Multipolar robust optimization

Walid Ben-Ameur , Adam Ouorou , Guanglei Wang , Mateusz Żotkiewicz

Abstract

We consider linear programs involving uncertain parameters and propose a new tractable robust counterpart which contains and generalizes several other models including the existing Affinely Adjustable Robust Counterpart and the Fully Adjustable Robust Counterpart. It consists in selecting a set of poles whose convex hull contains some projection of the uncertainty set, and computing a recourse strategy for each data scenario as a convex combination of some optimized recourses (one for each pole). We show that the proposed multipolar robust counterpart is tractable and its complexity is controllable. Further, we show that under some mild assumptions, two sequences of upper and lower bounds converge to the optimal value of the fully adjustable robust counterpart. We numerically investigate a couple of applications in the literature demonstrating that the approach can effectively improve the affinely adjustable policy.
Author Walid Ben-Ameur - National Center for Scientific Research (CNRS)
Walid Ben-Ameur,,
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, Adam Ouorou - Orange France
Adam Ouorou,,
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, Guanglei Wang - National Center for Scientific Research (CNRS)
Guanglei Wang,,
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, Mateusz Żotkiewicz (FEIT / IT)
Mateusz Żotkiewicz,,
- The Institute of Telecommunications
Journal seriesEURO Journal on Computational Optimization, ISSN 2192-4406 [2192-4414], (0 pkt)
Issue year2018
Vol6
No4
Pages395-434
Publication size in sheets1.95
Keywords in EnglishUncertainty, Robust optimization, Multistage optimization, Polyhedral approximation
DOIDOI:10.1007/s13675-017-0092-4
Languageen angielski
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2018 Ben Ameur Żotkiewicz Multipolar robust optimization.pdf 799.78 KB
Score (nominal)5
ScoreMinisterial score = 0.0, ArticleFromJournal
Ministerial score (2013-2016) = 5.0, ArticleFromJournal - czasopismo zagraniczne spoza list
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