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A simple greedy heuristic for linear assignment interdiction

Author

Listed:
  • Vladimir Stozhkov

    (University of Florida)

  • Vladimir Boginski

    (University of Florida
    University of Central Florida)

  • Oleg A. Prokopyev

    (University of Pittsburgh)

  • Eduardo L. Pasiliao

    (Air Force Research Laboratory)

Abstract

We consider a bilevel extension of the classical linear assignment problem motivated by network interdiction applications. Specifically, given a bipartite graph with two different (namely, the leader’s and the follower’s) edge costs, the follower solves a linear assignment problem maximizing his/her own profit, whereas the leader is allowed to affect the follower’s decisions by eliminating some of the vertices from the graph. The leader’s objective is to minimize the total cost given by the cost of the interdiction actions plus the cost of the assignments made by the follower. The considered problem is strongly $${ NP}$$ N P -hard. First, we formulate this problem as a linear mixed integer program (MIP), which can be solved by commercial MIP solvers. More importantly, we also describe a greedy-based construction heuristic, which provides (under some mild conditions) an optimal solution for the case, where the leader’s and the follower’s edge costs are equal to one. Finally, we present the results of our computational experiments comparing the proposed heuristic against an MIP solver.

Suggested Citation

  • Vladimir Stozhkov & Vladimir Boginski & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2017. "A simple greedy heuristic for linear assignment interdiction," Annals of Operations Research, Springer, vol. 249(1), pages 39-53, February.
  • Handle: RePEc:spr:annopr:v:249:y:2017:i:1:d:10.1007_s10479-016-2118-3
    DOI: 10.1007/s10479-016-2118-3
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    References listed on IDEAS

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    1. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    2. Gerald Brown & Matthew Carlyle & Javier Salmerón & Kevin Wood, 2006. "Defending Critical Infrastructure," Interfaces, INFORMS, vol. 36(6), pages 530-544, December.
    3. C. Audet & P. Hansen & B. Jaumard & G. Savard, 1997. "Links Between Linear Bilevel and Mixed 0–1 Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 273-300, May.
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    Cited by:

    1. Gabriel Lopez Zenarosa & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2021. "On exact solution approaches for bilevel quadratic 0–1 knapsack problem," Annals of Operations Research, Springer, vol. 298(1), pages 555-572, March.
    2. Jorge A. Sefair & J. Cole Smith, 2017. "Exact algorithms and bounds for the dynamic assignment interdiction problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(5), pages 373-387, August.

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