Differential Evolution: A survey of theoretical analyses

Abstract Differential Evolution (DE) is a state-of-the art global optimization technique. Considerable research effort has been made to improve this algorithm and apply it to a variety of practical problems. Nevertheless, analytical studies concerning DE are rather rare. This paper surveys the theoretical results obtained so far for DE. A discussion of genetic operators characteristic of DE is coupled with an overview of the population diversity and dynamics models. A comprehensive view on the current-day understanding of the underlying mechanisms of DE is complemented by a list of promising research directions.