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Interdiction Games and Monotonicity, with Application to Knapsack Problems

Author

Listed:
  • Matteo Fischetti

    (Department of Information Engineering, University of Padua, 351200 Padua PD, Italy)

  • Ivana Ljubić

    (ESSEC Business School Paris, 95021 Cergy Pontoise, France)

  • Michele Monaci

    (Department of Information Engineering, University of Bologna, 40136 Bologna, Italy)

  • Markus Sinnl

    (Department of Statistics and Operations Research, University of Vienna, 1090 Vienna, Austria)

Abstract

Two-person interdiction games represent an important modeling concept for applications in marketing, defending critical infrastructure, stopping nuclear weapons projects, or preventing drug smuggling. We present an exact branch-and-cut algorithm for interdiction games under the assumption that feasible solutions of the follower problem satisfy a certain monotonicity property. Prominent examples from the literature that fall into this category are knapsack interdiction, matching interdiction, and packing interdiction problems. We also show how practically relevant interdiction variants of facility location and prize-collecting problems can be modeled in our setting. Our branch-and-cut algorithm uses a solution scheme akin to Benders decomposition based on a family of so-called interdiction cuts. We present modified and lifted versions of these cuts along with exact and heuristic procedures for the separation of interdiction cuts and heuristic separation procedures for the other versions. In addition, we derive further valid inequalities and present a new heuristic procedure. We computationally evaluate the proposed algorithm on a benchmark of 360 knapsack interdiction instances from literature, including 27 instances for which the optimal solution was not known. Our approach is able to solve each of them to optimality within about one minute of computing time on a standard PC (in most cases, within just seconds), and it is up to some orders of magnitude faster than any previous approach from the literature. To further assess the effectiveness of our branch-and-cut algorithm, an additional computational study is performed on 144 randomly generated instances based on 0/1 multidimensional knapsack problems.

Suggested Citation

  • Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2019. "Interdiction Games and Monotonicity, with Application to Knapsack Problems," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 390-410, April.
  • Handle: RePEc:inm:orijoc:v:31:y:2019:i:2:p:390-410
    DOI: 10.1287/ijoc.2018.0831
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    References listed on IDEAS

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    1. H. Martin Weingartner & David N. Ness, 1967. "Methods for the Solution of the Multidimensional 0/1 Knapsack Problem," Operations Research, INFORMS, vol. 15(1), pages 83-103, February.
    2. Kelly J. Cormican & David P. Morton & R. Kevin Wood, 1998. "Stochastic Network Interdiction," Operations Research, INFORMS, vol. 46(2), pages 184-197, April.
    3. Yongjia Song & Siqian Shen, 2016. "Risk-Averse Shortest Path Interdiction," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 527-539, August.
    4. Clifford C. Petersen, 1967. "Computational Experience with Variants of the Balas Algorithm Applied to the Selection of R&D Projects," Management Science, INFORMS, vol. 13(9), pages 736-750, May.
    5. Leonardo Lozano & J. Cole Smith, 2017. "A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem," Operations Research, INFORMS, vol. 65(3), pages 768-786, June.
    6. Alberto Caprara & Margarida Carvalho & Andrea Lodi & Gerhard J. Woeginger, 2016. "Bilevel Knapsack with Interdiction Constraints," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 319-333, May.
    7. Gerald Brown & Matthew Carlyle & Javier Salmerón & Kevin Wood, 2006. "Defending Critical Infrastructure," Interfaces, INFORMS, vol. 36(6), pages 530-544, December.
    8. Vansteenwegen, Pieter & Souffriau, Wouter & Oudheusden, Dirk Van, 2011. "The orienteering problem: A survey," European Journal of Operational Research, Elsevier, vol. 209(1), pages 1-10, February.
    9. J. Cole Smith & Churlzu Lim, 2008. "Algorithms for Network Interdiction and Fortification Games," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Athanasios Migdalas & Leonidas Pitsoulis (ed.), Pareto Optimality, Game Theory And Equilibria, pages 609-644, Springer.
    10. James T. Moore & Jonathan F. Bard, 1990. "The Mixed Integer Linear Bilevel Programming Problem," Operations Research, INFORMS, vol. 38(5), pages 911-921, October.
    11. Shizuo Senju & Yoshiaki Toyoda, 1968. "An Approach to Linear Programming with 0-1 Variables," Management Science, INFORMS, vol. 15(4), pages 196-207, December.
    12. Silvano Martello & David Pisinger & Paolo Toth, 1999. "Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 45(3), pages 414-424, March.
    13. Alan Washburn & Kevin Wood, 1995. "Two-Person Zero-Sum Games for Network Interdiction," Operations Research, INFORMS, vol. 43(2), pages 243-251, April.
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