IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v351y2025i1d10.1007_s10479-024-06303-y.html
   My bibliography  Save this article

Volume-based branch-and-cut algorithm for large-scale fixed-charge multicommodity network design

Author

Listed:
  • Rui S. Shibasaki

    (UPJV
    UCA
    UFMG)

  • Mourad Baïou

    (UCA)

  • Francisco Barahona

    (IBM)

  • Philippe Mahey

    (UCA)

  • Maurício C. de Souza

    (UFMG)

Abstract

The fixed-charge multicommodity capacitated network design (FCMC) problem remains challenging, particularly in large-scale contexts. In this particular case, the ability to produce good-quality solutions in a reasonable amount of time depends on the availability of efficient algorithms. Therefore, this paper proposes a Volume-based branch-and-cut algorithm, which applies a relax-and-cut procedure to solve linear programs in each node of the enumeration tree. Moreover, a Lagrangian feasibility pump heuristic using the Volume Algorithm as a solver for linear programs was implemented to accelerate the search for good feasible solutions in large-scale cases. The obtained results showed that the proposed branch-and-cut scheme is competitive with other state-of-the-art algorithms, and presents better performance when solving large-scale instances.

Suggested Citation

  • Rui S. Shibasaki & Mourad Baïou & Francisco Barahona & Philippe Mahey & Maurício C. de Souza, 2025. "Volume-based branch-and-cut algorithm for large-scale fixed-charge multicommodity network design," Annals of Operations Research, Springer, vol. 351(1), pages 133-166, August.
    • Handle: RePEc:spr:annopr:v:351:y:2025:i:1:d:10.1007_s10479-024-06303-y
    DOI: 10.1007/s10479-024-06303-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-024-06303-y
    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/s10479-024-06303-y?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Paraskevopoulos, Dimitris C. & Bektaş, Tolga & Crainic, Teodor Gabriel & Potts, Chris N., 2016. "A cycle-based evolutionary algorithm for the fixed-charge capacitated multi-commodity network design problem," European Journal of Operational Research, Elsevier, vol. 253(2), pages 265-279.
    2. Ilfat Ghamlouche & Teodor Crainic & Michel Gendreau, 2004. "Path Relinking, Cycle-Based Neighbourhoods and Capacitated Multicommodity Network Design," Annals of Operations Research, Springer, vol. 131(1), pages 109-133, October.
    3. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    4. 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.
    5. Zonghao Gu & George L. Nemhauser & Martin W. P. Savelsbergh, 1998. "Lifted Cover Inequalities for 0-1 Integer Programs: Computation," INFORMS Journal on Computing, INFORMS, vol. 10(4), pages 427-437, November.
    6. Kaj Holmberg & Di Yuan, 2000. "A Lagrangian Heuristic Based Branch-and-Bound Approach for the Capacitated Network Design Problem," Operations Research, INFORMS, vol. 48(3), pages 461-481, June.
    7. Abilio Lucena, 2005. "Non Delayed Relax-and-Cut Algorithms," Annals of Operations Research, Springer, vol. 140(1), pages 375-410, November.
    8. Gianni Codato & Matteo Fischetti, 2006. "Combinatorial Benders' Cuts for Mixed-Integer Linear Programming," Operations Research, INFORMS, vol. 54(4), pages 756-766, August.
    9. Andrea Lodi & Giulia Zarpellon, 2017. "Rejoinder on: On learning and branching: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 247-248, July.
    10. Sridhar, Varadharajan & Park, June S., 2000. "Benders-and-cut algorithm for fixed-charge capacitated network design problem," European Journal of Operational Research, Elsevier, vol. 125(3), pages 622-632, September.
    11. Alysson Costa & Jean-François Cordeau & Bernard Gendron, 2009. "Benders, metric and cutset inequalities for multicommodity capacitated network design," Computational Optimization and Applications, Springer, vol. 42(3), pages 371-392, April.
    12. Mervat Chouman & Teodor Gabriel Crainic & Bernard Gendron, 2017. "Commodity Representations and Cut-Set-Based Inequalities for Multicommodity Capacitated Fixed-Charge Network Design," Transportation Science, INFORMS, vol. 51(2), pages 650-667, May.
    13. Mervat Chouman & Teodor Gabriel Crainic & Bernard Gendron, 2018. "The impact of filtering in a branch-and-cut algorithm for multicommodity capacitated fixed charge network design," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(2), pages 143-184, June.
    14. Andrea Lodi & Giulia Zarpellon, 2017. "On learning and branching: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 207-236, July.
    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. 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.
    2. Mervat Chouman & Teodor Gabriel Crainic & Bernard Gendron, 2018. "The impact of filtering in a branch-and-cut algorithm for multicommodity capacitated fixed charge network design," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(2), pages 143-184, June.
    3. Gendron, Bernard & Hanafi, Saïd & Todosijević, Raca, 2018. "Matheuristics based on iterative linear programming and slope scaling for multicommodity capacitated fixed charge network design," European Journal of Operational Research, Elsevier, vol. 268(1), pages 70-81.
    4. Robinson La Rocca, Charly & Cordeau, Jean-François & Frejinger, Emma, 2024. "Combining supervised learning and local search for the multicommodity capacitated fixed-charge network design problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 192(C).
    5. Fragkos, Ioannis & Cordeau, Jean-François & Jans, Raf, 2021. "Decomposition methods for large-scale network expansion problems," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 60-80.
    6. Mervat Chouman & Teodor Gabriel Crainic & Bernard Gendron, 2017. "Commodity Representations and Cut-Set-Based Inequalities for Multicommodity Capacitated Fixed-Charge Network Design," Transportation Science, INFORMS, vol. 51(2), pages 650-667, May.
    7. Masoud Yaghini & Mohammad Karimi & Mohadeseh Rahbar & Mohammad Hassan Sharifitabar, 2015. "A Cutting-Plane Neighborhood Structure for Fixed-Charge Capacitated Multicommodity Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 48-58, February.
    8. Bernard Gendron & Luis Gouveia, 2017. "Reformulations by Discretization for Piecewise Linear Integer Multicommodity Network Flow Problems," Transportation Science, INFORMS, vol. 51(2), pages 629-649, May.
    9. Ada Alvarez & José González-Velarde & Karim De-Alba, 2005. "Scatter Search for Network Design Problem," Annals of Operations Research, Springer, vol. 138(1), pages 159-178, September.
    10. Tobias Harks & Felix G. König & Jannik Matuschke & Alexander T. Richter & Jens Schulz, 2016. "An Integrated Approach to Tactical Transportation Planning in Logistics Networks," Transportation Science, INFORMS, vol. 50(2), pages 439-460, May.
    11. Rodriguez-Martin, Inmaculada & Salazar-Gonzalez, Juan Jose, 2008. "Solving a capacitated hub location problem," European Journal of Operational Research, Elsevier, vol. 184(2), pages 468-479, January.
    12. Clautiaux, François & Ljubić, Ivana, 2025. "Last fifty years of integer linear programming: A focus on recent practical advances," European Journal of Operational Research, Elsevier, vol. 324(3), pages 707-731.
    13. Ahmad Baubaid & Natashia Boland & Martin Savelsbergh, 2021. "The Value of Limited Flexibility in Service Network Designs," Transportation Science, INFORMS, vol. 55(1), pages 52-74, 1-2.
    14. Stefan Gollowitzer & Bernard Gendron & Ivana Ljubić, 2013. "A cutting plane algorithm for the Capacitated Connected Facility Location Problem," Computational Optimization and Applications, Springer, vol. 55(3), pages 647-674, July.
    15. Ahmad I. Jarrah & Ellis Johnson & Lucas C. Neubert, 2009. "Large-Scale, Less-than-Truckload Service Network Design," Operations Research, INFORMS, vol. 57(3), pages 609-625, June.
    16. Mike Hewitt & George L. Nemhauser & Martin W. P. Savelsbergh, 2010. "Combining Exact and Heuristic Approaches for the Capacitated Fixed-Charge Network Flow Problem," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 314-325, May.
    17. Bissan Ghaddar & Ignacio Gómez-Casares & Julio González-Díaz & Brais González-Rodríguez & Beatriz Pateiro-López & Sofía Rodríguez-Ballesteros, 2023. "Learning for Spatial Branching: An Algorithm Selection Approach," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1024-1043, September.
    18. SteadieSeifi, M. & Dellaert, N.P. & Nuijten, W. & Van Woensel, T., 2017. "A metaheuristic for the multimodal network flow problem with product quality preservation and empty repositioning," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 321-344.
    19. Brais González-Rodríguez & Joaquín Ossorio-Castillo & Julio González-Díaz & Ángel M. González-Rueda & David R. Penas & Diego Rodríguez-Martínez, 2023. "Computational advances in polynomial optimization: RAPOSa, a freely available global solver," Journal of Global Optimization, Springer, vol. 85(3), pages 541-568, March.
    20. Shen, Yunzhuang & Sun, Yuan & Li, Xiaodong & Eberhard, Andrew & Ernst, Andreas, 2023. "Adaptive solution prediction for combinatorial optimization," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1392-1408.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:annopr:v:351:y:2025:i:1:d:10.1007_s10479-024-06303-y. 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.