IDEAS home Printed from https://ideas.repec.org/h/spr/isochp/978-1-4939-3094-4_19.html
   My bibliography  Save this book chapter

Exact Methods for Multi-Objective Combinatorial Optimisation

In: Multiple Criteria Decision Analysis

Author

Listed:
  • Matthias Ehrgott

    (Lancaster University)

  • Xavier Gandibleux

    (Université de Nantes)

  • Anthony Przybylski

    (Université de Nantes)

Abstract

In this chapter we consider multi-objective optimisation problems with a combinatorial structure. Such problems have a discrete feasible set and can be formulated as integer (usually binary) optimisation problems with multiple (integer valued) objectives. We focus on a review of exact methods to solve such problems. First, we provide definitions of the most important classes of solutions and explore properties of such problems and their solution sets. Then we discuss the most common approaches to solve multi-objective combinatorial optimisation problems. These approaches include extensions of single objective algorithms, scalarisation methods, the two-phase method and multi-objective branch and bound. For each of the approaches we provide references to specific algorithms found in the literature. We end the chapter with a description of some other algorithmic approaches for MOCO problems and conclusions suggesting directions for future research.

Suggested Citation

  • Matthias Ehrgott & Xavier Gandibleux & Anthony Przybylski, 2016. "Exact Methods for Multi-Objective Combinatorial Optimisation," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 817-850, Springer.
    • Handle: RePEc:spr:isochp:978-1-4939-3094-4_19
    DOI: 10.1007/978-1-4939-3094-4_19
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Daş, Gülesin Sena & Gzara, Fatma & Stützle, Thomas, 2020. "A review on airport gate assignment problems: Single versus multi objective approaches," Omega, Elsevier, vol. 92(C).
    2. Tolga Bektaş, 2018. "Disjunctive Programming for Multiobjective Discrete Optimisation," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 625-633, November.
    3. Seyyed Amir Babak Rasmi & Ali Fattahi & Metin Türkay, 2021. "SASS: slicing with adaptive steps search method for finding the non-dominated points of tri-objective mixed-integer linear programming problems," Annals of Operations Research, Springer, vol. 296(1), pages 841-876, January.
    4. Barbati, Maria & Greco, Salvatore & Kadziński, Miłosz & Słowiński, Roman, 2018. "Optimization of multiple satisfaction levels in portfolio decision analysis," Omega, Elsevier, vol. 78(C), pages 192-204.
    5. Özarık, Sami Serkan & Lokman, Banu & Köksalan, Murat, 2020. "Distribution based representative sets for multi-objective integer programs," European Journal of Operational Research, Elsevier, vol. 284(2), pages 632-643.
    6. Stephan Helfrich & Arne Herzel & Stefan Ruzika & Clemens Thielen, 2022. "An approximation algorithm for a general class of multi-parametric optimization problems," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1459-1494, October.
    7. Guillermo Cabrera-Guerrero & Matthias Ehrgott & Andrew J. Mason & Andrea Raith, 2022. "Bi-objective optimisation over a set of convex sub-problems," Annals of Operations Research, Springer, vol. 319(2), pages 1507-1532, December.
    8. Barbati, Maria & Corrente, Salvatore & Greco, Salvatore, 2020. "A general space-time model for combinatorial optimization problems (and not only)," Omega, Elsevier, vol. 96(C).

    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:isochp:978-1-4939-3094-4_19. 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.