The synthesis of networks-on-chip topologies based on the evolutionary computations method is proposed. The optimality criteria of the networks-on-chip topologies and a new class of quasi-optimal topologies are proposed. The requirements for quasi-optimal topologies are defined. The genetic algorithm GeNoC for the synthesis of quasi-optimal networks-on-chip topologies with number of nodes up to 100 is developed. By using the mathematical methods of optimization, the analysis of the obtained quasi-optimal topologies for the number of nodes of 25 is performed. It is shown, that the properties of the obtained topologies are close to the theoretically possible optimal ones while the difference in their characteristics is less than 3,7%.