Based on the penalty function method combined with the improved genetic algorithm,the multi-objective and multi-restriction reliability optimal design of the reducer with hardened tooth surface and modified helical cylinder gear is carried out.According to the properties of the constraint conditions,the different methods are used for effectively avoiding the local optimum problem.The accurate three-dimensional description of the involute gear is carried out by the establishment of the tooth profile curve coordinate equation of the involute gear.According to the interface technology of VB and SolidWorks,the three-dimensional parametric modeling of the involute gear is achieved based on the optimal design results.