Abstract <p>The article considers the problem of optimal performance for a process described by a system of nonlinear differential equations. To determine an approximate solution to the problem, it is proposed to apply the evolutionary method of artificial immune systems, which is not sensitive to the choice of the initial approximation. To find a numerical solution to the problem of optimal performance, a step-by-step algorithm is formulated and tested on model problems. For each problem, a suboptimal control in terms of performance is obtained and the parameters of the algorithm are determined, at which the solution is calculated with the lowest computational costs. The efficiency of the developed algorithm is demonstrated by comparing the results of numerical calculations with the results of using the fixed point method and the method of artificial immune systems.</p>