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

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Discrete representation of non-dominated sets in multi-objective linear programming. / Shao, Lizhen; Ehrgott, Matthias.

In: European Journal of Operational Research, Vol. 255, No. 3, 16.12.2016, p. 687-698.

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Shao, Lizhen ; Ehrgott, Matthias. / Discrete representation of non-dominated sets in multi-objective linear programming. In: European Journal of Operational Research. 2016 ; Vol. 255, No. 3. pp. 687-698.

Bibtex

@article{5d7fb55495a44a8bbef6ce0cb7d39dd4,
title = "Discrete representation of non-dominated sets in multi-objective linear programming",
abstract = "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 computesa 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.",
keywords = "Multi-objective optimisation, linear programming, non-dominated set, discrete representation",
author = "Lizhen Shao and Matthias Ehrgott",
note = "This is the author{\textquoteright}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",
year = "2016",
month = dec,
day = "16",
doi = "10.1016/j.ejor.2016.05.001",
language = "English",
volume = "255",
pages = "687--698",
journal = "European Journal of Operational Research",
issn = "0377-2217",
publisher = "Elsevier Science B.V.",
number = "3",

}

RIS

TY - JOUR

T1 - Discrete representation of non-dominated sets in multi-objective linear programming

AU - Shao, Lizhen

AU - Ehrgott, Matthias

N1 - 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

PY - 2016/12/16

Y1 - 2016/12/16

N2 - 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 computesa 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.

AB - 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 computesa 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.

KW - Multi-objective optimisation

KW - linear programming

KW - non-dominated set

KW - discrete representation

U2 - 10.1016/j.ejor.2016.05.001

DO - 10.1016/j.ejor.2016.05.001

M3 - Journal article

VL - 255

SP - 687

EP - 698

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 3

ER -