IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v32y1984i4p837-846.html
   My bibliography  Save this article

Nonoptimal Edges for the Symmetric Traveling Salesman Problem

Author

Listed:
  • Roy Jonker

    (University of Amsterdam, Amsterdam, The Netherlands)

  • Ton Volgenant

    (University of Amsterdam, Amsterdam, The Netherlands)

Abstract

For the symmetric traveling salesman problem, we identify a set of (undirected) edges that can be eliminated while still retaining at least one optimal solution of the problem. The simple identification rules are based on the fact that a solution can be optimal only if it is 2-optimal. The rules are less stringent than those formulated for nonoptimal arcs (directed), applied to the symmetric case. So, in general, they identify more nonoptimal edges. Application of the theory in a 1-tree based traveling salesman algorithm roughly halves the average computation time for Euclidean problems. We indicate to what extent the theorems presented here can be adapted for variants of the traveling salesman problem.

Suggested Citation

  • Roy Jonker & Ton Volgenant, 1984. "Nonoptimal Edges for the Symmetric Traveling Salesman Problem," Operations Research, INFORMS, vol. 32(4), pages 837-846, August.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:4:p:837-846
    DOI: 10.1287/opre.32.4.837
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.32.4.837
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.32.4.837?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. R. Dekker & M. B. M. de Koster & K. J. Roodbergen & H. van Kalleveen, 2004. "Improving Order-Picking Response Time at Ankor's Warehouse," Interfaces, INFORMS, vol. 34(4), pages 303-313, August.
    2. Yuan Sun & Andreas Ernst & Xiaodong Li & Jake Weiner, 2021. "Generalization of machine learning for problem reduction: a case study on travelling salesman problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 607-633, September.

    More about this item

    Keywords

    491 nonoptimal edges;

    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:inm:oropre:v:32:y:1984:i:4:p:837-846. 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.