A Two-Stage Evolutionary Algorithm With Balanced Convergence and Diversity for Many-Objective Optimization

Multiobjective optimization evolutionary algorithms (MOEAs) have received significant achievements in recent years. However, they encounter many difficulties in dealing with many-objective optimization problems (MaOPs) due to the weak selection pressure. One possible way to improve the ability of MOEAs for these MaOPs is to balance the convergence and diversity in the high-dimensional objective space. Based on this consideration, this article proposes a novel generic two-stage (TS) framework for MaOPs. The entire evolutionary search process is divided into two stages: in the first stage, a new subregion dominance and a modified subregion density-based mating selection mainly purse the convergence and in the second stage, a novel level-based Pareto dominance cooperates with the traditional Pareto dominance that mainly promotes diversity. Integrated into NSGA-II, the TS NSGA-II, referred to as TS-NSGA-II, is proposed. To extensively evaluate the performance of our approach, 29 benchmark problems were used as the test suite. The experimental results demonstrate our approach obtained superior or competitive performance compared with eight state-of-the-art many-objective optimization evolutionary algorithms. To study its generality, the proposed TS strategy was also combined with four other advanced methods for MaOPs. The results show that it can also improve the performance of these four methods in terms of convergence and diversity.