An enhanced differential evolution optimization algorithm

Abstract

The Differential Evolution (DE) algorithm, introduced by Storn and Price in 1995, has become one of the most efficacious population-based optimization approaches. In this algorithm, use is made of the significant concepts of mutation, crossover, and selection. The tuning control parameters are population size, mutation scaling factor, and crossover rate. Over the last decade, several variants of DE have been presented to improve its performance aspects. In the present paper, we further enhance DE. The population size and mutation scaling factor are taken alone in the tuning process; the crossover rate is treated implicitly in the crossover stage. Five forms for crossover are suggested for the first 100 iterations of the computational algorithm. After this learning period, we pick the form which yields the best value of the objective function in the greatest number of iterations (among the 100). Our algorithm is tested on a total of 47 benchmark functions: 27 traditional functions and 20 special functions chosen from CEC2005 and CEC2013. The results are assessed in terms of the mean and standard deviation of the error, success rate, and average number of function evaluations over successful runs. Convergence characteristics are also investigated. Comparison is made with the original DE and Success-History based Adaptive DE (SHADE) as a state-of-the-art DE algorithm, and the results demonstrate the superiority of the proposed approach for the majority of the functions considered.