Discrete representation of non-dominated sets in multi-objective linear programming

Shao, Lizhen and Ehrgott, Matthias (2016) Discrete representation of non-dominated sets in multi-objective linear programming. European Journal of Operational Research, 255 (3). pp. 687-698. ISSN 0377-2217

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In this paper we address the problem of representing the continuous but non-convex set of nondominated points of a multi-objective linear programme by a finite subset of such points. We prove that a related decision problem is NP-complete. Moreover, we illustrate the drawbacks of the known global shooting, normal boundary intersection and normal constraint methods concerning the coverage error and uniformity level of the representation by examples. We propose a method which combines the global shooting and normal boundary intersection methods. By doing so, we overcome their limitations, but preserve their advantages. We prove that our method computes a set of evenly distributed non-dominated points for which the coverage error and the uniformity level can be guaranteed. We apply this method to an optimisation problem in radiation therapy and present illustrative results for some clinical cases. Finally, we present numerical results on randomly generated examples.

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Journal Article
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European Journal of Operational Research
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This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published inEuropean Journal of Operational Research, 255, 3, 2016 DOI: 10.1016/j.ejor.2016.05.001
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25 May 2016 08:06
Last Modified:
03 Jun 2022 23:34