A study of the Classical Differential Evolution control parameters

An extensive numerical study has been conducted to shed some light on the selection of parameters for the Classical Differential Evolution (DE/rand/1/bin) optimization method with the dither variant. It is well known that the crossover probability (Cr) has an active role in the convergence of the method. Our experiments show that even when the number of generations needed to achieve convergence as a function of the Cr parameter is of a stochastic nature, in some regions a reasonably well defined dependence of this number as a function of Cr can be observed. Motivated by this result, a self-adaptive DE methodology has been proposed. This new methodology applies the DE/rand/1/bin strategy itself to find a good value for the Cr parameter. Regarding the population size parameter, a phenomenological study involving the search space, the tolerance error, and the complexity of the function has been made. The proposed methodology has been applied to 10 of the most common test functions, giving the best success rate (100% in all the studied examples) and in general a faster convergence than the classical DE/rand/1/bin strategy.