IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v20y1972i5p1044-1056.html
   My bibliography  Save this article

Technical Note—Bounds for the Travelling-Salesman Problem

Author

Listed:
  • Nicos Christofides

    (Imperial College of Science and Technology, London, England)

Abstract

This paper concerns finding a tight lower bound to the travelling-salesman problem, with the hope that all the different branch-and-bound algorithms for this problem can benefit from it. The bound is calculated by an iterative procedure with guaranteed convergence and is shown to require a computation time only about 9 per cent greater than the time required to solve an equivalent assignment problem. This new bound was tested on 14 sample problems and, on the average, found to be only 4.7 per cent below the optimum for symmetrical, and 3.8 per cent below the optimum for asymmetrical problems.

Suggested Citation

  • Nicos Christofides, 1972. "Technical Note—Bounds for the Travelling-Salesman Problem," Operations Research, INFORMS, vol. 20(5), pages 1044-1056, October.
  • Handle: RePEc:inm:oropre:v:20:y:1972:i:5:p:1044-1056
    DOI: 10.1287/opre.20.5.1044
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.20.5.1044
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.20.5.1044?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. Douglas G. Macharet & Armando Alves Neto & Vila F. Camara Neto & Mario F. M. Campos, 2018. "Dynamic region visit routing problem for vehicles with minimum turning radius," Journal of Heuristics, Springer, vol. 24(1), pages 83-109, February.
    2. Raadsen, Mark P.H. & Bliemer, Michiel C.J. & Bell, Michael G.H., 2020. "Aggregation, disaggregation and decomposition methods in traffic assignment: historical perspectives and new trends," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 199-223.

    More about this item

    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:20:y:1972:i:5:p:1044-1056. 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.