Optimal K-node disruption on a node-capacitated network

Abstract

This paper examines a network disruption model from the perspective of a network attacker, who wishes to identify the subset of $$ K $$ nodes to disable on a node-capacitated directed flow network (e.g., air transport) such that the disrupted flow is maximized. Such models can also be used by a network defender who wishes to identify the nodes whose disruption would have the greatest impact on network performance. In this problem, the system flow is constrained not only by the disruption to nodes, but also by the limited capacity on nodes that are not disrupted. This paper presents multiple mixed-integer linear programming formulations for this problem, including a novel path-based formulation, and novel multi-commodity flow-based formulations. Computational testing is provided, demonstrating that the multi-commodity based formulation is able to solve relatively large-sized network instances, with the best performance obtained by a two-step procedure that utilizes an approximation to obtain an initial solution for the provably-optimal multi-commodity flow based formulation.