristic function used here is the Manhattan distance. It returns the path from the start to the goal if one is found.

import heapq def a_star(grid, start, goal): def heuristic(a, b): return abs(a[0] - b[0]) + abs(a[1] - b[1]) directions = [(0, 1), (1, 0), (0, -1), (-1, 0)] open_list = [] heapq.heappush(open_list, (0, start)) g_score = {start: 0} f_score = {start: heuristic(start, goal)} came_from = {} while open_list: _, current = heapq.heappop(open_list) if current == goal: path = [] while current in came_from: path.append(current) current = came_from[current] path.append(start) path.reverse() return path for direction in directions: neighbor = (current[0] + direction[0], current[1] + direction[1]) if 0 <= neighbor[0] < len(grid) and 0 <= neighbor[1] < len(grid[0]) and grid[neighbor[0]][neighbor[1]] == 0: tentative_g_score = g_score[current] + 1 if neighbor not in g_score or tentative_g_score < g_score[neighbor]: came_from[neighbor] = current g_score[neighbor] = tentative_g_score f_score[neighbor] = tentative_g_score + heuristic(neighbor, goal) heapq.heappush(open_list, (f_score[neighbor], neighbor)) return None

This step sets up the A* algorithm by defining the heuristic function, the movement directions, and the data structures for the open list and cost tracking. It returns the path from the start to the goal if one is found.

This step involves defining a function to visualize the path found by the A* algorithm on a grid using matplotlib . The function visualizes the grid and the path found by the A* algorithm. It uses different colors to represent empty cells, obstacles, the path, the start, and the goal.

import matplotlib.pyplot as plt import numpy as np def visualize_path(grid, path, start, goal): grid = np.array(grid) for (x, y) in path: grid[x, y] = 2 # Mark the path grid[start[0], start[1]] = 3 # Mark the start grid[goal[0], goal[1]] = 4 # Mark the goal cmap = plt.cm.get_cmap('Accent', 5) bounds = [0, 1, 2, 3, 4] norm = plt.Normalize(vmin=0, vmax=4) plt.imshow(grid, cmap=cmap, norm=norm) plt.colorbar(ticks=[0, 1, 2, 3, 4], format=plt.FuncFormatter(lambda val, loc: ['Empty', 'Obstacle', 'Path', 'Start', 'Goal'][int(val)])) plt.title("A* Pathfinding Visualization") plt.show()

This step involves defining a larger grid for the pathfinding problem and specifying the start and goal positions. This step defines a 10×10 grid with some cells marked as obstacles (value 1 ). The start position is set to the top-left corner (0, 0) and the goal position to the bottom-right corner (9, 9) .

grid = [ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 1, 1, 1, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 0, 1, 0], [0, 1, 1, 1, 1, 1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 1, 1, 1, 1, 1, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0] ] start = (0, 0) goal = (9, 9)

The final step runs the A* algorithm on the defined grid and visualizes the path if one is found. If no path is found, it prints a message indicating that no path is available.

path = a_star(grid, start, goal) if path: print("Path found:", path) visualize_path(grid, path, start, goal) else: print("No path found")

import heapq import matplotlib.pyplot as plt import numpy as np # Define the A* algorithm def a_star ( grid , start , goal ): def heuristic ( a , b ): return abs ( a [ 0 ] - b [ 0 ]) + abs ( a [ 1 ] - b [ 1 ]) directions = [( 0 , 1 ), ( 1 , 0 ), ( 0 , - 1 ), ( - 1 , 0 )] open_list = [] heapq . heappush ( open_list , ( 0 , start )) g_score = { start : 0 } f_score = { start : heuristic ( start , goal )} came_from = {} while open_list : _ , current = heapq . heappop ( open_list ) if current == goal : path = [] while current in came_from : path . append ( current ) current = came_from [ current ] path . append ( start ) path . reverse () return path for direction in directions : neighbor = ( current [ 0 ] + direction [ 0 ], current [ 1 ] + direction [ 1 ]) if 0 <= neighbor [ 0 ] < len ( grid ) and 0 <= neighbor [ 1 ] < len ( grid [ 0 ]) and grid [ neighbor [ 0 ]][ neighbor [ 1 ]] == 0 : tentative_g_score = g_score [ current ] + 1 if neighbor not in g_score or tentative_g_score < g_score [ neighbor ]: came_from [ neighbor ] = current g_score [ neighbor ] = tentative_g_score f_score [ neighbor ] = tentative_g_score + heuristic ( neighbor , goal ) heapq . heappush ( open_list , ( f_score [ neighbor ], neighbor )) return None # Visualization function with standard colors def visualize_path ( grid , path , start , goal ): grid = np . array ( grid ) for ( x , y ) in path : grid [ x , y ] = 2 # Mark the path grid [ start [ 0 ], start [ 1 ]] = 3 # Mark the start grid [ goal [ 0 ], goal [ 1 ]] = 4 # Mark the goal # Define a custom color map cmap = plt . cm . get_cmap ( 'Accent' , 5 ) bounds = [ 0 , 1 , 2 , 3 , 4 ] norm = plt . Normalize ( vmin = 0 , vmax = 4 ) plt . imshow ( grid , cmap = cmap , norm = norm ) plt . colorbar ( ticks = [ 0 , 1 , 2 , 3 , 4 ], format = plt . FuncFormatter ( lambda val , loc : [ 'Empty' , 'Obstacle' , 'Path' , 'Start' , 'Goal' ][ int ( val )])) plt . title ( "A* Pathfinding Visualization" ) plt . show () # Example grid: 0 - walkable, 1 - obstacle grid = [ [ 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ], [ 0 , 1 , 1 , 1 , 1 , 0 , 1 , 1 , 1 , 0 ], [ 0 , 0 , 0 , 0 , 1 , 0 , 1 , 0 , 0 , 0 ], [ 0 , 1 , 0 , 0 , 1 , 0 , 1 , 0 , 1 , 0 ], [ 0 , 1 , 0 , 0 , 0 , 0 , 1 , 0 , 1 , 0 ], [ 0 , 1 , 1 , 1 , 1 , 1 , 1 , 0 , 1 , 0 ], [ 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 ], [ 0 , 1 , 0 , 1 , 1 , 1 , 1 , 1 , 1 , 0 ], [ 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ], [ 0 , 0 , 0 , 1 , 1 , 1 , 1 , 1 , 1 , 0 ] ] # Define start and goal positions start = ( 0 , 0 ) goal = ( 9 , 9 ) # Run the A* algorithm path = a_star ( grid , start , goal ) if path : print ( "Path found:" , path ) visualize_path ( grid , path , start , goal ) else : print ( "No path found" )

Path found: [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 9), (2, 9), (3, 9), (4, 9), (5, 9), (6, 9), (7, 9), (8, 9), (9, 9)]

A* Path Finding Visualization

Heuristic functions find applications in various AI domains. Here are three notable examples:

• Game AI: In games like chess and tic-tac-toe, heuristic functions evaluate the board’s state, guiding the AI to make strategic moves that maximize its chances of winning.
• Robotics: Robotic path planning uses heuristics to navigate environments efficiently, avoiding obstacles and reaching target locations.
• Natural Language Processing (NLP): In NLP, heuristics help in parsing sentences, understanding context, and generating coherent text responses.

Heuristic functions are a powerful tool in AI, enhancing the efficiency and effectiveness of search algorithms. By providing estimates that guide the search process, heuristics enable practical solutions to complex problems across various domains. From game AI to robotics and natural language processing, heuristic functions continue to play a pivotal role in advancing AI capabilities.

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Enhancing service quality of on-demand transportation systems using a hybrid approach with customized heuristics.

1. Introduction

• A customized insertion heuristic is specifically designed to define an initial feasible vehicle’s plan with good quality. The use of this heuristic is claimed to be suitable for real-life on-demand transportation problems.
• A new tabu search method is introduced, which incorporates a novel customized neighborhood strategy. This neighborhood strategy is specifically designed to enhance both the operational costs and the service quality.
• Specific mutation operators are designed to address the characteristics and requirements of the problem at hand. These operators are dynamically exchanged to contribute to the discovery of high-quality solutions with improved service quality criteria.
• A specific crossover operator is proposed, which is carefully designed to inherit and preserve the advantageous service quality features discovered during the search. This contributes to the generation of new solutions that not only maintain the desired service quality features but also introduce variations that can potentially lead to further improvements.

2. Literature Review

3. the customer-oriented darp.

• A request is served exactly once by one vehicle.
• The precedence between pickup and delivery stations is ensured.
• The number of pickups is equal to the number of deliveries in a vehicle tour.
• It is the same vehicle that ensures the pickup and delivery of a request.
• The depot is the departure and arrival station of all the tours.
• The capacity of a vehicle is respected when charging and discharging passengers.
• The maximal total tour duration is a time limit that has to be respected by all the vehicles.

3.1. The Problem Formulation

3.2. a time windows application on a realistic case, 4. the evolutionary tabu search, 4.1. overview of the evolutionary tabu search algorithm, 4.2. the insertion heuristic.

4.3. Repair Operator

4.4. the mutation operators, 4.4.1. the interruption operator, 4.4.2. the swap operator, 4.5. the crossover operator.

• Positioning: choose two positions on the two routes, linked to the first pickup nodes in the routes that have similar or close beginnings of service.
• Mapping: temporarily remove the remaining sequences of requests from routes outside the selected cut points in each parent.
• Switching: exchange the two parts between the cut positions between the two routes, respecting the same positions in the time schedule.
• Filling: copy the deleted requests into the child, trying to maintain their initial positions from the parent without introducing redundancy of nodes.

4.6. The Tabu Search Method

5. computational experiments, 5.1. benchmark instances.

• The locations are marked by the real distances between them based on the GPS positions of French cities.
• The transportation network density is not the same for all the instances.
• The customers are distributed over a large area, varying according to the instances.
• Time windows are separately defined on both the pickup and destination locations. These time windows are of different sizes according to the customers.
• The maximum riding time for each customer depends on the customer and the distance they have to travel.
• The number of passengers in a location may be greater than 1 up to 4.
• All the vehicles have the same average speed equal to 1.33 km per minute.
• The maximal vehicle tour duration is equal to 480.
• The maximal capacity of the vehicles is equal to 8.

5.2. The Relevance of Customer-Oriented Time Windows in the Resolution by ETS

5.3. results obtained with the two evolutionary techniques on the benchmark problems, 6. statistical analysis of the results provided for the problem, 6.1. tests of differences, 6.2. pairwise comparisons, 6.3. interpretation of the statistical results, 7. discussion, 8. conclusions, author contributions, data availability statement, acknowledgments, conflicts of interest.

• Cordeau, J.F.; Laporte, G. A tabu search heuristic for the static multi-vehicle dial-a-ride problem. Transp. Res. Part Methodol. 2003 , 37 , 579–594. [ Google Scholar ] [ CrossRef ]
• Healy, P.; Moll, R. A new extension of local search applied to the dial-a-ride problem. Eur. J. Oper. Res. 1995 , 83 , 83–104. [ Google Scholar ] [ CrossRef ]
• Molenbruch, Y.; Braekers, K.; Caris, A. Typology and literature review for dial-a-ride problems. Ann. Oper. Res. 2017 , 259 , 295–325. [ Google Scholar ] [ CrossRef ]
• Chassaing, M.; Duhamel, C.; Lacomme, P. An ELS-based approach with dynamic probabilities management in local search for the Dial-A-Ride Problem. Eng. Appl. Artif. Intell. 2016 , 48 , 119–133. [ Google Scholar ] [ CrossRef ]
• Parragh, S.N. Introducing heterogeneous users and vehicles into models and algorithms for the dial-a-ride problem. Transp. Res. Part Emerg. Technol. 2011 , 19 , 912–930. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Braekers, K.; Kovacs, A.A. A multi-period dial-a-ride problem with driver consistency. Transp. Res. Part Methodol. 2016 , 94 , 355–377. [ Google Scholar ] [ CrossRef ]
• Masmoudi, M.A.; Braekers, K.; Masmoudi, M.; Dammak, A. A hybrid genetic algorithm for the heterogeneous dial-a-ride problem. Comput. Oper. Res. 2017 , 81 , 1–13. [ Google Scholar ] [ CrossRef ]
• Agrawal, V.; Lightner, C.; Lightner-Laws, C.; Wagner, N. A bi-criteria evolutionary algorithm for a constrained multi-depot vehicle routing problem. Soft Comput. 2017 , 21 , 5159–5178. [ Google Scholar ] [ CrossRef ]
• Bahadori-Chinibelagh, S.; Fathollahi-Fard, A.M.; Hajiaghaei-Keshteli, M. Two constructive algorithms to address a multi-depot home healthcare routing problem. IETE J. Res. 2019 , 68 , 1108–1114. [ Google Scholar ] [ CrossRef ]
• Masson, R.; Lehuédé, F.; Péton, O. The dial-a-ride problem with transfers. Comput. Oper. Res. 2014 , 41 , 12–23. [ Google Scholar ] [ CrossRef ]
• Molenbruch, Y.; Braekers, K.; Caris, A. Benefits of horizontal cooperation in dial-a-ride services. Transp. Res. Part Logist. Transp. Rev. 2017 , 107 , 97–119. [ Google Scholar ] [ CrossRef ]
• Nasri, S.; Bouziri, H.; Aggoune-Mtalaa, W. An evolutionary descent algorithm for customer-oriented mobility-on-demand problems. Sustainability 2022 , 14 , 3020. [ Google Scholar ] [ CrossRef ]
• Melachrinoudis, E.; Min, H. A tabu search heuristic for solving the multi-depot, multi-vehicle, double request dial-a-ride problem faced by a healthcare organisation. Int. J. Oper. Res. 2011 , 10 , 214–239. [ Google Scholar ] [ CrossRef ]
• Paquette, J.; Cordeau, J.F.; Laporte, G.; Pascoal, M.M. Combining multicriteria analysis and tabu search for dial-a-ride problems. Transp. Res. Part Methodol. 2013 , 52 , 1–16. [ Google Scholar ] [ CrossRef ]
• Torgal, M.; Dias, T.G.; Fontes, T. A multi objective approach for DRT service using tabu search. Transp. Res. Procedia 2021 , 52 , 91–98. [ Google Scholar ] [ CrossRef ]
• Carotenuto, P.; Paradisi, L.; Storchi, G. A flexible transport service for passengers. Transp. Res. Procedia 2014 , 3 , 442–451. [ Google Scholar ] [ CrossRef ]
• Viana, R.J.; Santos, A.G.; Martins, F.V.; Wanner, E.F. Optimization of a demand responsive transport service using multi-objective evolutionary algorithms. In Proceedings of the Genetic and Evolutionary Computation Conference Companion, Prague, Czech Republic, 13–17 July 2019; pp. 2064–2067. [ Google Scholar ]
• Belhaiza, S. A hybrid adaptive large neighborhood heuristic for a real-life dial-a-ride problem. Algorithms 2019 , 12 , 39. [ Google Scholar ] [ CrossRef ]
• Chu, J.C.Y.; Chen, A.Y.; Shih, H.H. Stochastic programming model for integrating bus network design and dial-a-ride scheduling. Transp. Lett. 2022 , 14 , 245–257. [ Google Scholar ] [ CrossRef ]
• Nguyen, J.; Powers, S.T.; Urquhart, N.; Farrenkopf, T.; Guckert, M. Modelling the impact of individual preferences on traffic policies. Comput. Sci. 2022 , 3 , 365. [ Google Scholar ] [ CrossRef ]
• Detti, P.; Papalini, F.; de Lara, G.Z.M. A multi-depot dial-a-ride problem with heterogeneous vehicles and compatibility constraints in healthcare. Omega 2017 , 70 , 1–14. [ Google Scholar ] [ CrossRef ]
• Zhang, Z.; Liu, M.; Lim, A. A memetic algorithm for the patient transportation problem. Omega 2015 , 54 , 60–71. [ Google Scholar ] [ CrossRef ]
• Braekers, K.; Caris, A.; Janssens, G.K. Exact and meta-heuristic approach for a general heterogeneous dial-a-ride problem with multiple depots. Transp. Res. Part Methodol. 2014 , 67 , 166–186. [ Google Scholar ] [ CrossRef ]
• Nasri, S.; Bouziri, H.; Aggoune-Mtalaa, W. Customer-Oriented Dial-A-Ride Problems: A Survey on Relevant Variants, Solution Approaches and Applications. In Emerging Trends in ICT for Sustainable Development ; Springer: Berlin/Heidelberg, Germany, 2021; pp. 111–119. [ Google Scholar ]
• Wong, K.I.; Han, A.; Yuen, C. On dynamic demand responsive transport services with degree of dynamism. Transp. Transp. Sci. 2014 , 10 , 55–73. [ Google Scholar ] [ CrossRef ]
• Carotenuto, P.; Martis, F. A double dynamic fast algorithm to solve multi-vehicle Dial a Ride Problem. Transp. Res. Procedia 2017 , 27 , 632–639. [ Google Scholar ] [ CrossRef ]
• Marković, N.; Nair, R.; Schonfeld, P.; Miller-Hooks, E.; Mohebbi, M. Optimizing dial-a-ride services in Maryland: Benefits of computerized routing and scheduling. Transp. Res. Part Emerg. Technol. 2015 , 55 , 156–165. [ Google Scholar ] [ CrossRef ]
• Hu, T.Y.; Chang, C.P. A revised branch-and-price algorithm for dial-a-ride problems with the consideration of time-dependent travel cost. J. Adv. Transp. 2015 , 49 , 700–723. [ Google Scholar ] [ CrossRef ]
• Ho, S.; Nagavarapu, S.C.; Pandi, R.R.; Dauwels, J. An improved tabu search heuristic for static dial-a-ride problem. arXiv 2018 , arXiv:1801.09547. [ Google Scholar ]
• Molenbruch, Y.; Braekers, K.; Caris, A. Operational effects of service level variations for the dial-a-ride problem. Cent. Eur. J. Oper. Res. 2017 , 25 , 71–90. [ Google Scholar ] [ CrossRef ]
• Paquette, J.; Cordeau, J.F.; Laporte, G. Quality of service in dial-a-ride operations. Comput. Ind. Eng. 2009 , 56 , 1721–1734. [ Google Scholar ] [ CrossRef ]
• Paquette, J.; Bellavance, F.; Cordeau, J.F.; Laporte, G. Measuring quality of service in dial-a-ride operations: The case of a Canadian city. Transportation 2012 , 39 , 539–564. [ Google Scholar ] [ CrossRef ]
• Parragh, S.N.; Pinho de Sousa, J.; Almada-Lobo, B. The dial-a-ride problem with split requests and profits. Transp. Sci. 2015 , 49 , 311–334. [ Google Scholar ] [ CrossRef ]
• Glover, F.; Kelly, J.P.; Laguna, M. Genetic algorithms and tabu search: Hybrids for optimization. Comput. Oper. Res. 1995 , 22 , 111–134. [ Google Scholar ] [ CrossRef ]
• Nasri, S.; Bouziri, H. Improving total transit time in dial-a-ride problem with customers-dependent criteria. In Proceedings of the IEEE/ACS 14th International Conference on Computer Systems and Applications (AICCSA), Hammamet, Tunisia, 30 October–3 November 2017; pp. 1141–1148. [ Google Scholar ]
• Cheikh-Graiet, S.B.; Dotoli, M.; Hammadi, S. A Tabu Search based metaheuristic for dynamic carpooling optimization. Comput. Ind. Eng. 2020 , 140 , 106217. [ Google Scholar ] [ CrossRef ]
• Gmira, M.; Gendreau, M.; Lodi, A.; Potvin, J.Y. Tabu Search for the Time-Dependent Vehicle Routing Problem with Time Windows on a Road Network. Eur. J. Oper. Res. 2020 , 288 , 129–140. [ Google Scholar ] [ CrossRef ]
• Aziz, H.A.; Garikapati, V.; Rodriguez, T.K.; Zhu, L.; Sun, B.; Young, S.E.; Chen, Y. An optimization-based planning tool for on-demand mobility service operations. Int. J. Sustain. Transp. 2022 , 16 , 45–56. [ Google Scholar ] [ CrossRef ]
• Chen, Z.G.; Zhan, Z.H.; Kwong, S.; Zhang, J. Evolutionary computation for intelligent transportation in smart cities: A survey. IEEE Comput. Intell. Mag. 2022 , 17 , 83–102. [ Google Scholar ] [ CrossRef ]
• Cubillos, C.; Urra, E.; Rodríguez, N. Application of genetic algorithms for the DARPTW problem. Int. J. Comput. Commun. Control. 2009 , 4 , 127–136. [ Google Scholar ] [ CrossRef ]
• Rekiek, B.; Delchambre, A.; Saleh, H.A. Handicapped person transportation: An application of the grouping genetic algorithm. Eng. Appl. Artif. Intell. 2006 , 19 , 511–520. [ Google Scholar ] [ CrossRef ]
• Jorgensen, R.M.; Larsen, J.; Bergvinsdottir, K.B. Solving the dial-a-ride problem using genetic algorithms. J. Oper. Res. Soc. 2007 , 58 , 1321–1331. [ Google Scholar ] [ CrossRef ]
• Sun, B.; Wei, M.; Yang, C.; Xu, Z.; Wang, H. Personalised and coordinated demand-responsive feeder transit service design: A genetic algorithms approach. Future Internet 2018 , 10 , 61. [ Google Scholar ] [ CrossRef ]
• Nasri, S.; Bouziri, H. Towards a fair mobility: An evolutionary algorithm for customers-dependent transport on demand problems. In Proceedings of the 2019 International Conference on Internet of Things, Embedded Systems and Communications (IINTEC), Tunis, Tunisia, 20–22 December 2019; pp. 34–40. [ Google Scholar ]
• Molenbruch, Y.; Braekers, K.; Hirsch, P.; Oberscheider, M. Analyzing the benefits of an integrated mobility system using a matheuristic routing algorithm. Eur. J. Oper. Res. 2021 , 290 , 81–98. [ Google Scholar ] [ CrossRef ]
• Chevrier, R.; Liefooghe, A.; Jourdan, L.; Dhaenens, C. Solving a dial-a-ride problem with a hybrid evolutionary multi-objective approach: Application to demand responsive transport. Appl. Soft Comput. 2012 , 12 , 1247–1258. [ Google Scholar ] [ CrossRef ]
• Ghoseiri, K.; Ghannadpour, S.F. Multi-objective vehicle routing problem with time windows using goal programming and genetic algorithm. Appl. Soft Comput. 2010 , 10 , 1096–1107. [ Google Scholar ] [ CrossRef ]
• Li, J.; Tomita, K.; Kamimura, A. A Novel Genetic Algorithm for a Multi-Vehicle Dial-a-Ride Problem. In Proceedings of the 2022 International Conference on Advanced Robotics and Mechatronics (ICARM), Guilin, China, 3–5 July 2022; pp. 682–689. [ Google Scholar ]
• Perera, T.; Prakash, A.; Gamage, C.N.; Srikanthan, T. Hybrid genetic algorithm for an on-demand first mile transit system using electric vehicles. In Proceedings of the International Conference on Computational Science, Las Vegas, NV, USA, 12–14 December 2018; Springer: Berlin/Heidelberg, Germany, 2018; pp. 98–113. [ Google Scholar ]
• Godart, A.; Manier, H.; Bloch, C.; Manier, M.A. Hybrid metaheuristic for the Pickup and Delivery Problem designed for passengers and goods transportation. IFAC-PapersOnLine 2019 , 52 , 2584–2589. [ Google Scholar ] [ CrossRef ]
• Chassaing. Instances of Chassaing. 2020. Available online: http://fc.isima.fr/~lacomme/Maxime/ (accessed on 19 July 2020).
• LaTorre, A.; Molina, D.; Osaba, E.; Poyatos, J.; Del Ser, J.; Herrera, F. A prescription of methodological guidelines for comparing bio-inspired optimization algorithms. Swarm Evol. Comput. 2021 , 67 , 100973. [ Google Scholar ] [ CrossRef ]
• Shaphiro, S.; Wilk, M. An analysis of variance test for normality. Biometrika 1965 , 52 , 591–611. [ Google Scholar ] [ CrossRef ]
• Razali, N.M.; Wah, Y.B. Power comparisons of shapiro-wilk, kolmogorov-smirnov, lilliefors and anderson-darling tests. J. Stat. Model. Anal. 2011 , 2 , 21–33. [ Google Scholar ]

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Nasri, S.; Bouziri, H.; Mtalaa, W.A. Enhancing Service Quality of On-Demand Transportation Systems Using a Hybrid Approach with Customized Heuristics. Smart Cities 2024 , 7 , 1551-1575. https://doi.org/10.3390/smartcities7040063

Nasri S, Bouziri H, Mtalaa WA. Enhancing Service Quality of On-Demand Transportation Systems Using a Hybrid Approach with Customized Heuristics. Smart Cities . 2024; 7(4):1551-1575. https://doi.org/10.3390/smartcities7040063

Nasri, Sonia, Hend Bouziri, and Wassila Aggoune Mtalaa. 2024. "Enhancing Service Quality of On-Demand Transportation Systems Using a Hybrid Approach with Customized Heuristics" Smart Cities 7, no. 4: 1551-1575. https://doi.org/10.3390/smartcities7040063

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