In real-world, more and more MaOP (MaOPs) have emerged, which pose great challenge for traditional multi-objective evolutionary algorithms (MOEAs). In this paper, a many-objective evolutionary computation based on adaptive hypersphere dynamic angle vector dominance (AHDAVD-MOEA) is proposed. The AHDAVD-MOEA has three remarkable characteristics: (1) Based on the angle domination, a dynamic angle vector dominance relationship is proposed. In the evolution process, DAVD can dynamically adjust the population target space coordinate system according to the distribution of each generation of population in the target space, and at the same time calculate the angle vector of individuals to compare the dominance relations. Therefore, DAVD can dynamically describe the convergence and diversity of population, so as to achieve the goal of balancing the convergence and diversity of many target population. (2) Based on DAVD, an adaptive hypersphere dynamic angle vector dominance (AHDAVD) is proposed. After the DAVD process, AHDAVD adds an adaptive radius R to all dimensions of each non-dominated solution to form a hypersphere to expand the dominance range of individuals. The dominance relationship among individuals is judged by the dominance range of the extended solution individuals, which further enhances the convergence of the population. (3) Based on the simplified harmonic normalized distance method, a simplified harmonic normalized distance method (SHNDM-L_p) based on L_p-norm (Where p is set to 1/M, and M is the target number) is proposed. SHNDM-L_p uses Euclidean distance to measure the distance between individuals in many space, and uses fractional normal form to evaluate the proximity distance of solution individuals in many target space more effectively. The validity of the adaptive hypersphere dynamic angle vector dominance and the AHDAVD-MOEA are tested by DTLZ and WFG series of 5-, 8- and 10-targets. The experimental results show that: (1) Compared with AD and other representative improved dominance relations, the adaptive hypersphere dynamic angle vector dominance relationship has significantly better performance; (2) Compared with other five classical many-objective evolutionary algorithms, AHDAVD-MOEA has obvious advantages in population convergence and diversity. Overall, the proposed AHDAVD-MOEA is a promising optimizer in many-objective optimization.

中文翻译：

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基于自适应超球面动态角矢量优势的多目标进化计算

在现实世界中，越来越多的 MaOP（MaOPs）出现，这对传统的多目标进化算法（MOEAs）提出了巨大的挑战。在本文中，提出了一种基于自适应超球面动态角度矢量优势（AHDAVD-MOEA）的多目标进化计算。AHDAVD-MOEA 具有三个显着特点： (1) 基于角度支配，提出了动态角度矢量支配关系。在进化过程中，DAVD可以根据目标空间中每一代种群的分布动态调整种群目标空间坐标系，同时计算个体的角度向量来比较优势关系。因此，DAVD 可以动态地描述种群的收敛性和多样性，从而达到平衡众多目标人群的收敛性和多样性的目的。(2)基于DAVD，提出了一种自适应超球面动态角度矢量优势(AHDAVD)。在 DAVD 过程之后，AHDAVD 添加了一个自适应半径R对每个非支配解的所有维度形成超球面以扩大个体的支配范围。个体间的优势关系通过扩展解个体的优势范围来判断，进一步增强了种群的收敛性。(3)在简化调和归一化距离法的基础上，提出了一种基于L _{p -}范数(其中p设为1/ M，M为目标数)的简化调和归一化距离法(SHNDM- L _p ) 。SHNDM-大号_p使用欧氏距离来衡量多个空间中个体之间的距离，并使用分数范式更有效地评估多个目标空间中解个体之间的接近距离。自适应超球面动态角矢量优势和 AHDAVD-MOEA 的有效性通过 DTLZ 和 WFG 系列的 5、8 和 10 目标进行测试。实验结果表明：（1）与AD等具有代表性的改进优势关系相比，自适应超球面动态角度矢量优势关系具有明显更好的性能；(2) 与其他五种经典的多目标进化算法相比，AHDAVD-MOEA在种群收敛性和多样性方面具有明显的优势。总体而言，所提出的 AHDAVD-MOEA 是多目标优化中很有前途的优化器。