The paper presents a numerical algorithm for calculating the control that converts a catalytic process from an initial state to a given final state in minimum time. The formulation of the problem of optimal speed for the chemical process on the basis of its mathematical model is performed. The temperature of the reaction mixture is considered as a control. A numerical algorithm based on the method of differential evolution for solving the problem is given. The advantage of the proposed approach is that in its application there is no need to set the initial approximation of the solution based on the physical and chemical sense of the problem. The work of the algorithm is tested on an industrially significant process of synthesis of phthalic anhydride. The optimum temperature regime and the shortest duration of the process at a given value of phthalic anhydride concentration, at a fixed content of naphthoquinone in the reaction mixture, under the condition of complete consumption of naphthalene have been calculated. The efficiency of application of the developed algorithm is demonstrated by comparing the found solutions of rapidity problems with the solutions calculated using other methods.