In recent years, various many-objective evolutionary algorithms (MaOEAs) have been proved to be successful in solving many-objective optimization problems (MaOPs). However, the performance of most MaOEAs is seriously affected when handling MaOPs with irregular Pareto fronts (PFs). In this paper, a new MaOEA variant based on parallel distance (called PDMaOEA) is proposed to solve MaOPs with irregular PFs. Firstly, two new metrics based on parallel distance are designed. The first one termed diversity metric can adapt to irregular PFs. The second one called comprehensive selection metric can consider both diversity and convergence simultaneously. Based on the two metrics, a mating selection method and an environmental selection strategy are proposed. In the mating selection, solutions with good convergence or diversity are chosen to improve the quality of offspring population. In the environmental selection, the selection pressure is significantly enhanced by the two metrics. Experimental study is validated on 19 irregular problems with different shapes of PFs. Performance of the proposed PDMaOEA is compared with six state-of-the-art algorithms. Statistical analysis shows that the proposed approach is competitive in handling MaOPs with irregular PFs.

中文翻译：

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处理不规则Pareto前沿的基于平行距离的多目标进化算法

近年来，各种多目标进化算法（MaOEA）已被证明可以成功解决多目标优化问题（MaOP）。然而，在处理具有不规则帕累托前沿（PF）的 MaOP 时，大多数 MaOEA 的性能受到严重影响。在本文中，提出了一种基于平行距离的新 MaOEA 变体（称为 PDMaOEA）来求解具有不规则 PF 的 MaOP。首先，设计了两个基于平行距离的新度量。第一个称为多样性度量可以适应不规则的 PF。第二种称为综合选择度量，可以同时考虑多样性和收敛性。基于这两个指标，提出了交配选择方法和环境选择策略。在交配选择中，选择具有良好收敛性或多样性的解决方案，以提高后代群体的质量。在环境选择中，这两个指标显着增强了选择压力。实验研究对 19 个具有不同形状 PF 的不规则问题进行了验证。将所提出的 PDMaOEA 的性能与六种最先进的算法进行了比较。统计分析表明，所提出的方法在处理具有不规则 PF 的 MaOP 方面具有竞争力。