To improve the computational cost and accuracy of approximate-based multi-objective optimization problems in engineering, an adaptive RBF neural network (ARBFNN) method integrating RBF neural network model, fuzzy subtractive clustering (FSC) sequence sampling method and non-dominated sorting genetic algorithm (NSGA-II) is proposed. To solve the problem that the number of new sample points is difficult to determine, FSC sequence sampling is proposed to select the clustering center points as newly added sample points. First, the ARBFNN method is verified by the five test functions. The results show that the ARBFNN method is significantly better than static RBFNN model based on multi-objective optimization (SRBFNN) in terms of global convergence and efficiency performance, and the other two adaptive approximate optimization methods in terms of overall efficiency. Based on the above, the accuracy and efficiency of ARBFNN method are very high. Finally, the method is applied to an engineering example: the lightweight and crashworthiness design of floor rails. The cab model coupled with implicit parameterized floor rails model is built using the SFE-CONCEPT software to achieve collaborative optimization design of shape-size-material. The optimization results show that the ARBFNN method can guarantee the error of the approximate optimal solution and the finite element solution (expensive solution) within 2%, so the accuracy of highly nonlinear (finite element analysis of collision conditions) approximate optimization is improved. Hence, the proposed ARBFNN method is feasible and effective in solving complex and expensive engineering optimization problems.

为了提高工程中基于近似的多目标优化问题的计算成本和准确性，结合了RBF神经网络模型，模糊减法聚类（FSC）序列采样方法和非支配排序遗传算法的自适应RBF神经网络（ARBFNN）方法（NSGA-II）。为了解决难以确定新采样点数量的问题，提出了FSC序列采样方法，选择聚类中心点作为新添加的采样点。首先，通过五个测试函数验证了ARBFNN方法。结果表明，在全局收敛性和效率方面，ARBFNN方法明显优于基于多目标优化（SRBFNN）的静态RBFNN模型，在总体效率方面，另两种自适应近似优化方法。基于以上所述，ARBFNN方法的准确性和效率都很高。最后，该方法被应用于一个工程实例：地板导轨的轻量化和耐撞性设计。使用SFE-CONCEPT软件构建了带有隐式参数化地板导轨模型的驾驶室模型，以实现形状尺寸材料的协同优化设计。优化结果表明，ARBFNN方法可以保证近似最优解和有限元解（昂贵解）的误差在2％以内，从而提高了高度非线性（碰撞条件的有限元分析）近似优化的精度。因此，