Abstract: To address the challenge of balancing convergence and diversity in multi-objective evolutionary algorithms when solving many-objective optimization problems (MaOPs), a subregion-based many-objective evolutionary algorithm (SR-MaOEA) is proposed. In this approach, the structure of the objective space is constructed by using a subregion division strategy, and the subregion density is quantified via shift-based density estimation (SDE). A hierarchical subregion dominance relation is then established to enhance the selection pressure among individuals. Furthermore, a convergence-diversity adaptive weighted selection mechanism is devised, in which the potential of each subregion is estimated by dynamically calculating the difference in weighted sums across successive generations. Individuals in subregions with higher potential are preferentially retained to update the population. Comparative experiments on the MaF benchmark suite are conducted against several representative many-objective optimization algorithms. The results demonstrate that SR-MaOEA exhibits competitive performance and robustness in high-dimensional objective spaces.

Key words: many-objective evolutionary, evolutionary algorithms, subregion partitioning, adaptive weighting, density estimation

摘要： 针对多目标进化算法求解超多目标优化问题难以平衡收敛性和多样性的困境，提出一种基于子区域的超多目标进化算法（subregion-based many-objective evolutionary algorithm, SR-MaOEA）。首先，通过子区域划分策略构建目标空间的分布结构，采用基于偏移密度估计量化子区域密度，并设计一种层级化的子区域支配关系排序策略，以增强个体选择压力；其次，提出一种收敛性与多样性自适应融合的加权选择机制，通过动态计算相邻代子区域加权和的差异，评估子区域潜力值，进而优先保留高潜力子区域内的个体更新种群。在 MaF基准测试集上，将SR-MaOEA与多种主流多目标优化方法进行对比，验证了该算法在高维目标空间中的有效性和稳定性。

关键词: 超多目标优化, 进化算法, 子区域划分, 自适应加权, 密度估计