Improving an adaptive differential evolution using hill-valley detection

Abstract

Differential Evolution (DE) is an evolutionary algorithm. DE has been successfully applied to optimization problems including non-linear, non-differentiable, non-convex and multi-modal functions. The performance of DE is affected by algorithm parameters such as a scaling factor F and a crossover rate CR. Many studies have been done to control the parameters adaptively. One of the most successful studies on parameter control is JADE. In JADE, two parameter values are generated according to a probability density function which is learned by the parameter values in success cases, where the child is better than the parent. In this study, landscape of an objective function is paid attention to in order to improve the performance of JADE. The efficiency and robustness of search process can be improved by detecting valleys and hills in search points and by adopting a small F for valley points and a large F for hill points because an optimal solution exists near valleys and far from hills in minimization problems. Valley points and hill points are detected by creating a proximity graph from search points and by selecting valley/hill points that are smaller/greater than neighbor points. The effect of the proposed method is shown by solving thirteen benchmark problems.