The effect of a stochastic step length on the performance of the differential evolution algorithm

In this paper, we present a novel efficient strategy to improve the performance of the differential evolution (DE) algorithm for real parameter optimization, by generating a variable step length based on a probability distribution, instead of using the conventional fixed step length approach. Previous studies investigated uniform and Gaussian distributions. In this study, we compare between these two distributions and a Cauchy distribution. The proposed strategy controls search parameters in a probabilistic manner. Experimental results are carried out on a wide range of fifteen standard test problems with different scenarios. The obtained results showed that the performance of the DE algorithm was best when using a Cauchy distribution (CD); thanks to its thick tails that enable it to generate considerable changes more frequently than other probability distributions and to escape a local optima for multimodal optimization problems.