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Necessary and sufficient conditions for Pareto efficiency in robust multiobjective optimization
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. RaySearch Laboratories, Sweden.ORCID iD: 0000-0001-6642-3282
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. RaySearch Laboratories, Sweden.
2017 (English)In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 262, no 2, 682-692 p.Article in journal (Refereed) Published
Abstract [en]

We provide necessary and sufficient conditions for robust efficiency (in the sense of Ehrgott et al., 2014) to multiobjective optimization problems that depend on uncertain parameters. These conditions state that a solution is robust efficient (under minimization) if it is optimal to a strongly increasing scalarizing function, and only if it is optimal to a strictly increasing scalarizing function. By counterexample, we show that the necessary condition cannot be strengthened to convex scalarizing functions, even for convex problems. We therefore define and characterize a subset of the robust efficient solutions for which an analogous necessary condition holds with respect to convex scalarizing functions. This result parallels the deterministic case where optimality to a convex and strictly increasing scalarizing function constitutes a necessary condition for efficiency. By a numerical example from the field of radiation therapy treatment plan optimization, we illustrate that the curvature of the scalarizing function influences the conservatism of an optimized solution in the uncertain case.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV , 2017. Vol. 262, no 2, 682-692 p.
Keyword [en]
Multiobjective optimization, Robust optimization, Scalarization, Uncertainty, Convexity
National Category
Economics and Business Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-210329DOI: 10.1016/j.ejor.2017.04.012ISI: 000403525300023Scopus ID: 2-s2.0-85018278140OAI: oai:DiVA.org:kth-210329DiVA: diva2:1120085
Note

QC 20170705

Available from: 2017-07-05 Created: 2017-07-05 Last updated: 2017-07-05Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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