A multiobjective evolutionary algorithm based on decision variable classification for many-objective optimization

Abstract

Multiobjective evolutionary algorithms (MOEAs) have faced the challenge of balancing diversity and convergence in dealing with many-objective optimization problems (MaOPs). Most of them use a series of strategies to increase the selection pressure among solutions for convergence promotion, or additional auxiliary strategies for diversity maintenance. Decision variable classification (DVC), as the method that analyzes the feature of an MaOP, can help MOEAs search for optimal solutions in terms of convergence and diversity through optimizing the corresponding category of decision variables. Therefore in this paper, we propose a new DVC method by analyzing the monotonicities of objectives. Unlike other DVC methods, it does not need to consider dominance relationships or help with extra vectors. Based on the classification results, we design a new directional crossover (DC) method for generating promising solutions. This crossover method has a higher probability that the generated offspring can integrate the advantages of the parents in convergence and diversity. Incorporating it with MOEA, a DVC-based MOEA (DVC-MOEA) is proposed for dealing with MaOPs. In DVC-MOEA, two archives focusing on convergence and diversity separately are maintained. In addition, an interval mapping(IM) strategy is designed to obtain solutions with good diversity, especially for some problems with biased features. To evaluate the performance of DVC-MOEA on MaOPs, comparison experiments are conducted on two wide used benchmarks with nine state-of-the-art MOEAs. The experimental results show that DVC-MOEA has high competitiveness over these MOEAs in dealing with MaOPs. Moreover, three variants are compared with DVC-MOEA respectively, and the comparison experimental results confirm the effect of the three strategies (DVC, DC, and IM) in our proposed algorithm.