IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v267y2018i1p40-51.html
   My bibliography  Save this article

A dynamic reformulation heuristic for Generalized Interdiction Problems

Author

Listed:
  • Fischetti, Matteo
  • Monaci, Michele
  • Sinnl, Markus

Abstract

We consider a subfamily of mixed-integer linear bilevel problems that we call Generalized Interdiction Problems. This class of problems includes, among others, the widely-studied interdiction problems, i.e., zero-sum Stackelberg games where two players (called the leader and the follower) share a set of items, and the leader can interdict the usage of certain items by the follower. Problems of this type can be modeled as Mixed-Integer Nonlinear Programming problems, whose exact solution can be very hard. In this paper we propose a new heuristic scheme based on a single-level and compact mixed-integer linear programming reformulation of the problem obtained by relaxing the integrality of the follower variables. A distinguished feature of our method is that general-purpose mixed-integer cutting planes for the follower problem are exploited, on the fly, to dynamically improve the reformulation. The resulting heuristic algorithm proved very effective on a large number of test instances, often providing an (almost) optimal solution within very short computing times.

Suggested Citation

  • Fischetti, Matteo & Monaci, Michele & Sinnl, Markus, 2018. "A dynamic reformulation heuristic for Generalized Interdiction Problems," European Journal of Operational Research, Elsevier, vol. 267(1), pages 40-51.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:1:p:40-51
    DOI: 10.1016/j.ejor.2017.11.043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717310548
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.11.043?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Calvete, Herminia I. & Gale, Carmen & Mateo, Pedro M., 2008. "A new approach for solving linear bilevel problems using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 188(1), pages 14-28, July.
    2. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2017. "A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs," Operations Research, INFORMS, vol. 65(6), pages 1615-1637, December.
    3. Gerald G. Brown & W. Matthew Carlyle & Robert C. Harney & Eric M. Skroch & R. Kevin Wood, 2009. "Interdicting a Nuclear-Weapons Project," Operations Research, INFORMS, vol. 57(4), pages 866-877, August.
    4. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    5. Alan Washburn & Kevin Wood, 1995. "Two-Person Zero-Sum Games for Network Interdiction," Operations Research, INFORMS, vol. 43(2), pages 243-251, April.
    6. Edward Rothberg, 2007. "An Evolutionary Algorithm for Polishing Mixed Integer Programming Solutions," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 534-541, November.
    7. 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.
    8. Gerald Brown & Matthew Carlyle & Javier Salmerón & Kevin Wood, 2006. "Defending Critical Infrastructure," Interfaces, INFORMS, vol. 36(6), pages 530-544, December.
    9. Fabio Furini & Manuel Iori & Silvano Martello & Mutsunori Yagiura, 2015. "Heuristic and Exact Algorithms for the Interval Min–Max Regret Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 392-405, May.
    10. Wen, U. P. & Huang, A. D., 1996. "A simple Tabu Search method to solve the mixed-integer linear bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 88(3), pages 563-571, February.
    11. James T. Moore & Jonathan F. Bard, 1990. "The Mixed Integer Linear Bilevel Programming Problem," Operations Research, INFORMS, vol. 38(5), pages 911-921, October.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Thomas Kleinert & Martin Schmidt, 2023. "Why there is no need to use a big-M in linear bilevel optimization: a computational study of two ready-to-use approaches," Computational Management Science, Springer, vol. 20(1), pages 1-12, December.
    2. Juan S. Borrero & Leonardo Lozano, 2021. "Modeling Defender-Attacker Problems as Robust Linear Programs with Mixed-Integer Uncertainty Sets," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1570-1589, October.
    3. Pferschy, Ulrich & Nicosia, Gaia & Pacifici, Andrea & Schauer, Joachim, 2021. "On the Stackelberg knapsack game," European Journal of Operational Research, Elsevier, vol. 291(1), pages 18-31.
    4. Furini, Fabio & Ljubić, Ivana & San Segundo, Pablo & Zhao, Yanlu, 2021. "A branch-and-cut algorithm for the Edge Interdiction Clique Problem," European Journal of Operational Research, Elsevier, vol. 294(1), pages 54-69.
    5. Casorrán, Carlos & Fortz, Bernard & Labbé, Martine & Ordóñez, Fernando, 2019. "A study of general and security Stackelberg game formulations," European Journal of Operational Research, Elsevier, vol. 278(3), pages 855-868.
    6. Tezcan, Barış & Maass, Kayse Lee, 2023. "Human trafficking interdiction with decision dependent success," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    7. Thomas Kleinert & Martin Schmidt, 2021. "Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 198-215, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Leitner, Markus & Ljubić, Ivana & Monaci, Michele & Sinnl, Markus & Tanınmış, Kübra, 2023. "An exact method for binary fortification games," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1026-1039.
    3. Thomas Kleinert & Martin Schmidt, 2021. "Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 198-215, January.
    4. Smith, J. Cole & Song, Yongjia, 2020. "A survey of network interdiction models and algorithms," European Journal of Operational Research, Elsevier, vol. 283(3), pages 797-811.
    5. Claudio Contardo & Jorge A. Sefair, 2022. "A Progressive Approximation Approach for the Exact Solution of Sparse Large-Scale Binary Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 890-908, March.
    6. Andrea Baggio & Margarida Carvalho & Andrea Lodi & Andrea Tramontani, 2021. "Multilevel Approaches for the Critical Node Problem," Operations Research, INFORMS, vol. 69(2), pages 486-508, March.
    7. George Kozanidis & Eftychia Kostarelou, 2023. "An Exact Solution Algorithm for Integer Bilevel Programming with Application in Energy Market Optimization," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 573-607, May.
    8. Richard Oberdieck & Nikolaos A. Diangelakis & Styliani Avraamidou & Efstratios N. Pistikopoulos, 2017. "On unbounded and binary parameters in multi-parametric programming: applications to mixed-integer bilevel optimization and duality theory," Journal of Global Optimization, Springer, vol. 69(3), pages 587-606, November.
    9. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2017. "A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs," Operations Research, INFORMS, vol. 65(6), pages 1615-1637, December.
    10. Furini, Fabio & Ljubić, Ivana & Martin, Sébastien & San Segundo, Pablo, 2019. "The maximum clique interdiction problem," European Journal of Operational Research, Elsevier, vol. 277(1), pages 112-127.
    11. Kübra Tanınmış & Markus Sinnl, 2022. "A Branch-and-Cut Algorithm for Submodular Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2634-2657, September.
    12. Liu, Shaonan & Wang, Mingzheng & Kong, Nan & Hu, Xiangpei, 2021. "An enhanced branch-and-bound algorithm for bilevel integer linear programming," European Journal of Operational Research, Elsevier, vol. 291(2), pages 661-679.
    13. R. Paulavičius & C. S. Adjiman, 2020. "New bounding schemes and algorithmic options for the Branch-and-Sandwich algorithm," Journal of Global Optimization, Springer, vol. 77(2), pages 197-225, June.
    14. Leonardo Lozano & J. Cole Smith, 2017. "A Backward Sampling Framework for Interdiction Problems with Fortification," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 123-139, February.
    15. O'Hanley, Jesse R. & Church, Richard L., 2011. "Designing robust coverage networks to hedge against worst-case facility losses," European Journal of Operational Research, Elsevier, vol. 209(1), pages 23-36, February.
    16. Juan S. Borrero & Leonardo Lozano, 2021. "Modeling Defender-Attacker Problems as Robust Linear Programs with Mixed-Integer Uncertainty Sets," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1570-1589, October.
    17. Junlong Zhang & Osman Y. Özaltın, 2021. "Bilevel Integer Programs with Stochastic Right-Hand Sides," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1644-1660, October.
    18. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    19. Laan, Corine M. & van der Mijden, Tom & Barros, Ana Isabel & Boucherie, Richard J. & Monsuur, Herman, 2017. "An interdiction game on a queueing network with multiple intruders," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1069-1080.
    20. Fränk Plein & Johannes Thürauf & Martine Labbé & Martin Schmidt, 2022. "A bilevel optimization approach to decide the feasibility of bookings in the European gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 409-449, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:267:y:2018:i:1:p:40-51. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.