IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v131y2004i1p325-37210.1023-banor.0000039525.80601.15.html
   My bibliography  Save this article

Multilevel Refinement for Combinatorial Optimisation Problems

Author

Listed:
  • Chris Walshaw

Abstract

We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (sometimes for the original problem, sometimes the coarsest) and then iteratively refined at each level. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (most notably in the form of multigrid techniques). However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial optimisation problems. In this paper we address the issue of multilevel refinement for such problems and, with the aid of examples and results in graph partitioning, graph colouring and the travelling salesman problem, make a case for its use as a metaheuristic. The results provide compelling evidence that, although the multilevel framework cannot be considered as a panacea for combinatorial problems, it can provide an extremely useful addition to the combinatorial optimisation toolkit. We also give a possible explanation for the underlying process and extract some generic guidelines for its future use on other combinatorial problems. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Chris Walshaw, 2004. "Multilevel Refinement for Combinatorial Optimisation Problems," Annals of Operations Research, Springer, vol. 131(1), pages 325-372, October.
    • Handle: RePEc:spr:annopr:v:131:y:2004:i:1:p:325-372:10.1023/b:anor.0000039525.80601.15
    DOI: 10.1023/B:ANOR.0000039525.80601.15
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/B:ANOR.0000039525.80601.15
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/B:ANOR.0000039525.80601.15?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.

    Citations

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


    Cited by:

    1. Philippe Galinier & Zied Boujbel & Michael Coutinho Fernandes, 2011. "An efficient memetic algorithm for the graph partitioning problem," Annals of Operations Research, Springer, vol. 191(1), pages 1-22, November.
    2. Renzo Zamprogno & André R. S. Amaral, 2007. "An efficient approach for large scale graph partitioning," Journal of Combinatorial Optimization, Springer, vol. 13(4), pages 289-320, May.
    3. Henning Meyerhenke & Peter Sanders & Christian Schulz, 2016. "Partitioning (hierarchically clustered) complex networks via size-constrained graph clustering," Journal of Heuristics, Springer, vol. 22(5), pages 759-782, October.

    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:131:y:2004:i:1:p:325-372:10.1023/b:anor.0000039525.80601.15. 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: 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.