Indicator based many-objective evolutionary algorithms generally introduce the performance indicator as the selection criterion in environmental selection. In the calculation of some indicators, the reference points as sampled points on Pareto fronts are very important for their calculation. However, it is difficult to obtain good reference points on various types of Pareto fronts. To address this issue, this paper proposes an enhanced-indicator based many-objective evolutionary algorithm with adaptive reference point, termed EIEA. The algorithm proposes a reference point adaptation method to dynamically adapt the reference points for the calculation of indicators. Moreover, the calculation of IGD-NS is enhanced by employing the modified distance calculation to introduce the Pareto compliant which can further comprehensively measure the convergence and diversity. The proposed EIEA adopts Pareto dominance and the enhanced IGD-NS as the first selection criterion and the secondary selection criterion in environmental selection, respectively. The intensive experiments demonstrate that the proposed algorithm has good performance in solving problems with various types of Pareto fronts, surpassing several representative many-objective evolutionary algorithms for many-objective optimization.

基于指标的多目标进化算法通常将性能指标作为环境选择的选择标准。在某些指标的计算中，参考点是帕累托前沿的采样点，对它们的计算非常重要。但是，很难在各种类型的帕累托前沿上获得良好的参考点。为了解决这个问题，本文提出了一种基于增强指标的具有自适应参考点的多目标进化算法，称为EIEA。该算法提出了一种参考点自适应方法，可以动态地将参考点自适应以用于指标的计算。此外，IGD-NS的计算通过采用改进的距离计算来引入Pareto兼容，从而可以进一步全面地测量收敛性和多样性。拟议的EIEA在环境选择中分别采用帕累托优势和增强的IGD-NS作为第一选择标准和第二选择标准。大量实验表明，该算法在解决各种类型的帕累托前沿问题方面具有良好的性能，超过了几种具有代表性的多目标进化算法进行多目标优化。