A Study of the Naïve Objective Space Normalization Method in MOEA/D

Complex Pareto fronts with objectives in different scales usually appear in real-world multi-objective optimization problems. So as to treat different objectives equally, the naïve normalization method is frequently used due to its simplicity in calculating the estimated ideal and nadir points (i.e., without generating a hyperplane). By directly making use of information from the obtained solutions, the estimated ideal point and the estimated nadir point are obtained. However, the naïve normalization method has rarely been investigated. Moreover, its formulation is often different in each study in the literature. In this paper, we first show four different formulations of the naïve normalization. They are based on different estimation mechanisms of the ideal point and the nadir point. Next we investigate the effect of each formulation on the performance of MOEA/D. Our results show that the search behavior of MOEA/D is significantly impacted due to the choice of a formulation of the naïve normalization method. Finally we suggest the most effective formulation of the naïve normalization method for MOEA/D.