## 3 Results and Discussion
### Modeling of UAE Using IFOA-LS-SVM  
In this work, the prediction model of the UAE of quercetin and rutin from _Euonymous alatus_ ([PERSON].) [PERSON] was established by the improved FOA optimized LS-SVM model. LS-SVM is more suitable for modeling using limited experimental data since it has higher generalization, more efficient than that of SVM. In order to construct a more practical and accurate IFOA-LS-SVM model for the UAE of quercetin and rutin, in this work, all training data and validating data are selected from the aforementioned experiment data. The extraction time, extraction temperature, ultrasound power, ultrasound frequency, solvent volume/sample ratio and ethanol solution concentration are used as the input of this model, while the rutin yield and quercetin yield are used as the output. The structure diagram for ultrasonic extraction process based on LS-SVM is represented in Figure 9.  
To prevent truncation error from experimental data for model developed, all input/output should be normalized to the range \([-1,+1]\) using Equations (16) and (17).  
\[x_{\text{scale}}=2\frac{x-x_{\text{min}}}{x_{\text{max}}-x_{\text{min}}}-1 \tag{16}\]  
\[y_{\text{scale}}=2\frac{y-y_{\text{min}}}{y_{\text{max}}-y_{\text{min}}}-1 \tag{17}\]  
where \(x_{\text{scale}}\) and \(y_{\text{scale}}\) are the scaled valves of input and output, respectively; \(x\) and \(y\) are the actual values of input and output, respectively; \(x_{\text{min}}\) and \(x_{\text{max}}\) represent the minimum and maximum actual values of input, respectively; and \(y_{\text{min}}\) and \(y_{\text{max}}\) represent the minimum and maximum actual values of output, respectively.  
In this work, a total of 60 batches of experimental data are used. Each batch of data represents a complete UAE process. Forty batches of data are used as the training sample to optimize the parameters of LS-SVM and to build the IFOA-LS-SVM model, and the remaining batches of data are used as the testing sample to verify the generalization ability of the model.  
The parameters of the IFOA-LS-SVM are set as follows: _maxgen_ (i.e., maximum iteration number) = 200, _sizepop_ (i.e., population size) = 40, \((X_{\text{axist}},Y_{\text{axist}})\) (i.e., the initial position coordinate) = (2.5, 2.5), the random flight distance range \(FR\)\(\subset\)\([-15,\)\(15]\), and step length = 2, \(a\) = 5. All mentioned calculations are performed by means of Matlab program (Mathworks, Natick, MA, USA). The LS-SVM toolbox (LS-SVM v 1.5, Suykens, Leuven, Belgium) is utilized to derive all models under the Windows 7 operating system using a high-performance (Lenovo Co., Beijing, China).  
In the LS-SVM model, the two key parameters of \"\(\gamma\)\" and \"\(\sigma^{2}\)\" are optimized by the IFOA. By iterative evolution, the IFOA continuously adjusts these two parameters until the optimum values of parameters are obtained. The procedure diagram of the IFOA-LS-SVM model is illustrated in Figure 10.  
Figure 9: Structure diagram for ultrasonic extraction process based on least squares support vector machine (LS-SVM) model.  
After optimizing processes, the values of \"\(\gamma\)\" and \"\(\sigma^{2}\)\" were obtained (Table 1). Based on the optimized parameters, we established a new optimum LS-SVM model and predicted the training set and the generalization set for the extraction of quercetin and rutin. Finally, comparison diagrams between the predicting value and the experimental value are drawn to validate the performance of the proposed model.