Multicommodity flow problems with a bounded number of paths: A flow deviation approach

  • Authors:

  • Christophe Duhamel;Philippe Mahey

  • Affiliations:

  • Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes, UMR 6158 CNRS, Université Blaise Pascal, Campus des Cézeaux, Aubière, France;Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes, UMR 6158 CNRS, Université Blaise Pascal, Campus des Cézeaux, Aubière, France

  • Venue:
  • Networks - Special Issue on Multicommodity Flows and Network Design
  • Year:
  • 2007

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Abstract

We propose a modified version of the Flow Deviation method of Fratta, Gerla, and Kleinrock to solve multicommodity problems with minimal congestion and a bounded number of active paths. We discuss the approximation of the min–max objective function by a separable convex potential function and give a mixed-integer nonlinear model for the constrained routing problem. Heuristic control of the path generation is then embedded in the original algorithm based on the concepts of cleaning the quasi inactive paths and reducing the flow width for each commodity. Numerical experiments show the validity of the approach for realistic medium-sized networks associated with routing problems in broadband communication networks with multiple protocols and label-switched paths (MPLS). © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(1), 80–89 2007