A Multi-Objective Optimization Approach for the Two-Stage Helical Gearbox Design Using NSGA-II: Balancing Efficiency and Structural Compactness
Received: 12 July 2025 | Revised: 16 August 2025 | Accepted: 2 September 2025 | Online: 16 October 2025
Corresponding author: Duong Vu
Abstract
The design of two-stage helical gearboxes inherently involves trade-offs between the structural compactness and transmission efficiency. Traditional design methods often fail to capture these competing objectives simultaneously. This study presents a comprehensive multi-objective optimization approach using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to identify the optimal trade-offs between minimizing the cross-sectional area and maximizing the efficiency of a two-stage helical gearbox. Drawing from the strengths of evolutionary algorithms and integrating insights from prior literature on hybrid and decision-making-based optimization methods, the proposed model formulates the gearbox design problem with realistic constraints and evaluates the Pareto front of optimal solutions. The results demonstrate that NSGA-II provides a well-distributed set of non-dominated solutions, offering engineers greater flexibility in balancing performance and structural requirements. The comparative analysis with existing approaches highlights the effectiveness of the proposed method in simultaneously achieving compactness and energy efficiency in gearbox systems.
Keywords:
NSGA-II, multi-objective optimization, gearbox design, helical gear, gear ratio, efficiency, cross-sectional area, trade-off analysisDownloads
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