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Exact Methods for Multi-Objective Combinatorial Optimisation

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Multiple Criteria Decision Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 233))

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.

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Authors and Affiliations

  1. Department of Management Science, Lancaster University, Bailrigg, Lancaster, LA1 4YX, UK

    Matthias Ehrgott

  2. Faculté des Sciences et des Techniques, Université de Nantes, 44322, Nantes Cedex 03, France

    Xavier Gandibleux & Anthony Przybylski

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  1. Matthias Ehrgott
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  2. Xavier Gandibleux
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Editors and Affiliations

  1. Department of Economics and Business; Portsmouth Business School, Operations & Systems Management, University of Catania; University of Portsmouth, Catania; Portsmouth, Italy

    Salvatore Greco

  2. Department of Management Science, Lancaster University, Lancaster, United Kingdom

    Matthias Ehrgott

  3. Universidade de Lisboa, CEG-IST, Instituto Superior Técnico, Lisboa, Portugal

    José Rui Figueira

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Ehrgott, M., Gandibleux, X., Przybylski, A. (2016). Exact Methods for Multi-Objective Combinatorial Optimisation. In: Greco, S., Ehrgott, M., Figueira, J. (eds) Multiple Criteria Decision Analysis. International Series in Operations Research & Management Science, vol 233. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3094-4_19

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