Effects of Objective Space Normalization in Multi-Objective Evolutionary Algorithms on Real-World Problems

Linjun He, Yang Nan, Hisao Ishibuchi, Dipti Srinivasan

Abstract: In real-world multi-objective problems, each objective has a totally different scale. However, some frequently-used multi-objective evolutionary algorithms (MOEAs) have no objective space normalization mechanisms. The effect of objective space normalization on the performance of decomposition-based MOEAs (e.g., MOEA/D and NSGA-III) has already been examined for artificial test problems (e.g., DTLZ and WFG) in the literature. In this paper, we examine its practical usefulness for real-world multi-objective problems using various MOEAs. Our experimental results clearly show that objective space normalization is needed not only in decomposition-based MOEAs but also in hypervolume-based MOEAs. We also explain why objective space normalization is needed in these two types of MOEAs.