IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v100y2024i1d10.1007_s00186-023-00843-y.html
   My bibliography  Save this article

A fast and robust algorithm for solving biobjective mixed integer programs

Author

Listed:
  • Diego Pecin

    (Erasmus University Rotterdam)

  • Ian Herszterg

    (Georgia Institute of Technology)

  • Tyler Perini

    (United States Naval Academy)

  • Natashia Boland

    (Georgia Institute of Technology)

  • Martin Savelsbergh

    (Georgia Institute of Technology)

Abstract

We present a fast and robust algorithm for solving biobjective mixed integer linear programs. Two existing methods are studied: $$\epsilon $$ ϵ -Tabu Method and the Boxed Line Method. By observing structural characteristics of nondominated frontiers and computational bottlenecks, we develop enhanced versions of each method. Limitations of the current state of test instances are observed, and a new body of instances are generated to diversify computational standards. We demonstrate efficacy with a computational study. The enhancement to $$\epsilon $$ ϵ -Tabu Method offers an average speed-up factor of 3 on some instances; the enhancement to Boxed Line Method offers an average speed-up factor of 18 on some instances. A hybrid, two-phase method is designed to leverage the strengths of each method with its corresponding enhancement, thus having a robust approach to a wider range of instances; it outperforms on all instances with a typical speed-up factor of 2–3. We also demonstrate that it is capable of producing a high-quality approximation of the nondominated frontier in a fraction of the time required to produce the complete nondominated frontier. Graphic Abstract

Suggested Citation

  • Diego Pecin & Ian Herszterg & Tyler Perini & Natashia Boland & Martin Savelsbergh, 2024. "A fast and robust algorithm for solving biobjective mixed integer programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 221-262, August.
    • Handle: RePEc:spr:mathme:v:100:y:2024:i:1:d:10.1007_s00186-023-00843-y
    DOI: 10.1007/s00186-023-00843-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-023-00843-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/s00186-023-00843-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:mathme:v:100:y:2024:i:1:d:10.1007_s00186-023-00843-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.