A Benson-type algorithm for bounded convex vector optimization problems with vertex selection

We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm presented by Löhne, Rudloff, and Ulus in 2014. There, vertices of...

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Veröffentlicht in:Optimization methods & software Jg. 37; H. 3; S. 1006 - 1026
Hauptverfasser: Dörfler, Daniel, Löhne, Andreas, Schneider, Christopher, Weißing, Benjamin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Abingdon Taylor & Francis 04.05.2022
Taylor & Francis Ltd
Schlagworte:
90-08
Algorithms
Apexes
Approximation
convex programming
Mathematical analysis
multiple objective optimization
Optimization
polyhedral approximation
Vector optimization
ISSN:1055-6788, 1029-4937
Online-Zugang:Volltext
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Zusammenfassung:We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm presented by Löhne, Rudloff, and Ulus in 2014. There, vertices of an already known outer approximation are successively cutoff to improve the approximation error. We propose a new and efficient selection rule for deciding which vertex to cutoff. Numerical examples are provided which illustrate that this method may solve fewer scalar problems overall and therefore may be faster while achieving the same approximation quality.
Bibliographie:ObjectType-Article-1
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content type line 14
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2021.1880579