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

Authors:
Andrea Raith;Matthias Ehrgott
Affiliations:
Department of Engineering Science, The University of Auckland, 70 Symonds Street, Auckland 1001, New Zealand;Department of Engineering Science, The University of Auckland, 70 Symonds Street, Auckland 1001, New Zealand and Laboratoire d'Informatique de Nantes Atlantique, Université de Nantes, France
Venue:
Computers and Operations Research
Year:
2009

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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.