Meta-level multi-objective formulations of set optimization for multi-objective optimization problems: multi-reference point approach to hypervolume maximization

Abstract

Hypervolume has been frequently used as an indicator to evaluate a solution set in indicator-based evolutionary algorithms (IBEAs). One important issue in such an IBEA is the choice of a reference point. A different solution set is often obtained from a different reference point since the hypervolume calculation depends on the location of the reference point. In this paper, we propose an idea of utilizing this dependency to formulate a meta-level multi-objective set optimization problem. Hypervolume maximization for a different reference point is used as a different objective.