Covers and approximations in multiobjective optimization

Abstract

Due to the growing interest in approximation for multiobjective optimization problems (MOPs), a theoretical framework for defining and classifying sets representing or approximating solution sets for MOPs is developed. The concept of tolerance function is proposed as a tool for modeling representation quality. This notion leads to the extension of the traditional dominance relation to $$t\hbox {-}$$t-dominance. Two types of sets representing the solution sets are defined: covers and approximations. Their properties are examined in a broader context of multiple solution sets, multiple cones, and multiple quality measures. Applications to complex MOPs are included.