Many‐objective evolutionary computation based on adaptive hypersphere dynamic angle vector dominance

Abstract

SummaryIn 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‐Lp) based on Lp‐norm (Where p is set to 1/M, and M is the target number) is proposed. SHNDM‐Lp 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.