For regular Pareto Fronts (PFs), such as those that are smooth, continuous, and uniformly distributed, using fixed weight vectors is sufficient for multi-objective optimization approaches using decomposition. However, when encountering irregular PFs-including degenerate, disconnected, inverted, etc. Fixed weight vectors can often cause a non-uniform distribution of the sets or even poor optimization results. To address this issue, this study proposes an adaptive many-objective evolutionary algorithm with a simplified hypervolume indicator. It synthesizes indicator assessment techniques with decomposition-based methods to facilitate self-adaptive and dynamic adjustment of the weight vectors in many-objective optimization methods. Specifically, based on the MOEA/D framework, it uses a simplified hypervolume indicator to accurately assess solution distribution. Simultaneously, applying the R2 indicator (as an approximation of hypervolume) dynamically regulates the update frequency of the weight vectors. Experimental results demonstrate that the proposed algorithm is efficient and effective when compared with six state-of-the-art algorithms.

翻译：对于规则帕累托前沿（PF），例如光滑、连续且均匀分布的情形，采用固定权重向量对于基于分解的多目标优化方法已足够。然而，当遇到不规则帕累托前沿——包括退化、不连通、反向等情况时，固定权重向量常导致解集分布不均匀甚至优化结果不佳。为解决此问题，本研究提出一种采用简化超体积指标的自适应多目标进化算法。该算法将指标评估技术与基于分解的方法相结合，以促进多目标优化方法中权重向量的自适应动态调整。具体而言，基于MOEA/D框架，算法使用简化超体积指标精确评估解分布，同时应用R2指标（作为超体积的近似）动态调控权重向量的更新频率。实验结果表明，与六种先进算法相比，所提算法具有高效性和有效性。