IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v36y2024i4p1084-1107.html
   My bibliography  Save this article

Exact and Heuristic Solution Techniques for Mixed-Integer Quantile Minimization Problems

Author

Listed:
  • Diego Cattaruzza

    (University Lille, CNRS, Centrale Lille, Inria, UMR 9189-CRIStAL, Lille, France)

  • Martine Labbé

    (Department of Computer Science, Université Libre de Bruxelles, 1050 Brussels, Belgium; Parc Scientifique de la Haute Borne, Inria Lille-Nord Europe, 59650 Villeneuve d’Ascq, France)

  • Matteo Petris

    (University Lille, CNRS, Centrale Lille, Inria, UMR 9189-CRIStAL, Lille, France)

  • Marius Roland

    (Department of Mathematics, Trier University, 54296 Trier, Germany)

  • Martin Schmidt

    (Department of Mathematics, Trier University, 54296 Trier, Germany)

Abstract

We consider mixed-integer linear quantile minimization problems that yield large-scale problems that are very hard to solve for real-world instances. We motivate the study of this problem class by two important real-world problems: a maintenance planning problem for electricity networks and a quantile-based variant of the classic portfolio optimization problem. For these problems, we develop valid inequalities and present an overlapping alternating direction method. Moreover, we discuss an adaptive scenario clustering method for which we prove that it terminates after a finite number of iterations with a global optimal solution. We study the computational impact of all presented techniques and finally show that their combination leads to an overall method that can solve the maintenance planning problem on large-scale real-world instances provided by the ROADEF/EURO challenge 2020 1 and that they also lead to significant improvements when solving a quantile-version of the classic portfolio optimization problem.

Suggested Citation

  • Diego Cattaruzza & Martine Labbé & Matteo Petris & Marius Roland & Martin Schmidt, 2024. "Exact and Heuristic Solution Techniques for Mixed-Integer Quantile Minimization Problems," INFORMS Journal on Computing, INFORMS, vol. 36(4), pages 1084-1107, July.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:4:p:1084-1107
    DOI: 10.1287/ijoc.2022.0105
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2022.0105
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2022.0105?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:4:p:1084-1107. 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.