To enhance the safety of children in frontal collisions of school buses, this study conducts the design optimization for a pre-inflation airbag under mixed conditions involving two child age groups (6 and 12 years old), three sitting postures, and two crash pulses. A coupling model integrating the school bus restraint system and the pre-inflation airbag is developed. Based on non-dominated sorting genetic algorithm III (NSGA-III), an improved variant called NSGA-III-SAA is proposed. This variant incorporates the symmetric Latin hypercube design method, adopts adaptive crossover and mutation rates, and modifies the environmental selection mechanism using an adaptive niche strategy. An experimental comparison between NSGA-III-SAA and five state-of-the-art multi-objective evolutionary algorithms (MOEAs) is conducted using Deb-Thiele-Laumanns-Zitzler and Walking-Fish-Group test suites. Based on the inverted generational distance (IGD) and hypervolume (HV), the performance scores of NSGA-III-SAA and the five other MOEAs are 1.06, 1.40, 2.00, 2.80, 2.85, and 3.81, respectively, lower scores signify better performance, indicating that NSGA-III-SAA outperforms the others. Additionally, it demonstrates clear advantages in computational efficiency and constraint handling. Through NSGA-III-SAA, the optimal configuration of the airbag design variables is as follows: upper strap length of 0.2645 m, installation height of 0.4092 m, opening pressure of 1.161 × 10⁵ Pa, and opening degree of 1.99. Compared to pre-optimization results, the head injury criterion (HIC₁₅), thorax injury values (T_3ms and THPC), and weighted injury criteria (WICC₆ and WICC₁₂) for children under twelve conditions show significant reductions. Specifically, the weighted injury criteria decrease by 41.38%, 43.13%, 34.20%, 30.21%, 34.08%, 27.09%, 25.38%, 30.80%, 28.91%, 19.45%, 26.86%, and 22.75%, respectively.

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Optimal design of pre-inflation airbag of school bus in mixed conditions using NSGA-III-SAA