This paper, intended for researchers, introduces a stochastic method for calculating the optimal tax schedule based on taxpayer utility, population skill distribution, and wages. It implements and extends the classic approach to optimal income tax calculation introduced by J.A. Mirrlees. A genetic algorithm is applied instead of the numerical or analytical method of solving the problem. In the experimental part of the article, we took basic statistics for Germany in 2017 to infer about the distribution skills and wages of the working population. Their aim was to verify whether our approach would give similar results to those known from the literature on the subject. Thus, we have calculated the impact of the taxpayer attitude to work and budget external flows on the income tax schedule. Then, we measured the convergence of the search process across multiple runs of the algorithm. Analysis of obtained results brought us to the conclusion that they are similar to one known from the literature.