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Exact and Heuristic Algorithms for the Weapon-Target Assignment Problem

Author

Listed:
  • Ravindra K. Ahuja

    (Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611)

  • Arvind Kumar

    (Innovative Scheduling, Inc., Gainesville, Florida 32641)

  • Krishna C. Jha

    (Innovative Scheduling, Inc., Gainesville, Florida 32641)

  • James B. Orlin

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

The weapon-target assignment (WTA) problem is a fundamental problem arising in defense-related applications of operations research. This problem consists of optimally assigning n weapons to m targets so that the total expected survival value of the targets after all the engagements is minimal. The WTA problem can be formulated as a nonlinear integer programming problem and is known to be NP-complete. No exact methods exist for the WTA problem that can solve even small-size problems (for example, with 20 weapons and 20 targets). Although several heuristic methods have been proposed to solve the WTA problem, due to the absence of exact methods, no estimates are available on the quality of solutions produced by such heuristics. In this paper, we suggest integer programming and network flow-based lower-bounding methods that we obtain using a branch-and-bound algorithm for the WTA problem. We also propose a network flow-based construction heuristic and a very large-scale neighborhood (VLSN) search algorithm. We present computational results of our algorithms, which indicate that we can solve moderately large instances (up to 80 weapons and 80 targets) of the WTA problem optimally and obtain almost optimal solutions of fairly large instances (up to 200 weapons and 200 targets) within a few seconds.

Suggested Citation

  • Ravindra K. Ahuja & Arvind Kumar & Krishna C. Jha & James B. Orlin, 2007. "Exact and Heuristic Algorithms for the Weapon-Target Assignment Problem," Operations Research, INFORMS, vol. 55(6), pages 1136-1146, December.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:6:p:1136-1146
    DOI: 10.1287/opre.1070.0440
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    References listed on IDEAS

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    Cited by:

    1. Ahmet Silav & Esra Karasakal & Orhan Karasakal, 2022. "Bi-objective dynamic weapon-target assignment problem with stability measure," Annals of Operations Research, Springer, vol. 311(2), pages 1229-1247, April.
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    8. Ahmet Silav & Orhan Karasakal & Esra Karasakal, 2019. "Bi‐objective missile rescheduling for a naval task group with dynamic disruptions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(7), pages 596-615, October.
    9. Hughes, Michael S. & Lunday, Brian J., 2022. "The Weapon Target Assignment Problem: Rational Inference of Adversary Target Utility Valuations from Observed Solutions," Omega, Elsevier, vol. 107(C).
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    11. Davis, Michael T. & Robbins, Matthew J. & Lunday, Brian J., 2017. "Approximate dynamic programming for missile defense interceptor fire control," European Journal of Operational Research, Elsevier, vol. 259(3), pages 873-886.
    12. Lu, Yiping & Chen, Danny Z., 2021. "A new exact algorithm for the Weapon-Target Assignment problem," Omega, Elsevier, vol. 98(C).
    13. Juan Li & Bin Xin & Panos M. Pardalos & Jie Chen, 2021. "Solving bi-objective uncertain stochastic resource allocation problems by the CVaR-based risk measure and decomposition-based multi-objective evolutionary algorithms," Annals of Operations Research, Springer, vol. 296(1), pages 639-666, January.
    14. Alexander G. Kline & Darryl K. Ahner & Brian J. Lunday, 2020. "A heuristic and metaheuristic approach to the static weapon target assignment problem," Journal of Global Optimization, Springer, vol. 78(4), pages 791-812, December.
    15. Cihan Çetinkaya & Samer Haffar, 2018. "A Risk-Based Location-Allocation Approach for Weapon Logistics," Logistics, MDPI, vol. 2(2), pages 1-15, May.
    16. Gülpınar, Nalan & Çanakoğlu, Ethem & Branke, Juergen, 2018. "Heuristics for the stochastic dynamic task-resource allocation problem with retry opportunities," European Journal of Operational Research, Elsevier, vol. 266(1), pages 291-303.
    17. Anissa Frini & Adel Guitouni & Abderrezak Benaskeur, 2017. "Solving Dynamic Multi-Criteria Resource-Target Allocation Problem Under Uncertainty: A Comparison of Decomposition and Myopic Approaches," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1465-1496, November.
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