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A Survey of Algorithms for Convex Multicommodity Flow Problems

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  • A. Ouorou

    (LIMOS---Université Blaise Pascal, ISIMA, BP 125, 63173 Aubière Cedex, France)

  • P. Mahey

    (LIMOS---Université Blaise Pascal, ISIMA, BP 125, 63173 Aubière Cedex, France)

  • J.-Ph. Vial

    (HEC, Section of Management Studies, University of Geneva, 102, Bd. Carl-Vogt, 1211 Geneva 4, Switzerland)

Abstract

Routing problems appear frequently when dealing with the operation of communication or transportation networks. Among them, the message routing problem plays a determinant role in the optimization of network performance. Much of the motivation for this work comes from this problem which is shown to belong to the class of nonlinear convex multicommodity flow problems. This paper emphasizes the message routing problem in data networks, but it includes a broader literature overview of convex multicommodity flow problems. We present and discuss the main solution techniques proposed for solving this class of large-scale convex optimization problems. We conduct some numerical experiments on the message routing problem with four different techniques.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:1:p:126-147
    DOI: 10.1287/mnsc.46.1.126.15132
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    References listed on IDEAS

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    4. Gürel, Sinan, 2011. "A conic quadratic formulation for a class of convex congestion functions in network flow problems," European Journal of Operational Research, Elsevier, vol. 211(2), pages 252-262, June.
    5. Wang, Shuaian, 2014. "A novel hybrid-link-based container routing model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 165-175.
    6. Morabito, Reinaldo & de Souza, Mauricio C. & Vazquez, Mariana, 2014. "Approximate decomposition methods for the analysis of multicommodity flow routing in generalized queuing networks," European Journal of Operational Research, Elsevier, vol. 232(3), pages 618-629.
    7. Lienkamp, Benedikt & Schiffer, Maximilian, 2024. "Column generation for solving large scale multi-commodity flow problems for passenger transportation," European Journal of Operational Research, Elsevier, vol. 314(2), pages 703-717.
    8. Srećko KRILE & Marina KRILE, 2015. "New approach in definition of multi-stop flight routes," Transport Problems, Silesian University of Technology, Faculty of Transport, vol. 10(1), pages 87-96, March.
    9. Maria Mitradjieva & Per Olov Lindberg, 2013. "The Stiff Is Moving---Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment ," Transportation Science, INFORMS, vol. 47(2), pages 280-293, May.
    10. Philippe Mahey & Jonas Koko & Arnaud Lenoir, 2017. "Decomposition methods for a spatial model for long-term energy pricing problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 137-153, February.
    11. Claude Lemaréchal, 2007. "The omnipresence of Lagrange," Annals of Operations Research, Springer, vol. 153(1), pages 9-27, September.
    12. Hammad, Ahmed W A & Akbarnezhad, Ali & Rey, David, 2017. "Sustainable urban facility location: Minimising noise pollution and network congestion," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 107(C), pages 38-59.
    13. Paraskevopoulos, Dimitris C. & Gürel, Sinan & Bektaş, Tolga, 2016. "The congested multicommodity network design problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 85(C), pages 166-187.
    14. Hela Masri & Saoussen Krichen, 2018. "Exact and approximate approaches for the Pareto front generation of the single path multicommodity flow problem," Annals of Operations Research, Springer, vol. 267(1), pages 353-377, August.
    15. Krzysztof C. Kiwiel & Torbjörn Larsson & P. O. Lindberg, 2007. "Lagrangian Relaxation via Ballstep Subgradient Methods," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 669-686, August.
    16. Artur Alves Pessoa & Michael Poss, 2015. "Robust Network Design with Uncertain Outsourcing Cost," INFORMS Journal on Computing, INFORMS, vol. 27(3), pages 507-524, August.
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    18. Ben-Israel, Adi & Levin, Genrikh & Levin, Yuri & Rozin, Boris, 2008. "Approximate methods for convex minimization problems with series-parallel structure," European Journal of Operational Research, Elsevier, vol. 189(3), pages 841-855, September.

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