Balancing the diversity and convergence of the population is challenging in multi-objective optimization. The work proposed a many-objective evolutionary algorithm based on indicator I_(ε+)(MaOEA/I) to solve the abov...Balancing the diversity and convergence of the population is challenging in multi-objective optimization. The work proposed a many-objective evolutionary algorithm based on indicator I_(ε+)(MaOEA/I) to solve the above problems. Indicator I_(ε+)(x,y) is used for environmental selection to ensure diversity and convergence of the population. I_(ε+)(x,y) can evaluate the quality of individual x compared with individual y instead of the whole population. If I_(ε+)(x,y) is less than 0, individual x dominates y. If I_(ε+)(x,y) is 0, individuals x and y are the same. If I_(ε+)(x,y) is greater than 0, no dominant relationship exists between individuals x and y. The smaller I_(ε+)(x,y), the closer the two individuals. The dominated individuals should be deleted in environmental selection because they do not contribute to convergence. If there is no dominant individual, the same individuals and similar individuals should be deleted because they do not contribute to diversity. Therefore, the environmental selection of MaOEA/I should consider the two individuals with the smallest I_(ε+)(x,y). If I_(ε+)(x,y) is not greater than 0, delete individual y;if I_(ε+)(x,y) is greater than 0, check the distance between individuals x, y, and the target point and delete the individual with a longer distance. MaOEA/I is compared with 6 algorithms until the population does not exceed the population size. Experimental results demonstrate that MaOEA/I can gain highly competitive performance when solving many-objective optimization problems.展开更多
基金Sponsored by the Tianjin Natural Science Foundation(Grant No.22JCZDJC00600)the Tianjin Research Innovation Project for Postgraduate Students(Grant No.2022SKYZ393)。
文摘Balancing the diversity and convergence of the population is challenging in multi-objective optimization. The work proposed a many-objective evolutionary algorithm based on indicator I_(ε+)(MaOEA/I) to solve the above problems. Indicator I_(ε+)(x,y) is used for environmental selection to ensure diversity and convergence of the population. I_(ε+)(x,y) can evaluate the quality of individual x compared with individual y instead of the whole population. If I_(ε+)(x,y) is less than 0, individual x dominates y. If I_(ε+)(x,y) is 0, individuals x and y are the same. If I_(ε+)(x,y) is greater than 0, no dominant relationship exists between individuals x and y. The smaller I_(ε+)(x,y), the closer the two individuals. The dominated individuals should be deleted in environmental selection because they do not contribute to convergence. If there is no dominant individual, the same individuals and similar individuals should be deleted because they do not contribute to diversity. Therefore, the environmental selection of MaOEA/I should consider the two individuals with the smallest I_(ε+)(x,y). If I_(ε+)(x,y) is not greater than 0, delete individual y;if I_(ε+)(x,y) is greater than 0, check the distance between individuals x, y, and the target point and delete the individual with a longer distance. MaOEA/I is compared with 6 algorithms until the population does not exceed the population size. Experimental results demonstrate that MaOEA/I can gain highly competitive performance when solving many-objective optimization problems.
