Two-Stage Double Niched Evolution Strategy for Multimodal Multiobjective Optimization
提出一种两阶段双小生进化策略DN-MMOES，通过决策空间小生策略和自适应密度调整，解决多模态多目标优化中决策空间多样性退化与子区域密度不均问题，在测试集上优于八种现有算法。
In recent years, numerous efficient and effective multimodal multiobjective evolutionary algorithms (MMOEAs) have been developed to search for multiple equivalent sets of Pareto optimal solutions simultaneously. However, some of the MMOEAs prefer convergent individuals over diversified individuals to construct the mating pool, and the individuals with slightly better decision space distribution may be replaced by significantly better objective space distribution. Therefore, the diversity in the decision space may become deteriorated, in spite of the decision and objective diversities have been taken into account simultaneously in most MMOEAs. Because the Pareto optimal subsets may have various shapes and locations in the decision space, it is very difficult to drive the individuals converged to every Pareto subregion with a uniform density. Some of the Pareto subregions may be overly crowded, while others are rather sparsely distributed. Consequently, many existing MMOEAs obtain Pareto subregions with imbalanced density. In this article, we present a two-stage double niched evolution strategy, namely DN-MMOES, to search for the equivalent global Pareto optimal solutions which can address the above challenges effectively and efficiently. The proposed DN-MMOES solves the multimodal multiobjective optimization problem (MMOP) in two stages. The first stage adopts the niching strategy in the decision space, while the second stage adapts double niching strategy in both spaces. Moreover, an effective decision density self-adaptive strategy is designed for improving the imbalanced decision space density. The proposed algorithm is compared against eight state-of-the-art MMOEAs. The inverted generational distance union (IGDunion) performance indicator is proposed to fairly compare two competing MMOEAs as a whole. The experimental results show that DN-MMOES provides a better performance to search for the complete Pareto Subsets and Pareto Front on IDMP and CEC 2019 MMOPs test suite.