The Bi-Objective Shortest Path Network Interdiction Problem: Subgraph Algorithm and Saturation Property

Critical network defense and attack problems, usually modeled as network interdiction, is of great significance. It is of great interest from the interdictor’s view to study saturation property of resource allocations. This paper presents a bi-objective shortest path network interdiction model with node interdiction, in which the interdictor seeks to interdict a set of nodes in the network that is Pareto-optimal with respect to two objectives, i.e., maximization of shortest path length and minimization of resources cost. A novel subgraph sequence algorithm is developed to identify the efficient frontier through a sequence of single-objective problems. Novel subgraph decomposition algorithms are proposed to solve single-objective problems. Features and time complexity of those problems and algorithms are analyzed. Moreover, to make a trade-off between the resource investment and the interdiction performance, the definition and the computing method of saturation point are introduced in this paper. Both simulated grid network and real-world transportation network data are used to evaluate the performance of algorithms in numerical experiments. The results show that the subgraph sequence algorithm can achieve the optimal Pareto-frontier of this bi-objective problem effectively.