IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v34y1986i5p698-717.html
   My bibliography  Save this article

An Optimal Solution Method for Large-Scale Multiple Traveling Salesmen Problems

Author

Listed:
  • Bezalel Gavish

    (University of Rochester, Rochester, New York)

  • Kizhanathan Srikanth

    (University of Illinois, Chicago, Illinois)

Abstract

We develop an efficient branch-and-bound based method for solving the Multiple Traveling Salesman Problem, and develop lower bounds through a Lagrangean relaxation that requires computing a degree-constrained minimal spanning tree. A subgradient optimization procedure updates the Lagrange multipliers. We use fast sensitivity analysis techniques to increase the underlying graph sparsity and reduce the problem size. The algorithm was tested on 416 problems with up to 500 cities and 10 salesmen. We also present computational results on different data sets and parameters in order to identify the major factors that influence the performance of the developed code.

Suggested Citation

  • Bezalel Gavish & Kizhanathan Srikanth, 1986. "An Optimal Solution Method for Large-Scale Multiple Traveling Salesmen Problems," Operations Research, INFORMS, vol. 34(5), pages 698-717, October.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:5:p:698-717
    DOI: 10.1287/opre.34.5.698
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.34.5.698
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.34.5.698?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
    ---><---

    Citations

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


    Cited by:

    1. Bektas, Tolga, 2006. "The multiple traveling salesman problem: an overview of formulations and solution procedures," Omega, Elsevier, vol. 34(3), pages 209-219, June.
    2. Tamás Kalmár-Nagy & Giovanni Giardini & Bendegúz Dezső Bak, 2017. "The Multiagent Planning Problem," Complexity, Hindawi, vol. 2017, pages 1-12, February.
    3. Yuan, Shuai & Skinner, Bradley & Huang, Shoudong & Liu, Dikai, 2013. "A new crossover approach for solving the multiple travelling salesmen problem using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 228(1), pages 72-82.
    4. Dodin, B. & Elimam, A.A., 2008. "Integration of equipment planning and project scheduling," European Journal of Operational Research, Elsevier, vol. 184(3), pages 962-980, February.
    5. Henan Liu & Huili Zhang & Yi Xu, 2021. "The m-Steiner Traveling Salesman Problem with online edge blockages," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 844-860, May.
    6. Brian Lunday & Hanif Sherali & Kevin Lunday, 2012. "The coastal seaspace patrol sector design and allocation problem," Computational Management Science, Springer, vol. 9(4), pages 483-514, November.
    7. José Alejandro Cornejo-Acosta & Jesús García-Díaz & Julio César Pérez-Sansalvador & Carlos Segura, 2023. "Compact Integer Programs for Depot-Free Multiple Traveling Salesperson Problems," Mathematics, MDPI, vol. 11(13), pages 1-25, July.
    8. Funke, Julia & Kopfer, Herbert, 2016. "A model for a multi-size inland container transportation problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 89(C), pages 70-85.
    9. Luigi Di Puglia Pugliese & Francesca Guerriero, 2016. "On the shortest path problem with negative cost cycles," Computational Optimization and Applications, Springer, vol. 63(2), pages 559-583, March.
    10. Kara, Imdat & Bektas, Tolga, 2006. "Integer linear programming formulations of multiple salesman problems and its variations," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1449-1458, November.
    11. Johanns, Patrick & Lowe, Tim & Plante, Robert, 2001. "Selection and sequencing heuristics to reduce variance in gas turbine engine nozzle assemblies," European Journal of Operational Research, Elsevier, vol. 132(3), pages 490-504, August.
    12. Çavdar, Bahar & Sokol, Joel, 2015. "TSP Race: Minimizing completion time in time-sensitive applications," European Journal of Operational Research, Elsevier, vol. 244(1), pages 47-54.

    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:34:y:1986:i:5:p:698-717. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.