Shortest-path Interdiction Problem Research Articles

Shortest path interdiction problem with convex piecewise-linear costs

Shortest path interdiction problem with convex piecewise-linear costs

Asymmetric stochastic shortest-path interdiction under conditional value-at-risk

We study a two-stage shortest-path interdiction problem between an interdictor and an evader, in which the cost for an evader to use each arc is given by the arc’s base cost plus an additional cost if the arc is attacked by the interdictor. The interdictor acts first to attack a subset of arcs, and then the evader traverses the network using a shortest path. In the problem we study, the interdictor does not know the exact value of each base cost, but instead only knows the (non-negative uniform) distribution of each arc’s base cost. The evader observes both the subset of arcs attacked by the interdictor and the true base cost values before traversing the network. The interdictor seeks to maximize the conditional value-at-risk of the evader’s shortest-path costs, given some specified risk parameter. We provide an exact method for this problem that utilizes row generation, partitioning, and bounding strategies, and demonstrate the efficacy of our approach on a set of randomly generated instances.

The Shortest Path Interdiction Problem with Randomized Interdiction Strategies: Complexity and Algorithms

New algorithms and models enable randomized network interdiction strategies

Shortest Path Network Interdiction With Goal Threshold

Network defense and attack problems can be modeled as network interdictions. In this paper, we consider a new version of the network interdiction problem that optimizes the interdictor’s resource consumption while limiting network capacities (e.g., the shortest path) to a specified threshold. Interdictors would balance the interdiction performance and resource consumption when maximizing the performance costs too much. The most frequently-used technique is to relax the maximization restraint to certain specified threshold; however, the known algorithms provide little help in calculating the threshold restraint. We present a novel model named minimizing the interdiction resource with goal threshold based on the shortest path interdiction problem and propose two basic algorithms to solve it based on Benders decomposition and Lagrange duality, respectively. To consider the situation of complete interdiction and that of a large threshold, a corresponding set-covering algorithm and a Lagrange approximate algorithm are presented. Computational experiments show that decomposition-based algorithms generally perform better on small-world networks while duality-based algorithms perform better on regular grid networks. Analyses on network property sensitivity show that the decomposition-based algorithms are sensitive to the threshold value while the duality-based algorithms become weaker as the interdiction increment grows. Furthermore, we evaluate the performance of these two basic algorithms on a real-world Chicago transportation network. The result illustrates a significant advance; both algorithms can compute an optimal strategy for problems that scale up to real-world sizes.