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An ant colony optimization metaheuristic for single-path multicommodity network flow problems

Author

Listed:
  • X-Y Li

    (Odette School of Business, University of Windsor)

  • Y P Aneja

    (Odette School of Business, University of Windsor)

  • F Baki

    (Odette School of Business, University of Windsor)

Abstract

This paper studies the single-path multicommodity network flow problem (SMNF), in which the flow of each commodity can only use one path linking its origin and destination in the network. We study two versions of this problem based on two different objectives. The first version is to minimize network congestion, an issue of concern in traffic grooming over wavelength division multiplexing (WDM), and in which there generally exists a commodity flow between every pair of nodes. The second problem is a constrained version of the general linear multicommodity flow problem, in which, for each commodity, a single path is allowed to send the required flow, and the objective is to determine a flow pattern that obeys the arc capacities and minimizes the total shipping cost. Based on the node-arc and the arc-chain representations, we first present two formulations. Owing to computational impracticality of exact algorithms for practical networks, we propose an ant colony optimization-(ACO) based metaheuristic to deal with SMNF. Considering different problem properties, we devise two versions of ACO metaheuristics to solve these two problems, respectively. The proposed algorithms’ efficiencies are experimentally investigated on some generated instances of SMNF. The test results demonstrate that the proposed ACO metaheuristics are computationally efficient and robust approaches for solving SMNF.

Suggested Citation

  • X-Y Li & Y P Aneja & F Baki, 2010. "An ant colony optimization metaheuristic for single-path multicommodity network flow problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1340-1355, September.
    • Handle: RePEc:pal:jorsoc:v:61:y:2010:i:9:d:10.1057_jors.2009.86
    DOI: 10.1057/jors.2009.86
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    References listed on IDEAS

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    1. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
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    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. C S Sung & H C Rim, 2004. "Receiver set partitioning and sequencing for multicasting traffic in a WDM lightwave single-hop network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(6), pages 630-639, June.
    5. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
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    Cited by:

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    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.
    3. Berna H. Ulutas, 2019. "An immune system based algorithm for cell formation problem," Journal of Intelligent Manufacturing, Springer, vol. 30(8), pages 2835-2852, December.
    4. Matthew Naybour & Rasa Remenyte-Prescott & Matthew Boyd, 2024. "Ant colony optimisation of a community pharmacy dispensing process using Coloured Petri-Net simulation and UK pharmacy in-field data," Journal of Risk and Reliability, , vol. 238(1), pages 29-43, February.

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