Abstract
This paper focuses on characterizing the optimality of a kind of partial set order robust solutions, which are defined by Minkowski set difference, for an uncertain multi-objective optimization problem via oriented distance function and image space analysis. Firstly, the relationships between partial set order robust efficiency and upper (lower) set order robust efficiency are illustrated. Secondly, the optimality conditions to partial set order robust solutions are presented by utilizing image space analysis. Furthermore, characterizations are also established for partial set order robust solutions under the assumption of generalized monotonicity, which is determined by an oriented distance function. Finally, an application, namely a shortest path problem, is discussed to verify the effectiveness for the obtained results.
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Acknowledgements
This research was supported by Natural Science Foundation of China under Grant No. 11861002; The Key Project of North Minzu University under Grant No. ZDZX201804.
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Han, W., Yu, G. Characterizations of multi-objective robustness solutions defined by Minkowski set difference. OR Spectrum 45, 1361–1380 (2023). https://doi.org/10.1007/s00291-023-00725-z
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DOI: https://doi.org/10.1007/s00291-023-00725-z