When addressing the challenge of complex multi-objective optimization problems, particularly those with non-convex and non-uniform Pareto fronts, Decomposition-based Multi-Objective Evolutionary Algorithms (MOEADs) often converge to local optima, thereby limiting solution diversity. Despite its significance, this issue has received limited theoretical exploration. Through a comprehensive geometric analysis, we identify that the traditional method of Reference Point (RP) selection fundamentally contributes to this challenge. In response, we introduce an innovative RP selection strategy, the Weight Vector-Guided and Gaussian-Hybrid method, designed to overcome the local optima issue. This approach employs a novel RP type that aligns with weight vector directions and integrates a Gaussian distribution to combine three distinct RP categories. Our research comprises two main experimental components: an ablation study involving 14 algorithms within the MOEADs framework, spanning from 2014 to 2022, to validate our theoretical framework, and a series of empirical tests to evaluate the effectiveness of our proposed method against both traditional and cutting-edge alternatives. Results demonstrate that our method achieves remarkable improvements in both population diversity and convergence.

翻译：在应对复杂多目标优化问题（尤其是具有非凸、非均匀帕累托前沿的问题）时，基于分解的多目标进化算法（MOEADs）常陷入局部最优，从而限制了种群多样性。尽管这一问题至关重要，但相关理论探索仍十分有限。通过全面的几何分析，我们发现传统参考点（RP）选择方法本质上导致了这一挑战。为此，我们提出了一种创新的参考点选择策略——权重向量引导与高斯混合方法，旨在克服局部最优问题。该方法采用一种与权重向量方向对齐的新型参考点类型，并结合高斯分布融合三种不同参考点类别。本研究包含两大实验部分：其一为消融实验，涵盖2014至2022年间MOEADs框架下的14种算法，以验证理论框架；其二为一系列实证测试，评估所提方法相较于传统与前沿替代方案的性能。结果表明，我们的方法在种群多样性与收敛性方面均取得了显著提升。