The determination of optimal design of the planetary gear train with a lightweight, a short center distance, and a high efficiency is an important issue in the preliminary design of power transmission systems. Conventional and traditional methods have been widely used in optimization. They are deterministic and limited to solve some mechanical problems with several variables and constraints. Therefore, some optimization methods have been developed, such as the nonconventional method, the genetic algorithm (GA). This paper describes a multiobjective optimization for the epicyclical gear train system using the GA. It is aimed to obtain the optimal dimensions for epicyclical gear components like a module, number of teeth, the tooth width, the shaft diameter of the gears, and a performed efficiency under the variation of operating mode of PGT system. The problem is formulated under the satisfaction of assembly and balance constraints, bending strength, contact strength of teeth, and other dimension conditions. The mathematical model and all steps of the GA are presented in detail.

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