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This study proposes a hybrid optimization approach combining the Non-dominated Sorting Genetic Algorithm II (NSGA-II) with the Multi-Attributive Ideal-Real Comparative Analysis (MAIRCA) method using entropy-based weights to achieve a balanced design of a two-stage helical gearbox. The optimization aims to simultaneously minimize the gearbox's cross-sectional area and maximize its transmission efficiency. The NSGA-II algorithm is employed to generate a set of Pareto-optimal solutions, while the MAIRCA method, enhanced with entropy-derived criterion weights, is applied to identify the most favorable compromise solution. Results reveal the influence of transmission ratios and design parameters on the trade-off between compactness and efficiency. The proposed methodology demonstrates its effectiveness in supporting design decisions for high-performance and space-constrained gear transmission systems.

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Hybrid NSGA-II–MAIRCA–Entropy Method for Multi-Objective Optimization of a Two-Stage Helical Gearbox: Balancing Efficiency and Cross-Sectional Area

  • 会议论文

  • 发表日期：

    2026年

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  • Dinh Van Thanh,
  • Vu Duong,
  • Nguyen Van Trang,
  • Hoang Minh Anh

摘要

This study proposes a hybrid optimization approach combining the Non-dominated Sorting Genetic Algorithm II (NSGA-II) with the Multi-Attributive Ideal-Real Comparative Analysis (MAIRCA) method using entropy-based weights to achieve a balanced design of a two-stage helical gearbox. The optimization aims to simultaneously minimize the gearbox's cross-sectional area and maximize its transmission efficiency. The NSGA-II algorithm is employed to generate a set of Pareto-optimal solutions, while the MAIRCA method, enhanced with entropy-derived criterion weights, is applied to identify the most favorable compromise solution. Results reveal the influence of transmission ratios and design parameters on the trade-off between compactness and efficiency. The proposed methodology demonstrates its effectiveness in supporting design decisions for high-performance and space-constrained gear transmission systems.