## 3 Results and Discussion
### Prediction and Comparstion of between SVM, LS-SVM and IFOA-LS-SVM Models  
To evaluate the prediction accuracy of the IFOA-LS-SVM model, the difference between the target values (i.e., the values of extraction yield of quercetin and rutin) and the predicted values (i.e., the actual output of the model) is considered as the error, and is represented in different ways. In this work, four measures, the mean relative error (MRE), the root of mean square error (RMSE), the mean absolute error (MAE) and Theil's inequality coefficient (TIC), are employed for model evaluation. They expresses are defined as follows. \[MRE=\frac{1}{n}\sum_{i=1}^{n}\frac{|y_{i}-\hat{y}_{i}|}{y_{i}}\times 100\% \tag{18}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & \(\boldsymbol{\gamma}\) & \(\boldsymbol{\sigma^{2}}\) \\ \hline Rutin yield & 9913.65 & 11.08 \\ Quercetin yield & 9896.80 & 10.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The optimum parameter values of LS-SVM model optimized by the IFOA. Figure 10: Procedure diagram of the least squares support vector machine the improved based on fruit fly optimization algorithm (IFOA-LS-SVM) model. \[MAE=\frac{1}{n}{\sum\limits_{i=1}^{n}{{{{\left|{{y_{i}}-{{\hat{y}}_{i}}}\right|}}}}} \tag{19}\]  
\[RMSE=\sqrt{\frac{1}{n}{\sum\limits_{i=1}^{n}{{{{\left({{y_{i}}-{{\hat{y}}_{i}}} \right)}^{2}}}}}} \tag{20}\]  
\[TIC=\sqrt{\frac{{\frac{{\frac{1}{n}\sum\limits_{i=1}^{n}{{{{\left({{y_{i}}-{{ \hat{y}}_{i}}}\right)}^{2}}}}}}}}{{\sqrt{\frac{{\sum\limits_{i=1}^{n}{{{{y_{i }}}^{2}}}}}+\sqrt{\sum\limits_{i=1}^{n}{{{{\hat{y}}_{i}}^{2}}}}}}}} \tag{21}\]  
where \({{{\hat{y}}_{i}}}\) and \({{{y}_{i}}}\) denote the predicted values of model and actual values, respectively; and \(n\) represents the total number of samples. RMSE, MRE and MAE are used to assess the prediction accuracy of model. TIC is applied for evaluating the fitness of model. To compare the predicting effect of extraction yield of quercetin and rutin, the SVM model and LS-SVM model are employed as the comparison basis. The prediction results of three models on the testing dataset are listed in Table 2.  
As can be seen, the prediction performance of IFOA-LS-SVM model is superior to other two models. That is, for rutin, the SVM model gave a RMSE of 0.1268, an MRE of 3.87%, an MAE of 0.0998 and a TIC of 0.0082; the LS-SVM model obtained a RMSE of 0.1035, an MRE of 1.88%, an MAE of 0.0566 and a TIC of 0.0028; and the IFOA-LS-SVM model obtained a RMSE of 0.0540, an MRE of 1.05%, an MAE of 0.0189 and a TIC of 0.0014. For quercetin, the SVM model obtained a RMSE of 0.1204, an MRE of 3.99%, an MAE of 0.0965 and a TIC of 0.0080; the LS-SVM model obtained a RMSE of 0.0997, an MRE of 2.05%, an MAE of 0.0557 and a TIC of 0.0030; and the IFOA-LS-SVM model gave a RMSE of 0.0536, an MRE of 0.97%, an MAE of 0.0183 and a TIC of 0.0013. Rutin and the MRE (%) indicator were chosen as illustration: comparing with that of SVM model and LS-SVM model, the predictive error of IFOA-LS-SVM model decreased 72.9% and 44.1%, respectively, which suggests the proposed IFOA-LS-SVM model has higher prediction accuracy for the extraction yield of rutin during the UAE process. For quercetin, a similar result was also found. A visual comparison between the prediction outputs and the experimental values are also depicted in Figure 11. As can be seen, compared with the SVM model and LS-SVM model, the prediction values of IFOA-LS-SVM model were closer to the experimental values and the errors of the IFOA-LS-SVM model were less than those of the SVM model and LS-SVM model. That is, the prediction performance of the proposed IFOA-LS-SVM model surpasses other two models in term of predicting the extraction yields of quercetin and rutin from _Euonymus alatus_ (Thumb.) [PERSON].