Pitting damage as a result of contact stress on the gears teeth flanks is one of the most important problems needing to be solved in the process of gearing design and calculation. According to current valid standards, such calculations can be resolved with a high level of reliability for all the usual gearing types. However, suitable calculations for HCR gears have not been adequately researched to date. It has been identified that in HCR gears some different process of pitting formation occurs during the gear‘s operation. In this article, the authors present original results of the HCR gearing research and describe a new method for finding optimal solutions for , and x1, using a Generalized Particle Swarm Optimization Algorithm.