IDEAS home Printed from https://ideas.repec.org/a/spr/orspec/v46y2024i4d10.1007_s00291-024-00746-2.html
   My bibliography  Save this article

Matheuristic fixed set search applied to the multidimensional knapsack problem and the knapsack problem with forfeit sets

Author

Listed:
  • Raka Jovanovic

    (Hamad bin Khalifa University)

  • Stefan Voß

    (University of Hamburg
    Pontificia Universidad Católica de Valparaíso)

Abstract

In this paper, we present a solution method for the multidimensional knapsack problem (MKP) and the knapsack problem with forfeit sets (KPFS) using a population-based matheuristic approach. Specifically, the learning mechanism of the fixed set search (FSS) metaheuristic is combined with the use of integer programming for solving subproblems. This is achieved by introducing a new ground set of elements that can be used for both the MKP and the KPFS that aim to maximize the information provided by the fixed set. The method for creating fixed sets is also adjusted to enhance the diversity of generated solutions. Compared to state-of-the-art methods for the MKP and the KPFS, the proposed approach offers an implementation that can be easily extended to other variants of the knapsack problem. Computational experiments indicate that the matheuristic FSS is highly competitive to best-performing methods from the literature. The proposed approach is robust in the sense of having a good performance for a wide range of parameter values of the method.

Suggested Citation

  • Raka Jovanovic & Stefan Voß, 2024. "Matheuristic fixed set search applied to the multidimensional knapsack problem and the knapsack problem with forfeit sets," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(4), pages 1329-1365, December.
    • Handle: RePEc:spr:orspec:v:46:y:2024:i:4:d:10.1007_s00291-024-00746-2
    DOI: 10.1007/s00291-024-00746-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00291-024-00746-2
    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/s00291-024-00746-2?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:orspec:v:46:y:2024:i:4:d:10.1007_s00291-024-00746-2. 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.