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    Rights statement: This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization 2018, available online: https://www.tandfonline.com/doi/full/10.1080/02331934.2018.1484922

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    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

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Primal and Dual Algorithms for Optimization over the Efficient Set

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>2018
<mark>Journal</mark>Optimization
Issue number10
Volume67
Number of pages16
Pages (from-to)1661-1686
Publication StatusPublished
Early online date26/06/18
<mark>Original language</mark>English

Abstract

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.

Bibliographic note

This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization 2018, available online: https://www.tandfonline.com/doi/full/10.1080/02331934.2018.1484922