An Enhanced Differential Evolution Algorithm with Multi-mutation Strategies and Self-adapting Control Parameters

Abstract

Differential evolution (DE) is a stochastic population-based optimization algorithm first introduced in 1995. It is an efficient search method that is widely used for solving global optimization problems. It has three control parameters: the scaling factor (F), the crossover rate (CR), and the population size (NP). As any evolutionary algorithm (EA), the performance of DE depends on its exploration and exploitation abilities for the search space. Tuning the control parameters and choosing a suitable mutation strategy play an important role in balancing the rate of exploration and exploitation. Many variants of the DE algorithm have been introduced to enhance its exploration and exploitation abilities. All of these DE variants try to achieve a good balance between exploration and exploitation rates. In this paper, an enhanced DE algorithm with multi-mutation strategies and self-adapting control parameters is proposed. We use three forms of mutation strategies with their associated self-adapting control parameters. Only one mutation strategy is selected to generate the trial vector. Switching between these mutation forms during the evolution process provides dynamic rates of exploration and exploitation. Having different rates of exploration and exploitation through the optimization process enhances the performance of DE in terms of accuracy and convergence rate. The proposed algorithm is evaluated over 38 benchmark functions: 13 traditional functions, 10 special functions chosen from CEC2005, and 15 special functions chosen from CEC2013. Comparison is made in terms of the mean and standard deviation of the error with the standard "DE/rand/1/bin" and five state-of-the-art DE algorithms. Furthermore, two nonparametric statistical tests are applied in the comparison: Wilcoxon signed-rank and Friedman tests. The results show that the performance of the proposed algorithm is better than other DE algorithms for the majority of the tested functions.