Volume-Efficiency Trade-Off Optimization of Two-Stage Helical Gearboxes via MOEA/D-DE Algorithm

The design of two-stage helical gearboxes inherently involves a trade-off between structural compactness and transmission efficiency. In this study, a multi-objective optimization framework based on the MOEA/D-DE (Multi-Objective Evolutionary Algorithm based on Decomposition with Differential Evolution) is proposed to simultaneously minimize gearbox volume and maximize power transmission efficiency. The optimization formulation integrates essential geometric and performance-related constraints to ensure feasible and manufacturable designs. By decomposing the bi-objective optimization problem into a set of scalar subproblems, the MOEA/D-DE algorithm effectively preserves solution diversity while achieving reliable convergence toward the Pareto-optimal front. Numerical investigations demonstrate that the proposed approach yields a well-distributed set of trade-off solutions, providing clear design insights into the balance between size reduction and efficiency enhancement. Comparative results indicate that the proposed framework achieves superior solution quality and computational performance compared to conventional optimization methods.