Differential Evolution based on population reduction with minimum distance

In Differential Evolution (DE), there are many adaptive DE algorithms proposed for parameter adaptation. However, they mainly focus on tuning the mutation factor F and the crossover probability CR. The adaptation of population size NP has not been widely studied in the literature of DE. Reducing population size without jeopardizing the performance of an algorithm could save computational resources and hence accelerate it´s convergence speed. This is beneficial to algorithms for optimization problems which need expensive evaluations. In this paper, we propose an improved population reduction method for DE, called dynNPMinD-DE, by considering the difference between individuals. When the reduction criterion is satisfied, dynNPMinD-DE selects the best individual and pairs of individuals with minimal-step difference vectors to form a new population. dynNPMinD-DE is tested on a set of 13 scalable benchmark functions in the number of dimensions of D=30 and D=50, respectively. The results show that dynNPMinD-DE outperforms the other peer DE algorithms in terms of both solution accuracy and convergence speed on most test functions.