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Weapon-target assignment problem: exact and approximate solution algorithms

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A new exact algorithm for the Weapon-Target Assignment problem

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The Specialized Threat Evaluation and Weapon Target Assignment Problem: Genetic Algorithm Optimization and ILP Model Solution

• Conference paper
• First Online: 09 April 2023
• Cite this conference paper

• Ahmet Burak Baraklı 10 , 11 ,
• Fatih Semiz 10 &
• Emre Atasoy 10  

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13989))

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• International Conference on the Applications of Evolutionary Computation (Part of EvoStar)

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In this study, we developed an algorithm that provides automatic protection against swarm drones by using directional jammers in anti-drone systems. Directional jammers are a special type of jammers that can be rotated to a certain angle and do jamming around only that angle. This feature is useful for jamming particular targets and not jamming areas where it is not desired. We worked on a specialized version of the threat evaluation and weapon allocation (TEWA) problem, in which weapons (jammers for this problem) should be assigned to angles to cover threats at a maximum rate by satisfying their priorities. In this problem, it is aimed at keeping the threat within jamming signals at the maximum rate by turning the directional jammers to appropriate angles, taking into account the threat priorities. We have presented an algorithm that solves this problem by meeting the physical constraints of the jammers and tactical constraints defined by the user. The solutions created include: using as few jammers as possible, minimizing the angle changes jammers make in each new plan, prioritizing threats according to their characteristics (type, direction, speed, and distance), and preventing jammers from returning to the physical constraints defined for them. We solved the threat evaluation problem with the help of genetic programming and the jammer angle assignment problem by transforming it into an integer linear programming (ILP) formulation. We also handled physical constraints unsuitable for ILP formulation with post-processing. Since there are few studies directly dealing with this version of the problem, we compared our study with the study that was claimed to be the first to solve this particular version of this problem. Furthermore, we compared our study with the different versions of the algorithm we created. Experiments have shown that threat coverage percentage is vastly increased, achieving this without a significant drop in problem-solving speed.

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Andersen, A.C., Pavlikov, K., Toffolo, T.A.: Weapon-target assignment problem: exact and approximate solution algorithms. Annals of Operations Research, pp. 1–26 (2022)

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Ahmet Burak Baraklı, Fatih Semiz & Emre Atasoy

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Baraklı, A.B., Semiz, F., Atasoy, E. (2023). The Specialized Threat Evaluation and Weapon Target Assignment Problem: Genetic Algorithm Optimization and ILP Model Solution. In: Correia, J., Smith, S., Qaddoura, R. (eds) Applications of Evolutionary Computation. EvoApplications 2023. Lecture Notes in Computer Science, vol 13989. Springer, Cham. https://doi.org/10.1007/978-3-031-30229-9_2

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Weapon-target assignment problem: exact and approximate solution algorithms

• Strategic Organization Design (SOD)
• Department of Business & Management (DBM)
• University of Southern Denmark
• Universidade Federal de Ouro Preto

Research output : Contribution to journal › Journal article › Research › peer-review

• Branch-and-adjust
• Integer programming
• Probability chains
• Weapon-target assignment problem

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• 10.1007/s10479-022-04525-6
• Open access version Accepted manuscript, 509 KB

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• Exact Solution Business & Economics 100%
• Assignment Problem Business & Economics 96%
• Approximation Business & Economics 12%
• Linearization Business & Economics 10%
• Branch and Bound Algorithm Business & Economics 9%
• Combinatorial Optimization Business & Economics 9%
• Optimality Business & Economics 9%
• Mixed Integer Linear Programming Business & Economics 8%

T1 - Weapon-target assignment problem

T2 - exact and approximate solution algorithms

AU - Andersen, Alexandre Colaers

AU - Pavlikov, Konstantin

AU - Toffolo, Túlio A. M.

PY - 2022/5

Y1 - 2022/5

N2 - The Weapon-Target Assignment (WTA) problem aims to assign a set of weapons to a number of assets (targets), such that the expected value of survived targets is minimized. The WTA problem is a nonlinear combinatorial optimization problem known to be NP-hard. This paper applies several existing techniques to linearize the WTA problem. One linearization technique (Camm et al. in Oper Res 50(6):946–955, 2002) approximates the nonlinear terms of the WTA problem via convex piecewise linear functions and provides heuristic solutions to the WTA problem. Such approximation problems are, though, relatively easy to solve from the computational point of view even for large-scale problem instances. Another approach proposed by O’Hanley et al. (Eur J Oper Res 230(1):63–75, 2013) linearizes the WTA problem exactly at the expense of incorporating a significant number of additional variables and constraints, which makes many large-scale problem instances intractable. Motivated by the results of computational experiments with these existing solution approaches, a specialized new exact solution approach is developed, which is called branch-and-adjust. The proposed solution approach involves the compact piecewise linear convex under-approximation of the WTA objective function and solves the WTA problem exactly. The algorithm builds on top of any existing branch-and-cut or branch-and-bound algorithm and can be implemented using the tools provided by state-of-the-art mixed integer linear programming solvers. Numerical experiments demonstrate that the proposed specialized algorithm is capable of handling very large scale problem instances with up to 1500 weapons and 1000 targets, obtaining solutions with optimality gaps of up to 2.0% within 2 h of computational runtime.

AB - The Weapon-Target Assignment (WTA) problem aims to assign a set of weapons to a number of assets (targets), such that the expected value of survived targets is minimized. The WTA problem is a nonlinear combinatorial optimization problem known to be NP-hard. This paper applies several existing techniques to linearize the WTA problem. One linearization technique (Camm et al. in Oper Res 50(6):946–955, 2002) approximates the nonlinear terms of the WTA problem via convex piecewise linear functions and provides heuristic solutions to the WTA problem. Such approximation problems are, though, relatively easy to solve from the computational point of view even for large-scale problem instances. Another approach proposed by O’Hanley et al. (Eur J Oper Res 230(1):63–75, 2013) linearizes the WTA problem exactly at the expense of incorporating a significant number of additional variables and constraints, which makes many large-scale problem instances intractable. Motivated by the results of computational experiments with these existing solution approaches, a specialized new exact solution approach is developed, which is called branch-and-adjust. The proposed solution approach involves the compact piecewise linear convex under-approximation of the WTA objective function and solves the WTA problem exactly. The algorithm builds on top of any existing branch-and-cut or branch-and-bound algorithm and can be implemented using the tools provided by state-of-the-art mixed integer linear programming solvers. Numerical experiments demonstrate that the proposed specialized algorithm is capable of handling very large scale problem instances with up to 1500 weapons and 1000 targets, obtaining solutions with optimality gaps of up to 2.0% within 2 h of computational runtime.

KW - Branch-and-adjust

KW - Integer programming

KW - Probability chains

KW - Weapon-target assignment problem

U2 - 10.1007/s10479-022-04525-6

DO - 10.1007/s10479-022-04525-6

M3 - Journal article

SN - 0254-5330

JO - Annals of Operations Research

JF - Annals of Operations Research

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Computer Science > Data Structures and Algorithms

Title: towards metric dbscan: exact, approximate, and streaming algorithms.

Abstract: DBSCAN is a popular density-based clustering algorithm that has many different applications in practice. However, the running time of DBSCAN in high-dimensional space or general metric space ({\em e.g.,} clustering a set of texts by using edit distance) can be as large as quadratic in the input size. Moreover, most of existing accelerating techniques for DBSCAN are only available for low-dimensional Euclidean space. In this paper, we study the DBSCAN problem under the assumption that the inliers (the core points and border points) have a low intrinsic dimension (which is a realistic assumption for many high-dimensional applications), where the outliers can locate anywhere in the space without any assumption. First, we propose a $k$-center clustering based algorithm that can reduce the time-consuming labeling and merging tasks of DBSCAN to be linear. Further, we propose a linear time approximate DBSCAN algorithm, where the key idea is building a novel small-size summary for the core points. Also, our algorithm can be efficiently implemented for streaming data and the required memory is independent of the input size. Finally, we conduct our experiments and compare our algorithms with several popular DBSCAN algorithms. The experimental results suggest that our proposed approach can significantly reduce the computational complexity in practice.

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