The article is devoted to the possibility of using and adapting genetic algorithms (GA) for rational design of cylindrical reducers gearboxes. The main theory of the LP-search method are considered, which allow to evaluate the possibilities of this method and analyze the prospects of its expansion using the ideology of GA. The basic theory concerning GA are considered. The main differences between GA and classical optimization methods are given. The algorithmic scheme of classical GA is described. An analysis of the main genetic selection of parents, cross-breeding and mutations is given. An estimation of the basic genetic operators is made on their productivity and convenience of use, and determined by their choice for further work. Possible variants of modifications of GA sequences are considered considering the features of the problem of rational design of geared cylindrical gearboxes. The first one provides an algorithm that allows a significant increase in the number of viable individuals, that is, test points satisfying the numerical and functional limitations of the data, thereby offsetting the lack of limitation on the maximum possible number of test points in the LP-search. The following describes an algorithm that focuses primarily on the selection of more qualitative test points and the creation of an appropriate population that is inherent in genetic-evolutionary algorithms (GEAs). It is based on the operator - the withdrawal of less quality points, as well as the mandatory use of the operator mutation. Thus, a theoretical basis for further testing of proposed modifications of GA algorithms was created.