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Multilevel Approaches for the Critical Node Problem

Author

Listed:
  • Andrea Baggio

    (Quant Research, swissQuant Group AG, CH-8001 Zurich, Switzerland;)

  • Margarida Carvalho

    (CIRRELT and DIRO, Université de Montréal, Montréal, Québec H3T 1J4, Canada;)

  • Andrea Lodi

    (École Polytechnique de Montréal, Montreal, Québec H3T 1J4, Canada;)

  • Andrea Tramontani

    (CPLEX Optimization, IBM, 40132 Bologna, Italy)

Abstract

In recent years, a lot of effort has been dedicated to develop strategies to defend networks against possible cascade failures or malicious viral attacks. On the one hand, network safety is investigated from a preventive perspective. On the other hand, blocking models have been proposed for scenarios in which the attack has already taken place causing a harmful spreading throughout the network. In this work, we combine these two perspectives. More precisely, following the framework defender–attacker–defender, we consider a model of prevention, attack, and damage containment using a three-stage, zero-sum game. The defender is not only able to adopt preventive strategies, but also to defend the network after an attack takes place. Assuming that the attacker acts optimally, we compute a defensive strategy for the first stage that minimizes the total damage to the network in the end of the third stage. Our contribution consists of considering this problem as a trilevel mixed-integer program and designing an exact algorithm for it based on tools developed for multilevel programming.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:69:y:2021:i:2:p:486-508
    DOI: 10.1287/opre.2020.2014
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    References listed on IDEAS

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    1. Mehdi Hemmati & J. Cole Smith & My Thai, 2014. "A cutting-plane algorithm for solving a weighted influence interdiction problem," Computational Optimization and Applications, Springer, vol. 57(1), pages 71-104, January.
    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. Paola Cappanera & Maria Paola Scaparra, 2011. "Optimal Allocation of Protective Resources in Shortest-Path Networks," Transportation Science, INFORMS, vol. 45(1), pages 64-80, February.
    4. P. M. Ghare & D. C. Montgomery & W. C. Turner, 1971. "Optimal interdiction policy for a flow network," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 18(1), pages 37-45, March.
    5. 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.
    6. H. Donald Ratliff & G. Thomas Sicilia & S. H. Lubore, 1975. "Finding the n Most Vital Links in Flow Networks," Management Science, INFORMS, vol. 21(5), pages 531-539, January.
    7. 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.
    8. Gerald Brown & Matthew Carlyle & Javier Salmerón & Kevin Wood, 2006. "Defending Critical Infrastructure," Interfaces, INFORMS, vol. 36(6), pages 530-544, December.
    9. 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.
    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.
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