Evolutionary algorithms (EA) are well-performing methods for global optimization. Differential evolution (DE) is successfully used EA for wide spectrum of the optimization tasks. DE has several control parameters and the quality of the founded solution depends on their setting. In the case of the very hard tasks, the situations arise where even DE is not able to solve them. Sometimes DE get stuck in the local minimum, sometimes DE is not able to converge to any solution. This paper is focused on the ability to avoid DE to get stuck in this situation. The speed of the convergence is studied and controlled in order to achieve better results in the numerous test problems.