IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v36y2024i6p1522-1542.html
   My bibliography  Save this article

Decision Diagram-Based Branch-and-Bound with Caching for Dominance and Suboptimality Detection

Author

Listed:
  • Vianney Coppé

    (UCLouvain, 1348 Louvain-la-Neuve, Belgium)

  • Xavier Gillard

    (UCLouvain, 1348 Louvain-la-Neuve, Belgium)

  • Pierre Schaus

    (UCLouvain, 1348 Louvain-la-Neuve, Belgium)

Abstract

The branch-and-bound algorithm based on decision diagrams is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width decision diagrams that can provide lower and upper bounds for any given subproblem. Eventually, every part of the search space will be either explored or pruned by the algorithm, thus proving optimality. This paper presents new ingredients to speed up the search by exploiting the structure of dynamic programming models. The key idea is to prevent the repeated expansion of nodes corresponding to the same dynamic programming states by querying expansion thresholds cached throughout the search. These thresholds are based on dominance relations between partial solutions previously found and on pruning inequalities given by rough upper bounds and local bounds — two additional filtering techniques recently introduced. Computational experiments show that the pruning brought by this caching mechanism allows for significantly reducing the number of nodes expanded by the algorithm. This results in more benchmark instances of difficult optimization problems being solved in less time while using narrower decision diagrams.

Suggested Citation

  • Vianney Coppé & Xavier Gillard & Pierre Schaus, 2024. "Decision Diagram-Based Branch-and-Bound with Caching for Dominance and Suboptimality Detection," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1522-1542, December.
  • Handle: RePEc:inm:orijoc:v:36:y:2024:i:6:p:1522-1542
    DOI: 10.1287/ijoc.2022.0340
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2022.0340
    Download Restriction: no

    File URL: https://libkey.io/10.1287/ijoc.2022.0340?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
    ---><---

    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:orijoc:v:36:y:2024:i:6:p:1522-1542. 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.