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

M. Schmidt, Anita Schöbel and Lisa Thom

European Journal of Operational Research, 2019, vol. 275, issue 2, 446-459

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 Γ-uncertainty). For interval uncertainty, we show that the resulting problems reduce to well-known single-objective problems.

Keywords: Multiple objective programming; Robust optimization; Multi-objective robust optimization; Combinatorial optimization; Scalarization (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:275:y:2019:i:2:p:446-459

DOI: 10.1016/j.ejor.2018.11.048

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