Robust Critical Node Selection by Benders Decomposition

Abstract

The critical node selection problem (CNP) has important applications in telecommunication, supply chain design, and disease propagation prevention. In practice, the weights on the connections are often uncertain or hard to estimate. For this reason, robust optimization approaches have been considered recently for CNP. In this article, we address very general uncertainty sets, only requiring a linear optimization oracle for the set of potential scenarios. In particular, we can deal with discrete scenario based uncertainty, gamma uncertainty, and ellipsoidal uncertainty. For this general class of robust critical node selection problems, we propose an exact solution method based on Benders decomposition. The Benders subproblem, which in our approach is a robust optimization problem, is efficiently solved by applying the Floyd-Warshall algorithm. The presented approach is tested on 384 instances based on Forest-Fire, Barabási-Albert, Erdős-Rényi, and Watts-Strogatz graphs with different number of nodes and edges, where running times are compared to CPLEX being directly applied to the robust problem formulation. The computational results show the advantage of the proposed approach in handling the uncertainty thus outperforming CPLEX most notably for the ellipsoidal uncertainty cases.