On the Normalization in Evolutionary Multi-Modal Multi-Objective Optimization

Yiping Liu, Hisao Ishibuchi, Gary G. Yen, Yusuke Nojima, Naoki Masuyama, Yuyan Han

Abstract: Multi-modal multi-objective optimization problems may have different Pareto optimal solutions with the same objective vector. A number of evolutionary multi-modal multiobjective algorithms have been developed to solve these problems. They aim to search for a Pareto optimal solution set with good diversity in both the objective and decision spaces. Although the normalization in both the objective and decision spaces is very important for these algorithms, there are few studies on this topic. In this paper, we investigate the effect of four normalization methods on two evolutionary multi-modal multiobjective algorithms. Six distance minimization problems are chosen as test problems. The experimental results show that the effect of normalization in evolutionary multi-modal multiobjective optimization is algorithm- and problem-dependent.