A Unified Characterization of Multiobjective Robustness via Separation - Wei, Hong-Zhi; Chen, Chun-Rong; Li, Sheng-Jie (Journal of optimization theory and applications, 2018)
This paper focuses on a unified approach to characterizing different kinds of multiobjective robustness concepts. Based on linear and nonlinear scalarization results for several set order relations, together with the help of image space analysis, some suitable subsets of scalarization image space are introduced to make equivalent characterizations for upper set (lower set, set, certainly, respectively) less ordered robustness for uncertain multiobjective optimization problems. In particular, the nonlinear scalarization functional plays a significant role in computing various multiobjective robust solutions. Finally, the corresponding examples are included to show the effectiveness of the results derived in this paper.