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Bi and tri-objective optimization in the deterministic network interdiction problem

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  • Rocco S., Claudio M.
  • Emmanuel Ramirez-Marquez, José
  • Salazar A., Daniel E.

Abstract

Solution approaches to the deterministic network interdiction problem have previously been developed for optimizing a single figure-of-merit of the network configuration (i.e. flow that can be transmitted between a source node and a sink node for a fixed network design) under constraints related to limited amount of resources available to interdict network links. These approaches work under the assumption that: (1) nominal capacity of each link is completely reduced when interdicted and (2) there is a single criterion to optimize. This paper presents a newly developed evolutionary algorithm that for the first time allows solving multi-objective optimization models for the design of network interdiction strategies that take into account a variety of figures-of-merit. The algorithm provides an approximation to the optimal Pareto frontier using: (a) techniques in Monte Carlo simulation to generate potential network interdiction strategies, (b) graph theory to analyze strategies’ maximum source–sink flow and (c) an evolutionary search that is driven by the probability that a link will belong to the optimal Pareto set. Examples for different sizes of networks and network behavior are used throughout the paper to illustrate and validate the approach.

Suggested Citation

  • Rocco S., Claudio M. & Emmanuel Ramirez-Marquez, José & Salazar A., Daniel E., 2010. "Bi and tri-objective optimization in the deterministic network interdiction problem," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 887-896.
    • Handle: RePEc:eee:reensy:v:95:y:2010:i:8:p:887-896
    DOI: 10.1016/j.ress.2010.03.008
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    References listed on IDEAS

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    1. Rocco S, Claudio M. & Ramirez-Marquez, José Emmanuel, 2009. "Deterministic network interdiction optimization via an evolutionary approach," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 568-576.
    2. Cook, Jason L. & Ramirez-Marquez, Jose Emmanuel, 2009. "Optimal design of cluster-based ad-hoc networks using probabilistic solution discovery," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 218-228.
    3. Johannes O. Royset & R. Kevin Wood, 2007. "Solving the Bi-Objective Maximum-Flow Network-Interdiction Problem," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 175-184, May.
    4. Richard Wollmer, 1964. "Removing Arcs from a Network," Operations Research, INFORMS, vol. 12(6), pages 934-940, December.
    5. Ramirez-Marquez, Jose Emmanuel, 2008. "Port-of-entry safety via the reliability optimization of container inspection strategy through an evolutionary approach," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1698-1709.
    6. Garg, Manish & Smith, J. Cole, 2008. "Models and algorithms for the design of survivable multicommodity flow networks with general failure scenarios," Omega, Elsevier, vol. 36(6), pages 1057-1071, December.
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    Citations

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    Cited by:

    1. Hernandez, Ivan & Emmanuel Ramirez-Marquez, Jose & Rainwater, Chase & Pohl, Edward & Medal, Hugh, 2014. "Robust facility location: Hedging against failures," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 73-80.
    2. Chi Zhang & Jose Ramirez-Marquez, 2013. "Protecting critical infrastructures against intentional attacks: a two-stage game with incomplete information," IISE Transactions, Taylor & Francis Journals, vol. 45(3), pages 244-258.
    3. Rocco S., Claudio M. & Emmanuel Ramirez-Marquez, José, 2013. "Identification of top contributors to system vulnerability via an ordinal optimization based method," Reliability Engineering and System Safety, Elsevier, vol. 114(C), pages 92-98.
    4. Rocco S., Claudio M. & Ramirez-Marquez, Jose Emmanuel, 2012. "Innovative approaches for addressing old challenges in component importance measures," Reliability Engineering and System Safety, Elsevier, vol. 108(C), pages 123-130.
    5. Claudio M Rocco S & Juan Carlos Ruiz, 2012. "Assessing the importance of components in a system modeled as a network," Journal of Risk and Reliability, , vol. 226(5), pages 464-475, October.
    6. Levitin, G. & Gertsbakh, I. & Shpungin, Y., 2013. "Evaluating the damage associated with intentional supply deprivation in multi-commodity network," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 11-17.
    7. Henry, Devanandham & Emmanuel Ramirez-Marquez, Jose, 2012. "Generic metrics and quantitative approaches for system resilience as a function of time," Reliability Engineering and System Safety, Elsevier, vol. 99(C), pages 114-122.
    8. Li, Y.F. & Sansavini, G. & Zio, E., 2013. "Non-dominated sorting binary differential evolution for the multi-objective optimization of cascading failures protection in complex networks," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 195-205.
    9. Claudio M Rocco & Kash Barker & Jose Moronta & Jose E Ramirez-Marquez, 2018. "Community detection and resilience in multi-source, multi-terminal networks," Journal of Risk and Reliability, , vol. 232(6), pages 616-626, December.
    10. Levitin, G. & Gertsbakh, I. & Shpungin, Y., 2011. "Evaluating the damage associated with intentional network disintegration," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 433-439.
    11. 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.
    12. Liberatore, Federico & Scaparra, Maria P. & Daskin, Mark S., 2012. "Hedging against disruptions with ripple effects in location analysis," Omega, Elsevier, vol. 40(1), pages 21-30, January.
    13. Jiang, J. & Liu, X., 2018. "Multi-objective Stackelberg game model for water supply networks against interdictions with incomplete information," European Journal of Operational Research, Elsevier, vol. 266(3), pages 920-933.
    14. Gedik, Ridvan & Medal, Hugh & Rainwater, Chase & Pohl, Ed A. & Mason, Scott J., 2014. "Vulnerability assessment and re-routing of freight trains under disruptions: A coal supply chain network application," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 45-57.

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