IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v50y2002i2p260-276.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.50.2.260.436
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.50.2.260.436?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2020. "Essentials of numerical nonsmooth optimization," 4OR, Springer, vol. 18(1), pages 1-47, March.
    3. Gondzio, J. & Sarkissian, R. & Vial, J.-P., 1997. "Using an interior point method for the master problem in a decomposition approach," European Journal of Operational Research, Elsevier, vol. 101(3), pages 577-587, September.
    4. Jean-Philippe Vial, 1997. "A path-following version of the Todd-Burrell procedure for linear programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 153-167, June.
    5. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2022. "Essentials of numerical nonsmooth optimization," Annals of Operations Research, Springer, vol. 314(1), pages 213-253, July.
    6. L. M. Graña Drummond & B. F. Svaiter, 1999. "On Well Definedness of the Central Path," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 223-237, August.
    7. 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.
    8. Alexandre Belloni, 2008. "Norm-Induced Densities and Testing the Boundedness of a Convex Set," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 235-256, February.
    9. Júlíus Atlason & Marina A. Epelman & Shane G. Henderson, 2008. "Optimizing Call Center Staffing Using Simulation and Analytic Center Cutting-Plane Methods," Management Science, INFORMS, vol. 54(2), pages 295-309, February.
    10. Zhang, M. & Pel, A.J., 2016. "Synchromodal hinterland freight transport: Model study for the port of Rotterdam," Journal of Transport Geography, Elsevier, vol. 52(C), pages 1-10.
    11. Rina R. Schneur & James B. Orlin, 1998. "A Scaling Algorithm for Multicommodity Flow Problems," Operations Research, INFORMS, vol. 46(2), pages 231-246, April.
    12. Dereniowski, Dariusz & Kubiak, Wiesław, 2020. "Shared processor scheduling of multiprocessor jobs," European Journal of Operational Research, Elsevier, vol. 282(2), pages 464-477.
    13. Balaji Gopalakrishnan & Seunghyun Kong & Earl Barnes & Ellis Johnson & Joel Sokol, 2011. "A least-squares minimum-cost network flow algorithm," Annals of Operations Research, Springer, vol. 186(1), pages 119-140, June.
    14. G. Y. Zhao, 1999. "Interior-Point Methods with Decomposition for Solving Large-Scale Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 169-192, July.
    15. Wang, Gang, 2024. "Order assignment and two-stage integrated scheduling in fruit and vegetable supply chains," Omega, Elsevier, vol. 124(C).
    16. Klose, Andreas & Gortz, Simon, 2007. "A branch-and-price algorithm for the capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1109-1125, June.
    17. Samir Elhedhli & Jean-Louis Goffin, 2005. "Efficient Production-Distribution System Design," Management Science, INFORMS, vol. 51(7), pages 1151-1164, July.
    18. 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.
    19. Kurt Jörnsten & Andreas Klose, 2016. "An improved Lagrangian relaxation and dual ascent approach to facility location problems," Computational Management Science, Springer, vol. 13(3), pages 317-348, July.
    20. Shoshana Anily, 1996. "The vehicle‐routing problem with delivery and back‐haul options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 415-434, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:50:y:2002:i:2:p:260-276. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.