Dynamic Normalization in MOEA/D for Multiobjective Optimization

Objective space normalization is important since a real-world multiobjective problem usually has differently scaled objective functions. Recently, bad effects of the commonly used simple normalization method have been reported for the popular decomposition-based algorithm MOEA/D. However, the effects of recently proposed sophisticated normalization methods have not been investigated. In this paper, we examine the effectiveness of these normalization methods in MOEA/D. We find that these normalization methods can cause performance deterioration. We also find that the sophisticated normalization methods are not necessarily better than the simple one. Although the negative effects of inaccurate estimation of the nadir point are well recognized in the literature, no solution has been proposed. In order to address this issue, we propose two dynamic normalization strategies which dynamically adjust the extent of normalization during the evolutionary process. Experimental results clearly show the necessity of considering the extent of normalization.