Network Shortest Path Interdiction Problem Based on Generalized Set Coverage

In the network shortest path interdiction problem, an evader attempts to find the shortest path between the origin and the destination in a network, while an interdictor attempts to maximize the length of this shortest path by interdicting network arcs with limited resources. Therefore, the problem can be formulated as a bi-level programming problem. Existing methods for solving this problem have either low accuracy or slow convergence speed. To address this, in this article, we propose a new algorithm to overcome the above challenges by transforming the problem into an iterative generalized set coverage problem and then solving it by using zero-one linear programming. At each step of the iteration, we obtain a better solution than at the previous step by setting a fixed parameter to interdict a dynamic set regarding the possible interdiction paths. We rigorously prove that the iterative algorithm can converge to the optimal solution. Additionally, the convergence speed is significantly faster than those of baseline methods. For the fixed parameter setting problem, we also propose a parameter adaptive algorithm to further accelerate the convergence speed. Finally, the excellent performance of the proposed algorithms is verified in randomly generated networks and real networks.