Characterizations of multi-objective robustness solutions defined by Minkowski set difference

Wenyan Han and Guolin Yu ()
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Wenyan Han: Ningxia University
Guolin Yu: North Minzu University

OR Spectrum: Quantitative Approaches in Management, 2023, vol. 45, issue 4, No 9, 1380 pages

Abstract: 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.

Keywords: Set difference; Robustness; Optimality conditions; Image space analysis; Monotonicity (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00291-023-00725-z

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