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Solving nonlinear multicommodity flow problems by the analytic center cutting plane method

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Abstract

The paper deals with nonlinear multicommodity flow problems with convex costs. A decomposition method is proposed to solve them. The approach applies a potential reduction algorithm to solve the master problem approximately and a column generation technique to define a sequence of primal linear programming problems. Each subproblem consists of finding a minimum cost flow between an origin and a destination node in an uncapacited network. It is thus formulated as a shortest path problem and solved with Dijkstra’s d-heap algorithm. An implementation is described that takes full advantage of the supersparsity of the network in the linear algebra operations. Computational results show the efficiency of this approach on well-known nondifferentiable problems and also large scale randomly generated problems (up to 1000 arcs and 5000 commodities).

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Author notes

  1. J. Gondzio

    Present address: Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

Authors and Affiliations

  1. GERAD, Faculty of Management, McGill University, H3A 1G5, Montreal, Que, Canada

    J. -L. Goffin

  2. Logilab, HEC, Section of Management Studies, University of Geneva, 102 Bd.Carl Vogt, CH-1211, Genève 4, Switzerland

    J. -L. Goffin, J. Gondzio, R. Sarkissian & J. -P. Vial

Authors
  1. J. -L. Goffin
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  2. J. Gondzio
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  3. R. Sarkissian
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  4. J. -P. Vial
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Additional information

This research has been supported by the Fonds National de la Recherche Scientifique Suisse, grant #12-34002.92, NSERC-Canada and FCAR-Quebec.

This research was supported by an Obermann fellowship at the Center for Advanced Studies at the University of Iowa.

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Goffin, J.L., Gondzio, J., Sarkissian, R. et al. Solving nonlinear multicommodity flow problems by the analytic center cutting plane method. Mathematical Programming 76, 131–154 (1997). https://doi.org/10.1007/BF02614381

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  • DOI: https://doi.org/10.1007/BF02614381

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