Environmental selection in Pareto-based many-objective evolutionary algorithms generally employ Pareto-dominance relation to first consider the convergence and give higher priority to convergence than diversity. When the many-objective optimization problem has a complicated Pareto front, this selection strategy can easily miss the promising areas and converge into a subregion of the Pareto front. To address this issue, we propose a many-objective evolutionary algorithm with diversity-first based environmental selection. Different from the existing selection strategies, the environmental selection procedure in the proposed algorithm adopts a diversity-first-and-convergence-second principle, which first selects the representative solutions that having better diversity and then considers using the well-converged solutions to replace them in subregions. This selection-replacement strategy can maintain the diversity and make contribution to the convergence. In addition, a selection criterion, termed adaptive angle penalized distance, is designed to judge whether the replacement is implemented or not. The proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms on a large number of test problems with various characteristics. Experimental studies demonstrate that the proposed algorithm has competitive performance on many-objective optimization problems.

在基于Pareto的多目标进化算法中，环境选择通常采用Pareto-优势关系来首先考虑收敛性，并且优先考虑收敛性而不是多样性。当多目标优化问题具有复杂的Pareto前沿时，这种选择策略很容易错过有前途的区域并收敛到Pareto前沿的一个子区域。为了解决这个问题，我们提出了一种基于多样性优先的环境选择的多目标进化算法。与现有的选择策略不同，该算法的环境选择过程采用了分集第一和收敛第二的原理，首先选择具有更好多样性的代表性解决方案，然后考虑使用融合良好的解决方案在子区域中替换它们。这种选择替换策略可以保持多样性并为收敛做出贡献。此外，选择标准，称为自适应角度补偿距离，用于判断是否执行了替换。在大量具有各种特征的测试问题上，将提出的算法与五种最新的多目标进化算法进行了比较。实验研究表明，该算法在多目标优化问题上具有竞争优势。称为自适应角度补偿距离的设计用于判断是否执行了替换。在大量具有各种特征的测试问题上，将提出的算法与五种最新的多目标进化算法进行了比较。实验研究表明，该算法在多目标优化问题上具有竞争优势。称为自适应角度补偿距离的设计用于判断是否执行了替换。在大量具有各种特征的测试问题上，将提出的算法与五种最新的多目标进化算法进行了比较。实验研究表明，该算法在多目标优化问题上具有竞争优势。