  To relieve the computational cost of design evaluations using expensive finite element 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 (HOpt) framework to deepen our understanding of the effect. 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. For each MLA model, the model accuracy and robustness before and after the HOpt are compared. The results show that HOpt can generally improve the performance of the MLA models in general. HOpt leads to few improvements in the MLAs accuracy and robustness for complex problems, which are featured by high-dimensional mixed-variable design space. The HOpt is recommended for the design problems with intermediate complexity. 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. To sum up, this study benefits the selection of HOpt method for the different types of design problems based on their complexity. 
Understanding the effect of hyperparameter optimization on machine   learning models for structure design problems