Hybrid NSGA-II–MARCOS Optimization of a Dual-Input Spur Gearbox: Targeting Efficiency and Minimal Length
Received: 15 December 2025 | Revised: 26 January 2026 | Accepted: 7 February 2026 | Online: 4 April 2026
Corresponding author: Luu Anh Tung
Abstract
This study presents a hybrid optimization framework for the design of a dual-input two-stage helical gearbox, in which the fast stage is split into two parallel power paths to improve load distribution and design flexibility. The design objectives are defined to explicitly reflect two conflicting physical requirements: minimizing the total axial length, which represents structural compactness under spatial constraints, and maximizing mechanical efficiency, which is governed by cumulative mechanical and tribological losses. The optimization process employs the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to generate Pareto-optimal solutions that represent trade-offs between conflicting objectives. To support engineering decision-making among Pareto-optimal configurations, the Multi-Attributive Real Comparative Analysis (MARCOS) method is subsequently integrated to rank candidate designs and identify balanced solutions based on compactness-efficiency compromise. A comprehensive gear system model is developed, incorporating gear geometry, shaft layout, meshing conditions, and detailed loss calculations. The results reveal clear physical trends: increasing the transmission ratio leads to longer gearbox structures and higher mechanical losses, while the dual-input first stage mitigates efficiency deterioration by redistributing torque and reducing localized loading. This approach offers not only algorithmic optimization but also mechanically meaningful design insights, providing valuable insights for engineers facing spatial constraints and high-performance requirements in modern mechanical transmission systems.
Keywords:
two-stage gearbox, multi-objective optimization, NSGA-II, gear ratio, face width coefficient, efficiency, volume, design trade-offDownloads
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Copyright (c) 2026 Nguyen Hong Linh, Do Thi Tam, Bui Thanh Hien, Hoang Xuan Tu, Luu Anh Tung
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