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Minimizing the maximal reliable path with a nodal interdiction model considering resource sharing

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  • Xiang, Yin

Abstract

This study presents a novel maximal reliable path interdiction (MRPI) problem in application to traffic inspection and intercepting invading attackers. This problem differs from traditional MRPI problems in that (1) interdiction acts on nodes, (2) binary interdiction variables are relaxed as integer variables, (3) the interdict effect is endogenously determined, and (4) resource sharing is considered among nodes. This problem is addressed as a two-player (i.e., defender–attacker) Stackelberg game, in which the defender seeks to minimize the attack's utility by coordinating inspection resources among nodes, and the attacker seeks to maximize the intrusion probability by selecting the maximal reliable path. To solve this problem, an improved Benders decomposition algorithm is proposed. Specifically, we improve the basic Benders decomposition algorithm in two ways: (1) To enhance Benders decomposition cuts and reduce iterations, a local search procedure is applied when solving the subproblem, and (2) to accelerate solving the master problem, an innovative two-stage method based on a relaxed linear programming model and a greedy algorithm is proposed. The algorithm is then tested in different sizes of grid networks and compared with other algorithms. The results show that the improved Benders decomposition algorithm performs very well. Finally, the MRPI model is also applied in a real-world north Xinjiang border network. The results verify the correctness and efficiency of the solution method.

Suggested Citation

  • Xiang, Yin, 2023. "Minimizing the maximal reliable path with a nodal interdiction model considering resource sharing," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    • Handle: RePEc:eee:reensy:v:239:y:2023:i:c:s095183202300409x
    DOI: 10.1016/j.ress.2023.109495
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