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Approximative solution methods for multiobjective combinatorial optimization

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Abstract

In this paper we present a review of approximative solution methods, that is, heuristics and metaheuristics designed for the solution of multiobjective combinatorial optimization problems (MOCO). First, we discuss questions related to approximation in this context, such as performance ratios, bounds, and quality measures. We give some examples of heuristics proposed for the solution of MOCO problems. The main part of the paper covers metaheuristics and more precisely non-evolutionary methods. The pioneering methods and their derivatives are described in a unified way. We provide an algorithmic presentation of each of the methods together with examples of applications, extensions, and a bibliographic note. Finally, we outline trends in this area.

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Authors and Affiliations

  1. Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland, New Zealand

    Matthias Ehrgott

  2. LAMIH — UMR CNRS 8530, University of Valenciennes, Campus “Le Mont Houy”, F-59313, Valenciennes cedex 9, France

    Xavier Gandibleux

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  1. Matthias Ehrgott
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  2. Xavier Gandibleux
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The research of M. Ehrgott has been partially supported by University of Auckland grant 3602178/9275 and grant Ka 477/27-1 of the Deutsche Forschungsgemeinschaft (DFG).

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Ehrgott, M., Gandibleux, X. Approximative solution methods for multiobjective combinatorial optimization. Top 12, 1–63 (2004). https://doi.org/10.1007/BF02578918

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