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Simplex and Interior Point Specialized Algorithms for Solving Nonoriented Multicommodity Flow Problems

Author

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  • P. Chardaire

    (School of Information Systems, University of East Anglia, Norwich NR4 7TJ, United Kingdom)

  • A. Lisser

    (Laboratoire de Recherche en Informatique, Bât 490, Université Paris Sud, 91405 Orsay Cedex, France)

Abstract

Multicommodity network flow models arise in a wide variety of contexts, typical among which is the dimensioning of telecommunication networks. In this paper, we present various approaches based on specialization of the simplex algorithm and interior-point methods to solve nonoriented multicommodity flowproblems. Algorithms are tested with data from the France-Telecom Paris district transmission network. First, we focus on a specialization for the node-arc formulation of the problem. A Primal simplex and Dual Affine Scaling algorithms exploiting the particular structure of the constraint matrix are presented and compared. Numerical results are provided for problems up to about 800,000 constraints and 6,000,000 variables. However, much more powerful approaches based on specialized decomposition methods can be implemented for solving the problem. A Dantzig-Wolfe decomposition method is designed and compared with a specialized implementation of the Analytic Center Cutting Plane Method (ACCPM). Partitioning techniques are used to exploit the structure of the master programs involved in those methods.

Suggested Citation

  • P. Chardaire & A. Lisser, 2002. "Simplex and Interior Point Specialized Algorithms for Solving Nonoriented Multicommodity Flow Problems," Operations Research, INFORMS, vol. 50(2), pages 260-276, April.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:2:p:260-276
    DOI: 10.1287/opre.50.2.260.436
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    References listed on IDEAS

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    1. Judith M. Farvolden & Warren B. Powell & Irvin J. Lustig, 1993. "A Primal Partitioning Solution for the Arc-Chain Formulation of a Multicommodity Network Flow Problem," Operations Research, INFORMS, vol. 41(4), pages 669-693, August.
    2. de GHELLINCK, Guy & VIAL, Jean-Philippe, 1986. "A polynomial Newton method for linear programming," LIDAM Reprints CORE 724, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. J. L. Goffin & A. Haurie & J. P. Vial, 1992. "Decomposition and Nondifferentiable Optimization with the Projective Algorithm," Management Science, INFORMS, vol. 38(2), pages 284-302, February.
    4. de GHELLI NCK, G. & VIAL, J.-Ph., 1986. "A polynomial Newton method for linear programming," LIDAM Discussion Papers CORE 1986014, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. James B. Orlin, 1993. "A Faster Strongly Polynomial Minimum Cost Flow Algorithm," Operations Research, INFORMS, vol. 41(2), pages 338-350, April.
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    Cited by:

    1. F. Babonneau & O. du Merle & J.-P. Vial, 2006. "Solving Large-Scale Linear Multicommodity Flow Problems with an Active Set Strategy and Proximal-ACCPM," Operations Research, INFORMS, vol. 54(1), pages 184-197, February.
    2. Frédéric Babonneau & Jean-Philippe Vial, 2008. "An Efficient Method to Compute Traffic Assignment Problems with Elastic Demands," Transportation Science, INFORMS, vol. 42(2), pages 249-260, May.
    3. R. Andrade & A. Lisser & N. Maculan & G. Plateau, 2005. "B&B Frameworks for the Capacity Expansion of High Speed Telecommunication Networks Under Uncertainty," Annals of Operations Research, Springer, vol. 140(1), pages 49-65, November.
    4. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.

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