The comparative analysis of the effectiveness of Goldberg and Holland’s classical models and their modifications using various options of the generational strategy is presented. The concept assuming that the number of individuals in a generation does not change is used in the classical genetic algorithms. An approach advancing the efficiency of standard Goldberg and Holland’s models through varying the number of individuals in a generation is considered. Various embodiments of the generational strategy are used to solve the homogeneous minimax scheduling problem related to the class of NP-complete problems. The computational experiment conducted for a various number of processors and works has shown that this approach can significantly improve the genetic algorithm efficiency by small changes in the standard models allowing obtain the solution that is closer to the accurate solution.