Differential Evolution: A Survey on Their Operators and Variants

The Differential Evolution (DE) algorithm is one of the most popular and studied approaches in Evolutionary Computation (EC). Its simple but efficient design, such as its competitive performance for many real-world optimization problems, has positioned it as the standard comparison scheme for any proposal in the field. Precisely, its simplicity has allowed the publication of a great number of variants and improvements since its inception in 1997. Moreover, several DE variants are recognized as well-founded and highly competitive algorithms in the literature. In addition, the multiple DE applications and their proposed modifications in the state-of-the-art have propitiated the drafting of many review and survey works. However, none of the DE compilation work has studied the different variants of DE operators exclusively, which would benefit future DE enhancements and other topics. Therefore, in this work, a survey analysis of the variants of DE operators is presented. This study focuses on the proposed DE operators and their impact on the EC literature over the years. The analysis allows understanding of each year’s trends, the improvements that marked a milestone in the DE research, and the feasible future directions of the algorithm. Finally, the results show a downward trend for mutation or crossover variants while readers are increasingly interested in initialization and selection enhancements.