Adaptive α-stable differential evolution in numerical optimization

Abstract

Although Differential Evolution (DE) is a simple yet powerful evolutionary algorithm, it requires an adaptive parameter control to achieve its optimal performance. In this paper, DE with an adaptive parameter control using the $$\alpha$$ -stable distribution is proposed. First, the proposed algorithm allocated a carefully calculated stable distribution, evaluated by an adaptation manner, to each individual. After that, each individual adjusts its own control parameters by using the assigned stable distribution. Thus, we propose a parameter control scheme that adapts the stability parameter of the $$\alpha$$ -stable distribution to allocate proper stable distributions to each individual, used for tuning control parameters. We compared the optimization performances of the proposed algorithm with conventional DE and state-of-the-art DE variants at 30 and 100 dimensions of conventional benchmark problems. Also, we evaluated the optimization performances at high dimensional problems i.e., 100, 200, and 300 dimensions of CEC2008 benchmark problems. Our experiment results showed that the proposed algorithm is able to discover better final solutions than the compared DE algorithms and has the robust performance at both lower and higher dimensions.