Differential evolution with improved population reduction

In the Differential Evolution (DE), there are many adaptive DE algorithms proposed for parameter adaptation. However, they are mainly focus on the the mutation factor F and crossover probability CR. The adaptation of population size NP is not widely studied in the scope of DE. If reduce population size but not jeopardize performance of the algorithm significantly, it could reduce the number of evaluations for individuals and accelerate algorithm's convergence speed. This is beneficial to the optimization problems which need expensive evaluations. In this paper, we propose an improved population reduction method, considering the difference between individuals, and embed it into classic DE/rand/1/bin strategy, named dynNPMinD-DE. When population needs to reduce, select the best individual and the individuals with minimal-step difference vectors to form a new population. dynNPMinD-DE is applied to minimize a set of 13 scalable benchmark functions of dimensions D=30. The results show that compared with selecting better individuals and DE/rand/1/bin, dynNPMinD-DE can get better results on average, and the convergence becomes faster and faster as each population reduction.