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

•Discrete representation of non-dominated sets relates to NP-hard location problems.•Known methods do not have the coverage property or bound the uniformity level.•Under some assumptions the RNBI method has bounded uniformity level and coverage error.•Empirical tests on applied problems and random e...

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Veröffentlicht in:European journal of operational research Jg. 255; H. 3; S. 687 - 698
Hauptverfasser: Shao, Lizhen, Ehrgott, Matthias
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 16.12.2016
Elsevier Sequoia S.A
Schlagworte:
Decision making
Discrete representation
Linear programming
Multi-objective optimisation
Non-dominated set
Optimization techniques
Problem solving
Radiation therapy
Studies
Linear programming
Non-dominated set
Discrete representation
Multi-objective optimisation
ISSN:0377-2217, 1872-6860
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Zusammenfassung:•Discrete representation of non-dominated sets relates to NP-hard location problems.•Known methods do not have the coverage property or bound the uniformity level.•Under some assumptions the RNBI method has bounded uniformity level and coverage error.•Empirical tests on applied problems and random examples validate the RNBI method. In this paper we address the problem of representing the continuous but non-convex set of non-dominated 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.
Bibliographie:SourceType-Scholarly Journals-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2016.05.001