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Sequential Shortest Path Interdiction with Incomplete Information

Author

Listed:
  • Juan S. Borrero

    (Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261)

  • Oleg A. Prokopyev

    (Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261)

  • Denis Sauré

    (Department of Industrial Engineering, Universidad de Chile)

Abstract

We study sequential interdiction when the interdictor has incomplete initial information about the network and the evader has complete knowledge of the network, including its structure and arc costs. In each time period, the interdictor blocks at most k arcs from the network observed up to that period, after which the evader travels along a shortest path between two (fixed) nodes in the interdicted network. By observing the evader’s actions, the interdictor learns about the network structure and arc costs and adjusts its actions to maximize the cumulative cost incurred by the evader. A salient feature of our work is that the feedback in each period is deterministic and adversarial. In addition to studying the regret minimization problem, we also discuss time stability of a policy, which is the number of time periods until the interdictor’s actions match those of an oracle interdictor with prior knowledge of the network. We propose a class of simple interdiction policies that have a finite regret and detect when the instantaneous regret reaches zero in real time. More importantly, we establish that this class of policies belongs to the set of efficient policies.

Suggested Citation

  • Juan S. Borrero & Oleg A. Prokopyev & Denis Sauré, 2016. "Sequential Shortest Path Interdiction with Incomplete Information," Decision Analysis, INFORMS, vol. 13(1), pages 68-98, March.
  • Handle: RePEc:inm:ordeca:v:13:y:2016:i:1:p:68-98
    DOI: 10.1287/deca.2015.0325
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    Citations

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    Cited by:

    1. Juan S. Borrero & Oleg A. Prokopyev & Denis Sauré, 2019. "Sequential Interdiction with Incomplete Information and Learning," Operations Research, INFORMS, vol. 67(1), pages 72-89, January.
    2. Jing Yang & Juan S. Borrero & Oleg A. Prokopyev & Denis Sauré, 2021. "Sequential Shortest Path Interdiction with Incomplete Information and Limited Feedback," Decision Analysis, INFORMS, vol. 18(3), pages 218-244, September.
    3. Tezcan, Barış & Maass, Kayse Lee, 2023. "Human trafficking interdiction with decision dependent success," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    4. Kosmas, Daniel & Sharkey, Thomas C. & Mitchell, John E. & Maass, Kayse Lee & Martin, Lauren, 2023. "Interdicting restructuring networks with applications in illicit trafficking," European Journal of Operational Research, Elsevier, vol. 308(2), pages 832-851.
    5. Keskin, Burcu B. & Griffin, Emily C. & Prell, Jonathan O. & Dilkina, Bistra & Ferber, Aaron & MacDonald, John & Hilend, Rowan & Griffis, Stanley & Gore, Meredith L., 2023. "Quantitative Investigation of Wildlife Trafficking Supply Chains: A Review," Omega, Elsevier, vol. 115(C).
    6. Karwowski, Jan & Mańdziuk, Jacek, 2019. "A Monte Carlo Tree Search approach to finding efficient patrolling schemes on graphs," European Journal of Operational Research, Elsevier, vol. 277(1), pages 255-268.
    7. Nguyen, Di H. & Smith, J. Cole, 2022. "Network interdiction with asymmetric cost uncertainty," European Journal of Operational Research, Elsevier, vol. 297(1), pages 239-251.
    8. 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.
    9. Yan, Xihong & Ren, Xiaorong & Nie, Xiaofeng, 2022. "A budget allocation model for domestic airport network protection," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    10. 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.
    11. 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.
    12. M. Hosein Zare & Oleg A. Prokopyev & Denis Sauré, 2020. "On Bilevel Optimization with Inexact Follower," Decision Analysis, INFORMS, vol. 17(1), pages 74-95, March.

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