Optimal Design of a Two-Stage Helical Gear Reducer with Split Output Stage: A Multi-Objective Approach Based on NSGA-II and TOPSIS

This study presents a novel approach for the optimal design of a two-stage helical gear reducer with a split output stage, to achieve a balance between the mechanical compactness and transmission performance. The optimization problem considers two conflicting objectives: minimizing the cross-sectional area of the gearbox structure and maximizing its mechanical efficiency. To solve this Multi-Objective Optimization Problem (MOOP), the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed, aiming to generate a set of Pareto-optimal solutions, capturing the trade-offs between the two design goals. Subsequently, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is applied to rank and identify the most preferable solution among the Pareto front based on decision-makers' preferences. The proposed hybrid framework enables a systematic exploration of the design space, providing engineering insights into how the gear ratio distribution and geometric parameters influence the gearbox’s performance. The results demonstrate that the integration of NSGA-II and TOPSIS effectively supports the optimal design of compact and high-efficiency gear reducers with split-stage configurations.