On the approximate solution of a nonlinear problem of optimal performance

The article proposes an approach to finding an approximate solution to a nonlinear problem of optimal performance based on genetic algorithms. The use of genetic algorithms implies a finite-dimensional approximation of the original problem and the search for control parameters in the class of piecewise constant functions. The advantages of the proposed approach are the lack of need to use additional methods and transformations of the problem, the possibility of using it to solve multi-extremal problems, the absence of requirements for the type of process model equations, and the independence of the solution from the initial approximation. A modified genetic algorithm with real coding is given for solving a finite-dimensional problem. The algorithm is tested on examples of nonlinear problems of optimal performance. The obtained results of solving the problems are compared with the results of using other methods. The independence of the calculated solution from the choice of the initial approximation is shown.