An empirical study on the search directions of differential evolution

Among various evolutionary computation methods, differential evolution (DE) is recognized as one of the most promising methods for solving continuous global optimization problems. Although DE has been used by many researchers, the reasons how and why it can generally solve such problems so well are not fully explained. To find the reasons, we study the common behavior of individuals in DE through various numerical experiments. Regarding DE as a multi-point directional search model, we investigate convergence and practicality of the search directions used by its individuals. Specifically, we focus on the characteristics of two difference vectors for each individual: (a) a vector from the target vector, i.e., the individual itself, to the corresponding mutant vector, and (b) another vector from it to the corresponding trial vector. The experimental results, in which famous benchmark problems are solved by DE/rand/1/bin, exhibit the phenomenon that both of the vectors (a) and (b) automatically decrease their length exponentially, and show the possibility that the mutant vectors improve the corresponding individuals more frequently than the trial vectors.