Abstract: People often need to optimize many conflicting objectives at the same time both in engineering application and real life. These optimization problems are called many-objective optimization problems (MaOPs). The evolutionary algorithms based on Pareto dominance will lose the convergence pressure when dealing with MaOPs. The decomposition based algorithm needs a set of preset reference vectors in objective space, which make the poor robustness when dealing with MaOPs with irregular PFs. In order to improve the convergence and maintain the flexible diversity strategy in dominance based algorithms, this paper proposes a two phase many-objective optimization algorithm based on Pareto dominance. The proposed algorithm centralizes computing resources to search the nadir point of optimization problems in the first phase. Then the inner and outward space can be divided according to the nadir point, and the convergence of algorithms can be improved by selecting the solutions in the inner space. In the second phase, the dynamic minimal distance method is proposed to improve the diversity of the algorithm. Compared with four state-of-art many-objective optimization algorithms, the experimental results show that the performance of the proposed algorithm is significantly better than that of compared algorithms on the MaOPs with irregular PFs. Meanwhile, the proposed algorithm also obtains competitive results on MaOPs with regular PFs. In a word, these experimental results indicate that the proposed algorithm has better robustness.

Key words: many-objective optimization, Pareto dominance relationship, diversity

摘要： 工程应用和现实生活中广泛存在着高维多目标优化问题。基于Pareto支配的多目标演化算法在处理高维多目标优化问题时会面临收敛压力丧失的缺点，基于分解的多目标优化算法在处理Pareto前沿不规则的问题时鲁棒性较差。为了提高基于支配的多目标优化算法的选择压力同时保留基于支配算法多样性保持的灵活性，提出一种基于Pareto支配关系的两阶段进化高维多目标优化算法。在算法的第一阶段，集中计算资源搜索优化问题的极值点，通过优先选择内部空间的解来提高基于支配算法的收敛性能。在算法的第二阶段，利用动态最小距离法改善算法的多样性，使得算法获得一组均匀分布的精英解。实验表明，该算法在PF形状不规则的问题上显著优于与之比较的其他算法，且在PF形状规则的问题上性能良好，这表明该算法具有较好的鲁棒性。

关键词: 高维多目标优化, Pareto支配关系, 多样性