## 2 Materials and Methods
### Dynamic Ensemble of Surrogates  
Generally speaking, there is no single surrogate that outperforms other surrogates in all kinds of problems. Therefore, the ensemble surrogate, which consists of several component surrogates that can fully utilize the benefits of each surrogate, has been widely used. The prediction of the ensemble surrogate is obtained through weighting the predicted value of multiple surrogates, so the approximate fitness of the samples can be determined by the following:  
\[\hat{y}_{\textit{eras}}(\mathbf{x})=\sum_{i=1}^{N_{\textit{eras}}}\omega_{i}(\mathbf{x} )\hat{y}_{i}(\mathbf{x}) \tag{9}\]  
where \(\hat{y}_{\textit{eras}}(\mathbf{x})\) is the prediction of the ensemble of surrogates, \(\hat{y}_{i}(\mathbf{x})\) denotes the prediction of the ith surrogate, and \(N_{\textit{eras}}\) is the number of surrogates, \(\omega_{i}(\mathbf{x})\) is the weight factor of the ith surrogate, and \(\omega_{i}(\mathbf{x})\) needs to meet the formula \(\sum_{i=1}^{N_{\textit{eras}}}\omega_{i}(\mathbf{x})=1\). According to the characteristics of weight coefficients, the existing methods for ensemble modeling can be classified into global measures-based, local measures-based, and mixed measures-based. The weight coefficient in global measures is a constant calculated according to the global error of each surrogate, while the weight coefficient in local measures is influenced by the location of the prediction sample. The former ignores the difference in fitting accuracy of the model in local areas, while the accuracy of the latter may decline away from the sample points. Mixed measures-based combines the advantages of the two, taking into account the regions near and away from the samples. On the basis of the existing methods, [PERSON] et al. [38] suggested a new unified ensemble of surrogates (UES), which integrates global and local measures, and the weight coefficients are determined according to the position of the predicted sample within the entire decision space as follows:  
\[\omega_{i}(\mathbf{x})=\frac{\omega_{i}^{G}(\mathbf{x})\lambda(\mathbf{x})+\omega_{i}^{L} (\mathbf{x})(1-\lambda(\mathbf{x}))}{\sum_{j=1}^{N_{\textit{eras}}}\left[\omega_{j}^ {G}(\mathbf{x})\lambda(\mathbf{x})+\omega_{j}^{L}(\mathbf{x})(1-\lambda(\mathbf{x}))\right]} \tag{10}\]  
where \(\omega_{i}^{G}(\mathbf{x})\) and \(\omega_{i}^{L}(\mathbf{x})\) represent the global and local weight coefficients of the ith surrogate, respectively and \(\lambda(\mathbf{x})=sin\left\{\frac{\pi}{2}\left(\frac{d_{1}(\mathbf{x})}{d_{2}(\mathbf{x })}\right)\right\}\) is the control function used to determine the impact of the global and local measures, where \(d_{1}(\mathbf{x})\) and \(d_{2}(\mathbf{x})\) represent the distances between the predicted sample and its closest and second-closest samples, respectively. As a fixed ensemble of KRG, RBF, and PRS, the UES is difficult to apply to high-dimensional problems. For one thing, the time cost of constructing the KRG model is gradually exceed the affordable range as the dimensions increase. For other things, the UES uses leave-one-out cross-validation to calculate weight coefficients, which can consume a lot of time if the fixed ensemble of component surrogates is used. To alleviate the running cost, [PERSON] et al. [28] developed a dynamic ensemble of surrogates (DES) based on a UES, which takes RBF, PRS, and SVR as component surrogates and uses the determination coefficient \(R^{2}\) and the normalized root mean square error \(NRMSE\) to filter the models.