MULTI-OBJECTIVE OPTIMIZATION OF TWO-STAGE HELICAL GEARBOXES USING NSGA-II AND MCDM METHODS: MINIMIZING MASS AND MAXIMIZING EFFICIENCY - Van Thanh, Dinh; Duong, Vu; Van Tung, Nguyen; Thu Huong, Truong; Thanh Hien, Bui; Xuan Tu, Hoang (Journal of Applied Engineering Science, 2026)
This study presents a multi-criteria design approach for two-stage helical gearboxes using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) in combination with MCDM methods. The optimization problem was formulated with two conflicting objectives: minimizing gearbox mass and maximizing transmission efficiency. NSGA-II was employed to generate a set of Pareto-optimal solutions, while three different MCDM methods—MARCOS (the Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS), TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), and SAW (Simple Additive Weighting)— was applied to identify the most preferred compromise design among them. Regression analysis revealed a strong linear relationship between the stage-one gear ratio (u1) and the overall transmission ratio (uh), ensuring practical feasibility of the optimized gear allocation. Numerical results demonstrated that gearboxes designed with transmission ratios in the range of uh=15–25 achieved the most balanced trade-off between reduced mass and high efficiency. The proposed hybrid NSGA-II–MCDM framework thus provides a powerful decision-support tool for gearbox designers, enabling both lightweight and energy-efficient configurations. In addition, the findings have clear practical implications, as the proposed framework can support the development of more compact and efficient gearboxes in automotive and industrial applications, where reducing mass and improving efficiency are critical design requirements.