Primal and Dual Algorithms for Optimization over the Efficient Set

Liu, Zhengliang and Ehrgott, Matthias (2018) Primal and Dual Algorithms for Optimization over the Efficient Set. Optimization, 67 (10). pp. 1661-1686. ISSN 0233-1934

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Optimisation over the efficient set of a multi-objective optimisation problem is a mathematical model for the problem of selecting a most preferred solution that arises in multiple criteria decision making to account for trade-offs between objectives within the set of efficient solutions. In this paper we consider a particular case of this problem, namely that of optimising a linear function over the image of the efficient set in objective space of a convex multi-objective optimisation problem. We present both primal and dual algorithms for this task. The algorithms are based on recent algorithms for solving convex multi-objective optimisation problems in objective space with suitable modifications to exploit specific properties of the problem of optimisation over the efficient set. We first present the algorithms for the case that the underlying problem is a multi-objective linear programme. We then extend them to be able to solve problems with an underlying convex multiobjective optimisation problem.We compare the new algorithms with several state of the art algorithms from the literature on a set of randomly generated instances to demonstrate that they are considerably faster than the competitors.

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Journal Article
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This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization 2018, available online:
Uncontrolled Keywords:
?? multi-objective optimisation, optimisation over the efficient set, objective space algorithm, duality.optimisation over the efficient setobjective space algorithmdualitymathematics(all)control and optimizationmanagement science and operations researchappl ??
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01 Jun 2018 15:18
Last Modified:
30 Nov 2023 01:48