Shortest Path Network Interdiction With Goal Threshold

Abstract

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.