Bi and tri-objective optimization in the deterministic network interdiction problem

Solution approaches to the deterministic network interdiction problem have previously been developed for optimizing a single figure-of-merit of the network configuration (i.e. flow that can be transmitted between a source node and a sink node for a fixed network design) under constraints related to limited amount of resources available to interdict network links. These approaches work under the assumption that: (1) nominal capacity of each link is completely reduced when interdicted and (2) there is a single criterion to optimize. This paper presents a newly developed evolutionary algorithm that for the first time allows solving multi-objective optimization models for the design of network interdiction strategies that take into account a variety of figures-of-merit. The algorithm provides an approximation to the optimal Pareto frontier using: (a) techniques in Monte Carlo simulation to generate potential network interdiction strategies, (b) graph theory to analyze strategies’ maximum source–sink flow and (c) an evolutionary search that is driven by the probability that a link will belong to the optimal Pareto set. Examples for different sizes of networks and network behavior are used throughout the paper to illustrate and validate the approach.