A two-phase algorithm for the biobjective integer minimum cost flow problem

Abstract

We present an algorithm to compute a complete set of efficient solutions for the biobjective integer minimum cost flow problem. We use the two phase method, with a parametric network simplex algorithm in phase 1 to compute all non-dominated extreme points. In phase 2, the remaining non-dominated points (non-extreme supported and non-supported) are computed using a k best flow algorithm on single-objective weighted sum problems. We implement the algorithm and report run-times on problem instances generated with a modified version of the NETGEN generator and also for networks with a grid structure.