IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v81y2021i3d10.1007_s10898-020-00967-z.html
   My bibliography  Save this article

An exact separation algorithm for unsplittable flow capacitated network design arc-set polyhedron

Author

Listed:
  • Liang Chen

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

  • Wei-Kun Chen

    (Beijing Institute of Technology)

  • Mu-Ming Yang

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

  • Yu-Hong Dai

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

Abstract

In this paper, we concentrate on generating cutting planes for the unsplittable capacitated network design problem. We use the unsplittable flow arc-set polyhedron of the considered problem as a substructure and generate cutting planes by solving the separation problem over it. To relieve the computational burden, we show that, in some special cases, a closed form of the separation problem can be derived. For the general case, a brute-force algorithm, called exact separation algorithm, is employed in solving the separation problem of the considered polyhedron such that the constructed inequality guarantees to be facet-defining. Furthermore, a new technique is presented to accelerate the exact separation algorithm, which significantly decreases the number of iterations in the algorithm. Finally, a comprehensive computational study on the unsplittable capacitated network design problem is presented to demonstrate the effectiveness of the proposed algorithm.

Suggested Citation

  • Liang Chen & Wei-Kun Chen & Mu-Ming Yang & Yu-Hong Dai, 2021. "An exact separation algorithm for unsplittable flow capacitated network design arc-set polyhedron," Journal of Global Optimization, Springer, vol. 81(3), pages 659-689, November.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:3:d:10.1007_s10898-020-00967-z
    DOI: 10.1007/s10898-020-00967-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-020-00967-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-020-00967-z?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bezalel Gavish & Kemal Altinkemer, 1990. "Backbone Network Design Tools with Economic Tradeoffs," INFORMS Journal on Computing, INFORMS, vol. 2(3), pages 236-252, August.
    2. F. Sibel Salman & R. Ravi & John N. Hooker, 2008. "Solving the Capacitated Local Access Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 243-254, May.
    3. Itzhak Gilboa & Sunil Chopra & S. Trilochan Sastri, 1998. "Source Sink Flows with Capacity Installation in Batches," Post-Print hal-00753123, HAL.
    4. Matteo Fischetti & Michele Monaci, 2014. "Exploiting Erraticism in Search," Operations Research, INFORMS, vol. 62(1), pages 114-122, February.
    5. Pasquale Avella & Maurizio Boccia & Igor Vasilyev, 2010. "A computational study of exact knapsack separation for the generalized assignment problem," Computational Optimization and Applications, Springer, vol. 45(3), pages 543-555, April.
    6. David Pisinger, 2000. "A Minimal Algorithm for the Bounded Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 75-82, February.
    7. 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.
    8. Thomas L. Magnanti & Prakash Mirchandani & Rita Vachani, 1995. "Modeling and Solving the Two-Facility Capacitated Network Loading Problem," Operations Research, INFORMS, vol. 43(1), pages 142-157, February.
    9. E. Andrew Boyd, 1994. "Fenchel Cutting Planes for Integer Programs," Operations Research, INFORMS, vol. 42(1), pages 53-64, February.
    Full references (including those not matched with items on IDEAS)

    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. F. Sibel Salman & R. Ravi & John N. Hooker, 2008. "Solving the Capacitated Local Access Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 243-254, May.
    2. Yogesh K. Agarwal, 2002. "Design of Capacitated Multicommodity Networks with Multiple Facilities," Operations Research, INFORMS, vol. 50(2), pages 333-344, April.
    3. Jinil Han & Kyungsik Lee & Chungmok Lee & Sungsoo Park, 2013. "Exact Algorithms for a Bandwidth Packing Problem with Queueing Delay Guarantees," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 585-596, August.
    4. Seohee Kim & Chungmok Lee, 2021. "A branch and price approach for the robust bandwidth packing problem with queuing delays," Annals of Operations Research, Springer, vol. 307(1), pages 251-275, December.
    5. Bita Tadayon & J. Cole Smith, 2014. "Algorithms for an Integer Multicommodity Network Flow Problem with Node Reliability Considerations," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 506-532, May.
    6. Pasquale Avella & Maurizio Boccia & Igor Vasilyev, 2012. "Computational Testing of a Separation Procedure for the Knapsack Set with a Single Continuous Variable," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 165-171, February.
    7. Ashwin Arulselvan & Mohsen Rezapour, 2017. "Exact Approaches for Designing Multifacility Buy-at-Bulk Networks," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 597-611, November.
    8. Gendron, Bernard & Potvin, Jean-Yves & Soriano, Patrick, 2002. "Diversification strategies in local search for a nonbifurcated network loading problem," European Journal of Operational Research, Elsevier, vol. 142(2), pages 231-241, October.
    9. Babonneau, F. & Vial, J.-P., 2010. "A partitioning algorithm for the network loading problem," European Journal of Operational Research, Elsevier, vol. 204(1), pages 173-179, July.
    10. Christopher Hojny & Tristan Gally & Oliver Habeck & Hendrik Lüthen & Frederic Matter & Marc E. Pfetsch & Andreas Schmitt, 2020. "Knapsack polytopes: a survey," Annals of Operations Research, Springer, vol. 292(1), pages 469-517, September.
    11. Ali Amiri & Hasan Pirkul, 1997. "Routing in packet‐switched communication networks with different criticality classes of communicating node pairs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(5), pages 485-505, August.
    12. Linos F. Frantzeskakis & Hanan Luss, 1999. "The network redesign problem for access telecommunications networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 487-506, August.
    13. Andrew P. Armacost & Cynthia Barnhart & Keith A. Ware, 2002. "Composite Variable Formulations for Express Shipment Service Network Design," Transportation Science, INFORMS, vol. 36(1), pages 1-20, February.
    14. Fortz, Bernard & Gouveia, Luís & Joyce-Moniz, Martim, 2017. "Models for the piecewise linear unsplittable multicommodity flow problems," European Journal of Operational Research, Elsevier, vol. 261(1), pages 30-42.
    15. Chardy, M. & Costa, M.-C. & Faye, A. & Trampont, M., 2012. "Optimizing splitter and fiber location in a multilevel optical FTTH network," European Journal of Operational Research, Elsevier, vol. 222(3), pages 430-440.
    16. Elisangela Martins de Sá & Ivan Contreras & Jean-François Cordeau & Ricardo Saraiva de Camargo & Gilberto de Miranda, 2015. "The Hub Line Location Problem," Transportation Science, INFORMS, vol. 49(3), pages 500-518, August.
    17. Agarwal, Y.K. & Aneja, Y.P. & Jayaswal, Sachin, 2022. "Directed fixed charge multicommodity network design: A cutting plane approach using polar duality," European Journal of Operational Research, Elsevier, vol. 299(1), pages 118-136.
    18. C S Sung & S H Song, 2003. "Integrated service network design for a cross-docking supply chain network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(12), pages 1283-1295, December.
    19. Melchiori, Anna & Sgalambro, Antonino, 2020. "A branch and price algorithm to solve the Quickest Multicommodity k-splittable Flow Problem," European Journal of Operational Research, Elsevier, vol. 282(3), pages 846-857.
    20. Amy Cohn & Michael Magazine & George Polak, 2009. "Rank‐Cluster‐and‐Prune: An algorithm for generating clusters in complex set partitioning problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(3), pages 215-225, 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:spr:jglopt:v:81:y:2021:i:3:d:10.1007_s10898-020-00967-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.