Effects of duplicated objectives in many-objective optimization problems on the search behavior of hypervolume-based evolutionary algorithms

A number of evolutionary multiobjective optimization (EMO) algorithms have already been proposed and applied to various problems. Each EMO algorithm has a different search behavior on a different problem. It is important to understand characteristics of the search behavior of each EMO algorithm when we choose an appropriate EMO algorithm for a particular multiobjective problem. However, the search behavior on many-objective optimization problems has not been well studied yet. In this paper, we examine how the existence of duplicated objectives affects the search behavior of SMS-EMOA, which is a well-known hypervolume-based EMO algorithm with high search ability. First we explain that hypervolume calculation depends on the choice of a reference point and the normalization of each objective. Next we illustrate the effect of duplicated objectives on the hypervolume calculation. Then we discuss the effect of these three factors (i.e., reference point, objective value normalization, and duplicated objectives) on the search behavior of SMS-EMOA. It is shown through computational experiments that the existence of duplicated objectives biases the multiobjective search by SMS-EMOA towards a part of the Pareto front with good objective values of the duplicated objectives.