Due to the low selection pressure of the Pareto-dominance relation and the ineffectivity of diversity maintenance schemes in the environmental selection, the classical Pareto-dominance based multi-objective evolutionary algorithms (MOEAs) fail to handle many-objective optimization problems. The recently presented non-dominated sorting genetic algorithm III (NSGA-III) employs the uniformly distributed reference points to significantly promote population diversity, but the convergence based on the Pareto-dominance relation could still be enhanced. For this purpose, an improved NSGA-III algorithm based on elimination operator (NSGA-III-EO) is proposed. In the proposed algorithm, the elimination operator first identifies the reference point with maximum niche count and then employs the penalty-based boundary intersection distance to rank the individuals associated with it. To this end, the selection scheme is used to remove the worse individuals rather than to select the superior individuals. The proposed NSGA-III-EO is tested on a number of well-known benchmark problems with up to fifteen objectives and shows the competitive performance compared with five state-of-the-art MOEAs. Additionally, it is also tested on constrained problems having a large number of objectives and shows good performance.

中文翻译：

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一种基于消除算子的改进NSGA-III多目标优化算法

由于帕累托优势关系的选择压力低以及多样性选择方案在环境选择中的效率低下，传统的基于帕累托优势的多目标进化算法（MOEA）无法解决多目标优化问题。最近提出的非支配排序遗传算法III（NSGA-III）使用均匀分布的参考点显着促进了种群多样性，但仍可以增强基于Pareto-优势关系的收敛性。为此，提出了一种基于消除算子的改进NSGA-III算法（NSGA-III-EO）。在提出的算法中，消除算子首先识别具有最大生态位计数的参考点，然后使用基于惩罚的边界相交距离对与之关联的个体进行排名。为此，选择方案用于删除较差的个人，而不是选择较高的个人。拟议的NSGA-III-EO已针对多达15个目标的许多众所周知的基准问题进行了测试，与5个最先进的MOEA相比，具有竞争优势。此外，它还针对具有大量目标的受限问题进行了测试，并显示出良好的性能。拟议的NSGA-III-EO已针对多达15个目标的许多众所周知的基准问题进行了测试，并且与五个最先进的MOEA相比，具有竞争优势。此外，它还针对具有大量目标的受限问题进行了测试，并显示出良好的性能。拟议的NSGA-III-EO已针对多达15个目标的许多众所周知的基准问题进行了测试，并且与五个最先进的MOEA相比，具有竞争优势。此外，它还针对具有大量目标的受限问题进行了测试，并显示出良好的性能。