Pedestrian lower-leg protection and lower-speed crashworthiness often present two important yet competing criteria on the design of front-bumper structures. Conventional design optimization is largely focused on a single loading condition without considering multiple impact cases. Furthermore, design of front-bumper structures is usually discrete in engineering practice and impacting conditions are commonly random. To cope with such a sophisticated nondeterministic design problem, this study aimed to develop a successive multiple attribute decision making (MADM) algorithm for optimizing a functionally graded thickness (FGT) front-bumper structure subject to multiple impact loading cases. The finite element (FE) model of front-end vehicle was constructed and validated with the in-house experimental tests under the loads of both Flexible Pedestrian Legform Impactor (Flex-PLI) impact and lower-speed impact. In the proposed successive MADM algorithm, the order preference by similarity to ideal solution (TOPSIS) based upon relative entropy was coupled with the analytic hierarchy process (AHP) to develop a MADM model for converting multiple conflicting objectives into a unified single cost function. The presented optimization procedure is algorithmically iterated using the successive Taguchi method to deal with a large number of design variables and design levels. The results showed that not only the algorithm enabled to generate an optimal design efficiently, but also the robustness of Flex-PLI impact is significantly enhanced. The proposed algorithm can be potentially used for other engineering design problems with similar complexity.

行人小腿保护和低速耐撞性通常是前保险杠结构设计的两个重要但相互竞争的标准。传统的设计优化主要集中在单一载荷条件上，而不考虑多种冲击情况。此外，前保险杠结构的设计在工程实践中通常是离散的，撞击条件通常是随机的。为了应对这种复杂的非确定性设计问题，本研究旨在开发一种连续多属性决策 (MADM) 算法，用于优化受多个冲击载荷情况影响的功能梯度厚度 (FGT) 前保险杠结构。前端车辆的有限元 (FE) 模型是在柔性行人腿部冲击器 (Flex-PLI) 冲击和低速冲击载荷下通过内部实验测试构建和验证的。在所提出的连续 MADM 算法中，基于相对熵的理想解相似度优先顺序 (TOPSIS) 与层次分析法 (AHP) 相结合，开发了一个 MADM 模型，用于将多个相互冲突的目标转换为统一的单个成本函数。所提出的优化程序是使用连续田口方法在算法上迭代的，以处理大量的设计变量和设计水平。结果表明，该算法不仅能够有效地生成优化设计，而且显着增强了 Flex-PLI 影响的鲁棒性。