PROBABILISTIC ANALYSIS OF THE CONVERGENCE OF THE DIFFERENTIAL EVOLUTION ALGORITHM

Differential evolution algorithms represent an efficient framework to tackle complicated optimization problems with many variables and involved constraints. Nevertheless, the classic differential evolution algorithms in general do not ensure the convergence to the global minimum of the cost function. Therefore, the authors of the article designed a modification of these algorithms that guarantees the global convergence in the asymptotic and probabilistic sense. The modification consists in adding a certain ratio of random individuals to each generation formed by the algorithm. The random individuals limit the premature convergence to the local minimum and contribute to more thorough exploration of the search space. This article concentrates specifically on the role of random individuals in the identification of the global minimum of the cost function. Besides, the paper also contains some useful estimates of the probability of finding the global minimum of the corresponding cost function.