Exact Methods for Multi-Objective Combinatorial Optimisation

Matthias Ehrgott (), Xavier Gandibleux () and Anthony Przybylski ()
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Matthias Ehrgott: Lancaster University
Xavier Gandibleux: Université de Nantes
Anthony Przybylski: Université de Nantes

Chapter Chapter 19 in Multiple Criteria Decision Analysis, 2016, pp 817-850 from Springer

Abstract: 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.

Keywords: Multi-objective optimisation; Combinatorial optimisation; Exact methods; Scalarisation; Branch and bound; Two-phase method (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-1-4939-3094-4_19

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