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  4. Min-ordering and max-ordering scalarization methods for multi-objective robust optimization
 
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2019
Journal Article
Title

Min-ordering and max-ordering scalarization methods for multi-objective robust optimization

Abstract
Several robustness concepts for multi-objective uncertain optimization have been developed during the last years, but not many solution methods. In this paper we introduce two methods to find min-max robust efficient solutions based on scalarizations: the min-ordering and the max-ordering method. We show that all point-based min-max robust weakly efficient solutions can be found with the max-ordering method and that the min-ordering method finds set-based min-max robust weakly efficient solutions, some of which cannot be found with formerly developed scalarization based methods. We then show how the scalarized problems may be approached for multi-objective uncertain combinatorial optimization problems with special uncertainty sets. We develop compact mixed-integer linear programming formulations for multi-objective extensions of bounded uncertainty (also known as budgeted or G-uncertainty). For interval uncertainty, we show that the resulting problems reduce to well-known single-objective problems.
Author(s)
Schmidt, Marie
Rotterdam School of Management, Erasmus University Rotterdam
Schöbel, Anita  
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM  
Thom, Lisa
Institut für Numerische und Angewandte Mathematik, Universität Göttingen
Journal
European Journal of Operational Research  
Funder
Deutsche Forschungsgemeinschaft DFG  
Open Access
DOI
10.1016/j.ejor.2018.11.048
Language
English
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM  
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