A Hybrid NSGA-II and EAMR Approach for Dual-Objective Optimization of a Two-Stage Gearbox with Split Input Stage
Received: 28 April 2025 | Revised: 21 June 2025 | Accepted: 28 June 2025 | Online: 6 October 2025
Corresponding author: Thi Thu Huong Truong
Abstract
This study proposes a hybrid Multi-Objective Optimization (MOO) approach that integrates the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and the Evaluation by an Area-based Method of Ranking (EAMR) to optimize the design of a two-stage helical gearbox featuring a split input stage. The optimization simultaneously targets two conflicting objectives: minimizing the base area of the gearbox housing and maximizing the transmission efficiency. A parametric design model was developed to capture the key geometrical and performance parameters, while ensuring compliance with the practical constraints related to gear strength and manufacturing limitations. The NSGA-II algorithm was employed to generate a set of Pareto-optimal solutions, which were subsequently ranked using the EAMR method to support decision-making. The results demonstrate the effectiveness of the hybrid approach in identifying high-performance design alternatives that offer an optimal balance between compactness and efficiency. This is the first study to apply a combination of NSGA-II and a Multi-Criteria Decision-Making (MCDM) method to the dual-objective optimization of a two-stage gearbox with a split input stage. In particular, the proposed approach successfully identifies the optimal design parameters across a wide range of transmission ratios, thereby facilitating the initial selection of appropriate gearbox transmission ratios in the early-stage design. This study also provides valuable design guidelines for engineers seeking to improve space utilization and performance in gear transmission systems.
Keywords:
two-stage gearbox, split input stage, NSGA-II, EAMR, multi-objective optimization, gear design, gearbox efficiency, base area minimization, helical gears, Pareto frontDownloads
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Copyright (c) 2025 Van Thanh Dinh, Duc Binh Vu, Manh Cuong Nguyen, Thi Thu Huong Truong
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