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A multi-start variable neighborhood search for solving the single path multicommodity flow problem

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  • Masri, H.
  • Krichen, S.
  • Guitouni, A.

Abstract

In this paper, we propose a new global routing algorithm supporting advance reservation. A predefined number of messages are to be routed in a capacitated network including a set of nodes that can be producers and/or consumers of information. We assume that the same information can be held by different sources. We first propose the non-linear mathematical formulation for this problem by extending the single path multicommodity flow formulation. To solve such an NP-hard optimization problem, we develop a multi-start variable neighborhood search method (MVNS). The results of extensive computational experiments across a variety of networks from the literature are reported. For small and medium scale instances, the results are compared with the optimal solution generated by LINGO in terms of time and optimality. For large size instances, a comparison to a state-of-the-art ant colony system approach is performed. The obtained results show that the MVNS algorithm is computationally effective and provides high-quality solutions.

Suggested Citation

  • Masri, H. & Krichen, S. & Guitouni, A., 2015. "A multi-start variable neighborhood search for solving the single path multicommodity flow problem," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 132-142.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:132-142
    DOI: 10.1016/j.amc.2014.10.123
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    References listed on IDEAS

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    1. Jeff L. Kennington, 1978. "A Survey of Linear Cost Multicommodity Network Flows," Operations Research, INFORMS, vol. 26(2), pages 209-236, April.
    2. Kaj Holmberg & Di Yuan, 2003. "A Multicommodity Network-Flow Problem with Side Constraints on Paths Solved by Column Generation," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 42-57, February.
    3. Cynthia Barnhart & Christopher A. Hane & Pamela H. Vance, 2000. "Using Branch-and-Price-and-Cut to Solve Origin-Destination Integer Multicommodity Flow Problems," Operations Research, INFORMS, vol. 48(2), pages 318-326, April.
    4. A. Ouorou & P. Mahey & J.-Ph. Vial, 2000. "A Survey of Algorithms for Convex Multicommodity Flow Problems," Management Science, INFORMS, vol. 46(1), pages 126-147, January.
    5. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
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    Cited by:

    1. 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.
    2. François Lamothe & Emmanuel Rachelson & Alain Haït & Cedric Baudoin & Jean-Baptiste Dupé, 2021. "Randomized rounding algorithms for large scale unsplittable flow problems," Journal of Heuristics, Springer, vol. 27(6), pages 1081-1110, December.

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