A Combinatorial Benders Decomposition Algorithm for the Directed Multiflow Network Diversion Problem

Abstract

The network diversion problem is to identify a minimum cost, minimal cut separating a source node from a sink node that includes a predefined diversion arc and guarantees existence of a directed path between the source and sink nodes that includes no arc in the cut except for the diversion arc. We extend this to a problem having many source-sink pairs and call this extended problem the multiple flows network diversion problem. We propose optimization algorithms for the multiple flows network diversion problem using a combinatorial Benders decomposition approach incorporated into a branch-and-cut algorithm. We report computational results on four types of network topologies including two real-world networks that indicate that the proposed algorithms outperform state-of-the-art integer programming formulations.