On the properties of lexicographic tolerable robust solution sets for uncertain multi-objective optimization problems

Abstract

This study provides the important properties of the lexicographic tolerable robust solution for uncertain multi-objective optimization problems which was introduced by Boriwan et al. [Boriwan, P.; Ehrgott, M.; Kuroiwa, D.; Petrot, N. The lexicographic tolerable robustness concept for uncertain multi-objective optimization problems: a study on water resources management. Sustainability. 12 (2020), no. 18, article number 7582.]. Also, the relationship between the lexicographic tolerable solution concept and the well-known robust solution, as the set-based robust efficiency [Ehrgott, M.; Ide, J.; Schöbel, A. Minmax robustness for multi-objective optimization problems. Eur. J. Oper. Res. 239 (2014), no. 1, 17–31.], are provided.