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 multimodal 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, the two parameter values are generated according to two probability density functions which are learned by the parameter values in success cases, where a child solution is better than the parent solution. In this study, the performance of JADE is improved by detecting hills and valleys of an objective function. Since an optimal solution exists near valleys and far from hills in minimization problems, search near valleys is performed by adopting a small F for valley points and search far from hills is performed by adopting a large F$ for hill points in order to realize efficient and robust search. The valley points and the hill points are identified by creating a proximity graph called a Gabriel graph from search points and by selecting valley/hill points that are smaller/greater than all neighbor points. The effect of the proposed method, JADE-HV is shown by solving thirteen benchmark problems and by comparing the results of JADE-HV with those of some algorithms including JADE.