Abstract
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.
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The authors gratefully thank the anonymous referees and the Editor-in-Chief for their valuable suggestions and comments, which helped to improve the paper.
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This research was supported by the National Natural Science Foundation of China (Grant Numbers: 11301567 and 11571055).
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Wei, HZ., Chen, CR. & Li, SJ. A Unified Characterization of Multiobjective Robustness via Separation. J Optim Theory Appl 179, 86–102 (2018). https://doi.org/10.1007/s10957-017-1196-y
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DOI: https://doi.org/10.1007/s10957-017-1196-y
Keywords
- Linear and nonlinear scalarization
- Set order relations
- Image space analysis
- Uncertain multiobjective optimization
- Robustness