中文摘要：

针对优化函数未知的昂贵区间多目标优化问题,提出一种基于主曲线建模的NSGA-II算法.该算法首先根据决策空间流形分布的种群数据构建K主曲线;然后利用所构建的K主曲线模型,通过插值和延展的方法生成子代.与遗传算法的随机生成子代策略相比,通过所提出方法生成有效子代效率会更高.由于目标空间拥挤距离无法求出,为此利用K主曲线找出待测解的前、后近距离解,按照决策空间拥挤距离对同序值解进行筛选,从而实现NSGA-II算法的改进.

英文摘要：

In this paper, an improved NSGA - II algorithm is proposed based on the principal curve modeling for solving the expensive interval multi-objective optimization with unknown objective function. Firstly, the proposed algorithm builds a K principal curve using the population data of the manifold distribution in decision space. Then, a new offspring is generated through interpolation and extension according to the built K principal curve, and the proposed strategy of offspring generation is more efficient than that of random offspring generation in the genetic algorithm. Finally, because of the absence of the crowding distance in objective space, the closest solutions before and after the candidate solution can be found based on the built K principal curve, so the solutions with same sequence are screened by crowding distance in decision space, thus the NSGA-II is improved.