IDEAS home Printed from https://ideas.repec.org/a/spr/joheur/v27y2021i6d10.1007_s10732-021-09484-y.html
   My bibliography  Save this article

A probabilistic analysis of neighborhoods for combinatorial optimization problems and its application

Author

Listed:
  • Taichi Kaji

    (Otaru University of Commerce)

Abstract

Metaheuristics are a class of approximate methods, which are designed to attack hard combinatorial optimization problems. In metaheuristics, a neighborhood is defined by the specified move operation for a solution. The neighborhood plays an essential role in the performance of its algorithms. It is important to capture the statistical properties of neighborhoods. In this paper, we present a theoretical analysis of neighborhoods for a wide class of combinatorial optimization problems, instead of just for restricted instances. First, we give a probabilistic model which allows us to compute statistics for various types of neighborhoods. Here we introduce an approach in which the solution space (the landscape) for a wide class of combinatorial optimization problems can be approximated to AR(1), which can be used to capture the statistics of the solution space. The theoretical results obtained from our proposed model closely match empirically observed behavior. Second, we present an application in which we use our probabilistic model of neighborhoods.

Suggested Citation

  • Taichi Kaji, 2021. "A probabilistic analysis of neighborhoods for combinatorial optimization problems and its application," Journal of Heuristics, Springer, vol. 27(6), pages 1057-1079, December.
    • Handle: RePEc:spr:joheur:v:27:y:2021:i:6:d:10.1007_s10732-021-09484-y
    DOI: 10.1007/s10732-021-09484-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10732-021-09484-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/s10732-021-09484-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 search for a different version of it.

    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:joheur:v:27:y:2021:i:6:d:10.1007_s10732-021-09484-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.

    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.