Abstract: As the number of objectives increases, the Pareto front of many-objective optimization problem becomes increasingly complex. Traditional decomposition-based many-objective evolutionary algorithms struggle to select populations with both good diversity and convergence characteristics. To address this issue, a novel dual-stage dual-population evolutionary algorithm for many-objective optimization is proposed. In this algorithm, the evolutionary process is divided into two stages. In the first stage, it determines whether the shape of the Pareto front is regular. In the second stage, it adjusts the weight vectors based on the shape of the Pareto front, ensuring that the population can achieve good diversity on both regular and irregular Pareto fronts. To perform weight vector adjustments without affecting the convergence of the algorithm, two populations are used for evolution：one main population evolves normally, and the other auxiliary population serves as the weight vectors. Finally, to obtain a set of weight vectors that adapt well to populations distributed on irregular Pareto fronts, the concept of energy balance in nature is introduced to collect a well-diverse auxiliary population as weight vectors. The proposed algorithm is compared with other algorithms on test problems with 3-10 objectives. Experimental results demonstrate that the proposed algorithm outperforms the compared algorithms on the majority of the test problems.

Key words: many-objective optimization, evolutionary algorithm, dual-stage, dual-population, weight vector, energy balance

摘要： 随着目标维度的上升，高维多目标优化问题的帕累托前沿越来越复杂，传统的基于分解的高维多目标进化算法难以挑选出多样性和收敛性良好的种群。针对以上问题提出了一种面向高维多目标优化的双阶段双种群进化算法。该算法将进化过程划分为两个阶段，在第一阶段判断帕累托前沿的形状是否规则，而在第二阶段则根据帕累前沿的形状选择是否对权重向量进行调整，以保证种群在规则及不规则帕累托前沿上都能获得良好的多样性。为了对权重向量进行调整且不影响算法的收敛性，该算法使用了两个种群进行进化，一个主种群正常进化，另一个辅种群作为权重向量。为了在不规则的帕累托前沿上获得一组适应种群分布的权重向量，引入了自然界中能量平衡的概念收集了多样性良好的辅种群作为权重向量。将提出的算法与其他算法在3-10目标的测试问题上进行比较。实验结果表明，提出的算法在大多数测试问题上性能优于比较的算法。

关键词: 高维多目标优化, 进化算法, 双阶段, 双种群, 权重向量, 能量平衡