Evolutionary computation for many-objective optimization problems using massive population sizes on the K supercomputer

The advantages of evolutionary computation with very large populations for many-objective optimization problems are investigated. The effects of a population size of up to 1,000,000 are studied, with the number of generations fixed at 100. To overcome difficulty in computational time, we use a many-objective evolutionary algorithm designed for massive parallelization (CHEETAH) on the K supercomputer. For unimodal test problems DTLZ2 and DTLZ4, the inverted generational distance (IGD) decreases as the population increases while the generational distance (GD) is saturated with a population size of 10,000. This means an evolutionary computation with massive population size mainly contributes to improvement of diversity of obtained non-dominated solutions. Even when the total number of evaluations is fixed, this conclusion is unchanged. For the multimodal test problems DTLZ1 and DTLZ3, GD and IGD are reduced with increasing population size of up to 10,000 but are not significantly improved with population sizes larger than this. This is probably due to the difficulty in obtaining good non-dominated solutions for DTLZ1 and DTLZ3 with current CHEETAH. Because CHEETAH is bases on NSGA-II (only the non-dominated sort portion is modified for more effective many-objective optimization and parallelization), we expect that the current conclusion qualitatively stays the same for other NSGA-II-based algorithms. To take advantage of the larger population size, development of operators such as selection and crossover designed for very large population size may be required.