An adaptive differential evolution with adaptive archive selection and hill-valley detection

Differential Evolution (DE) has been successfully applied to various optimization problems. 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 the child is better than the parent. Also, an optional external archive which consists of defeated parents is introduced to keep diversity. However, the effect of the archive much depends on the optimization problems. In this study, an adaptive method for using the archive is proposed where probability for selecting an operation with the archive or an operation without the archive is adaptively controlled based on the success probability of the operations. Also, hills and valleys in an objective function are detected 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.