Set-Based Min-Max and Min-Min Robustness for Multi-Objective Robust Optimization
Abstract
Min-max and min-min robustness are two extreme approaches discussed for single-objective robust optimization problems. Recently, multi-objective robust optimization problems are studied and robust Pareto efficiency definitions have been proposed. In particular, the set-based min-max robust efficiency defined for multi-objective robust optimization problems is analogous to the min-max robust optimality definition for single-objective robust optimization problems. In this study, we define the set-based min-min robust efficiency in addition to the existing definition of the min-max robust efficiency for multi-objective robust optimization problems. We discuss a method to determine the set of set-based min-max robust efficient solutions and propose an evolutionary algorithm to approximate this set. Furthermore, a modification of the algorithm is discussed to approximate the set of set-based min-min robust Pareto efficient solutions. The outcomes based on the two robust efficiency, i.e., set-based min-max and set-based min-min, are compared using numerical examples. Our results show that set-based min-min robust efficiency can be used by optimistic decision makers and can be combined with set-based min-max robust efficiency to model the preferences of the decision makers, who are not ultimately pessimistic.
Recommended Citation
H. Farhangi and D. Konur, "Set-Based Min-Max and Min-Min Robustness for Multi-Objective Robust Optimization," Proceedings of the 67th Annual Conference and Expo of the Institute of Industrial Engineers (2017, Pittsburgh, PA), pp. 1217 - 1222, Institute of Industrial Engineers (IIE), May 2017.
Meeting Name
67th Annual Conference and Expo of the Institute of Industrial Engineers 2017 (2017: May 20-23, Pittsburgh, PA)
Department(s)
Engineering Management and Systems Engineering
Research Center/Lab(s)
Intelligent Systems Center
Keywords and Phrases
Decision making; Efficiency; Engineers; Multiobjective optimization; Pareto principle; Decision makers; Multi objective; Pareto efficiency; Pareto efficient solutions; Robust efficiency; Robust multi-objective optimizations; Robust optimization; Single objective; Optimization; Multi-objective optimization; Robust multi-objective optimization; Set-based robust efficiency
International Standard Book Number (ISBN)
978-1-5108-4802-3
Document Type
Article - Conference proceedings
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2017 Institute of Industrial Engineers (IIE), All rights reserved.
Publication Date
01 May 2017
Comments
This work is partially supported by the US Department of Defense through the Systems Engineering Research Center (SERC) under Contract HQ0034-13-D-0004. SERC is a federally funded University Affiliated Research Center managed by Stevens Institute of Technology.