To relieve the computational cost of design evaluations using expensive finite element (FE) simulations, surrogate models have been widely applied in computer-aided engineering design. Machine learning algorithms (MLAs) have been implemented as surrogate models due to their capability of learning the complex interrelations between the design variables and the response from big datasets. Typically, an MLA regression model contains model parameters and hyperparameters. The model parameters are obtained by fitting the training data. Hyperparameters, which govern the model structures and the training processes, are assigned by users before training. There is a lack of systematic studies on the effect of hyperparameters on the accuracy and robustness of the surrogate model. In this work, we proposed to establish a hyperparameter optimization framework to deepen our understanding of the effect. Based on the sequential model-based optimization method, the Pareto front is generated by running the optimal acquisition and updating the surrogate model iteratively. The optimum acquisition works by repeating a design space shrinking process. Using the acquired optimum, the surrogate model is updated, which describes the relationship between the hyperparameter combinations (inputs) generated by Latin hypercube sampling from the design space and structural response (outputs) to evaluate the modeling accuracy. The updated model will then be used for the next iteration of optimal acquisition until the termination criterion is met. Four frequently used MLAs, namely Gaussian Process Regression (GPR), Support Vector Machine (SVM), Random Forest Regression (RFR), and Artificial Neural Network (ANN), are tested on four benchmark examples of structure design optimization. For each MLA model, the model accuracy and robustness before and after the hyperparameters optimization (HOpt) are compared. The results show that HOpt can generally improve the performance of the MLA models in general with dependency on model complexity. HOpt leads to unstable improvements in the MLAs accuracy and robustness for complex problems, which are featured by high-dimensional mixed-variable design space. We also investigated the additional computational costs incurred by HOpt. The training cost is closely related to the MLA architecture. After HOpt, the training cost of ANN and RFR is increased more than that of the GPR and SVM. In summary, this study benefits the selection of HOpt method for different types of design problems based on their complexity (i.e. design domain continuity and the number of design variables, etc.).

为了减轻使用昂贵的有限元（FE）仿真进行设计评估的计算成本，替代模型已广泛应用于计算机辅助工程设计中。机器学习算法（MLA）由于能够学习设计变量与大数据集的响应之间的复杂相互关系而被实现为替代模型。通常，MLA回归模型包含模型参数和超参数。通过拟合训练数据获得模型参数。用户在训练之前分配用于控制模型结构和训练过程的超参数。缺乏关于超参数对替代模型的准确性和鲁棒性的影响的系统研究。在这项工作中，我们建议建立一个超参数优化框架，以加深对效果的理解。基于基于顺序模型的优化方法，通过运行最佳采集并迭代更新替代模型来生成帕累托前沿。最佳设计是通过重复设计空间缩小过程来实现的。使用获取的最优值，替代模型将更新，该模型描述了由拉丁超立方体采样从设计空间生成的超参数组合（输入）与结构响应（输出）之间的关系，以评估建模精度。然后，更新的模型将用于最佳采集的下一次迭代，直到满足终止标准为止。四个常用的MLA，即高斯过程回归（GPR），支持向量机（SVM），随机森林回归（RFR）和人工神经网络（ANN）在结构设计优化的四个基准示例上进行了测试。对于每个MLA模型，都对超参数优化（HOpt）之前和之后的模型准确性和鲁棒性进行了比较。结果表明，HOpt通常可以依赖于模型复杂性来总体上改善MLA模型的性能。HOpt导致MLA的准确性和对复杂问题的鲁棒性的不稳定提高，这些特征以高维混合变量设计空间为特征。我们还调查了HOpt产生的额外计算成本。培训费用与MLA体系结构密切相关。HOpt之后，与GPR和SVM相比，ANN和RFR的培训成本增加得更多。总之，