A multi-objective optimal model of a K-H-V cycloid pin gear planetary reducer is presented in this article. The optimal model is established by taking the objective functions of the reducer volume, the force of the turning arm bearing, and the maximum bending stress of the pin. The optimization aims to decrease these objectives and obtains a set of Pareto optimal solutions. In order to improve the spread of the Pareto front, the density estimation metric (crowding distance) of non-dominated sorting genetic algorithm II is replaced by the k nearest neighbor distance. Then, the improved algorithm is used to solve this optimal model. The results indicate that the modified algorithm can obtain the better Pareto optimal solutions than the solution by the routine design.
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