The Traveling Salesman Problem
Optimization with the Attractor-Based Search System
- © 2024
School of Management, University of Michigan, Flint, USA
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- Provides a complete understanding of the attractor concept in heuristic local searches
- Presents a new search paradigm for solving a NP-complete combinatorial problem
- Introduces the use of the attractor concept in dynamical systems theory to reduce the search space for TSP
Part of the book series: Synthesis Lectures on Operations Research and Applications (SLORA)
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Table of contents (8 chapters)
Front matter, introduction, traveling salesman problem, the attractor-based search system, analysis of the attractor-based search system, solving multi-objective traveling salesman problem, solving probabilistic traveling salesman problem, solving dynamic traveling salesman problem, solving dynamic multi-objective traveling salesman problem.
- Combinatorial Optimization
- Heuristic Local Search
- Computing Theory and Algorithms
- Operations Research
- Global Optimization
- Design and Analysis of Algorithms
- P Versus NP Problem
- Computational Complexity
- Traveling Salesman Problem (TSP)
- Dynamical Systems
- NP-complete Combinatorial Problem
About this book
This book presents a new search paradigm for solving the Traveling Salesman Problem (TSP). The intrinsic difficulty of the TSP is associated with the combinatorial explosion of potential solutions in the solution space. The author introduces the idea of using the attractor concept in dynamical systems theory to reduce the search space for exhaustive search for the TSP. Numerous examples are used to describe how to use this new search algorithm to solve the TSP and its variants including: multi-objective TSP, dynamic TSP, and probabilistic TSP. This book is intended for readers in the field of optimization research and application.
Authors and Affiliations
About the author.
Weiqi Li, PhD, is an Associate Professor at the University of Michigan – Flint and an affiliated faculty in the Michigan Institute for Data Science at the University of Michigan. His research interests include combinatorial optimization, heuristics, supply chain management, and artificial intelligence. Specifically, Dr. Li’s research focuses on new search methods to solve the traveling salesman problem (TSP).
Bibliographic Information
Book Title : The Traveling Salesman Problem
Book Subtitle : Optimization with the Attractor-Based Search System
Authors : Weiqi Li
Series Title : Synthesis Lectures on Operations Research and Applications
DOI : https://doi.org/10.1007/978-3-031-35719-0
Publisher : Springer Cham
eBook Packages : Synthesis Collection of Technology (R0)
Copyright Information : The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Hardcover ISBN : 978-3-031-35718-3 Published: 09 July 2023
Softcover ISBN : 978-3-031-35721-3 Due: 09 August 2023
eBook ISBN : 978-3-031-35719-0 Published: 08 July 2023
Series ISSN : 2770-6303
Series E-ISSN : 2770-6311
Edition Number : 1
Number of Pages : XIV, 141
Number of Illustrations : 58 b/w illustrations, 8 illustrations in colour
Topics : Operations Research, Management Science , Optimization , Applications of Mathematics , Complexity , Dynamical Systems and Ergodic Theory , Vibration, Dynamical Systems, Control
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The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest formulation, such as planning, logistics, and the manufacture of microchips; and can be slightly modified to appear as a sub-problem in many areas, such as DNA sequencing. In this paper, a study on parallelization of the Brute Force approach (under several paradigms) of the Travelling Salesman Problem is presented. Detailed timing studies for the serial and various parallel implementations of the Travelling Salesman Problem have also been illustrated.
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The Travelling Salesman Problem (TSP) [3] and Vehicle Routing Problem (VRP) [4][5][6] can be used to represent the routing problem in Operational Research [7]. The research on TSP and VRP problems ...
The traveling salesman problem (TSP) is one of the most studied problems in computational intelligence and operations research. Since its first formulation, a myriad of works has been published proposing different alternatives for its solution. ... Additional valuable related research can be found in papers such as Liu and Zhang (2018), Xu et ...
The generalized traveling salesman problem (GTSP) is an extension of the classical traveling salesman problem (TSP) and it is among the most researched combinatorial optimization problems due to its theoretical properties, complexity aspects and real-life applications in various areas: location-routing problems, material flow design problem, distribution of medical supplies, urban waste ...
PDF | On May 1, 2020, Eneko Osaba and others published Traveling salesman problem: a perspective review of recent research and new results with bio-inspired metaheuristics | Find, read and cite ...
This paper gives an introduction to the Traveling Salesman Problem that includes current research. Additionally, the algorithms are used to nd a route traveling through twenty US colleges. As well, we use the Geometric Algorithm to assign scouts for the ... The traveling salesman problem is solved if there exists a shortest route that visits each
For the best of the algorithms investigated in , R w → 2, as n, the number of cities in the travelling salesman problem (TSP), tends to be ∞. In this paper, we describe a heuristic algorithm with O(n 3) growth rate and for which R w < 3/2 for all n. This represents an improvement of 50% over the previously best known value of R w for the TSP.
The Traveling Salesman Problem (TSP) is one of the most well-known combinatorial optimization problems. Its popularity and importance can be attributed to its simple ... making it an ideal research problem for design of new algorithms, development of complexity theory, and analysis of search space [3-5]. The intrinsic difficulty of the TSP ...
A concise guide to the Traveling Salesman Problem G Laporte* Canada Research Chair in Distribution Management, HEC Montréal, Canada The Traveling Salesman Problem (TSP) is one of the most famous problems in combinatorial optimization. Hundreds of papers have been written on the TSP and several exact and heuristic algorithms are available for it.
Stay informed on the latest trending ML papers with code, research developments, libraries, methods, and datasets. ... Use these libraries to find Traveling Salesman Problem models and implementations khalil-research/pyepo 2 papers 386 . Datasets. TSP/HCP Benchmark set ...
During the course of the last few years, attacks on the traveling salesman problem have resulted in a variety of often innovative and rather powerful computational procedures. In this article, we present a review of these results for problems defined on weighted and unweighted graphs.
Traveling Salesman Problem: an Overview of Applications, Formulations, and Solution Approaches. November 2010. November 2010. DOI: 10.5772/12909. In book: Traveling Salesman Problem, Theory and ...
European Journal of Operational Research 59 (1992) 231-247 231 North-Holland Invited Review The Traveling Salesman Problem: An overview of exact and approximate algorithms Gilbert Laporte Centre de recherche sur les transports, Universit~ de Montr&l, C.P. 6128, Station A, Montreal, Canada H3C M7 Received May 1991; received July 1991 Abstract: In this paper, some of the main known algorithms ...
TSP (Travelling Salesman Problem) is a typical issue of combinatorial optimization problem in the domain of mathematics, which aims at finding the shortest pathway among the given cities, and visit each city only once. This essay introduces an efficient way to solve TSP based on virtual instrument technology, combining the genetic algorithm and annealing algorithm. Because it takes the ...
The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest formulation, such as planning, logistics, and the manufacture of microchips; and can be slightly modified ...
To investigate DB1 with capabilities of handling the optimization in operations research, we select the traveling salesman problem (TSP) Gavish and Graves (1978), one of the best-known ...
This paper presents a review of different algorithms to solve TSP and find the shortest route through all the cities that the salesman has to travel. The Travelling Salesman Problem (TSP) is one of the NP-complete and NP-hard problems in combinatorial optimization, and there are lot of algorithms attacking it.
The new formulations are extended to include a variety of transportation scheduling problems, such as the Multi-Travelling Salesman problem, the Delivery problem, the School Bus problem and the Dial-a-Bus problem. A Benders decomposition procedure is applied on the new formulations and the resulting computational rocedure is seen to be ...
In this paper, we shall investigate the Miller, et. al. 201 formulation and investigate its relationship to the highly successful Lagrangean Relaxation method developed by Held and Karp [15,16] for solving the Travelling Salesman Problem. In addition, alternative formulations of the Travelling Salesman Problem are developed which have the ...
Introduction. The Traveling Salesman Problem, also known as the Traveling Salesperson Problem or the. TSP, is a well-known optimization problem in computer science and operations research. It is ...
Minimum Travel Cost Approach for Travelling Salesman Problem. The Travelling Salesman Problem (TSP) is one of the NP-complete and NP-hard problems in combinatorial optimization, and there are lot of algorithms attacking it. This paper addresses the TSP using a new approach to calculate the minimum... more. Download.
Research Paper on Travelling Salesman Problem And it'sResearch Paper on Travelling Sal. ience Dronacharya College Of Engineering,Gurgaon-122506Abstract- Genetic Algorithm is used to solve an optimization problems and Trav. lling Salesman Problem (TSP) is an optimization problem. TSP is an NP hard problem in combinational optimization important.
In this paper assignment based integer linear formulation presented for solving traveling salesman problem. Unfortunately, the assignment model can lead to infeasible solutions. Infeasibility ...