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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
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    Citations

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    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. 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.
    3. Pedersen, Jaap & Weinand, Jann Michael & Syranidou, Chloi & Rehfeldt, Daniel, 2024. "An efficient solver for large-scale onshore wind farm siting including cable routing," European Journal of Operational Research, Elsevier, vol. 317(2), pages 616-630.
    4. 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.
    5. 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.
    6. 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.
    7. Tolga Bektaş, 2018. "Disjunctive Programming for Multiobjective Discrete Optimisation," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 625-633, November.
    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).
    9. 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.

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