# A Gradient-Based Particle-Bat Algorithm for Stochastic Configuration Network
## 4 Numerical Experiments
### Performance of SCN Based on the G-BAPSO Algorithm
#### 4.2.1 Dataset Information  
Dataset 1 is generated by function \(f(x)=0.2e^{-(10x-4)^{2}}+0.5e^{-(80x-40)^{2}}+0.3e^{-(80x-20)^{2}}\), \(x\in[0,1]\), 1000 points are randomly collected as the training set, and the test set is 300 equidistant points on the interval \([0,1]\)[9].  
Dataset 2 is the current data (SM) [37; 38] in the UCI database. The task is to find the nonlinear relationship between synchronous motor excitation current and the input  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Function** & **Popsize** & **Iterations** & \(c_{1}\) & \(c_{2}\) & \(c_{3}\) & **Rf** & **r0** \\ \hline \(f_{1}\) & 50 & 20 & 0.3 & 0.3 & 0.4 & 0.9 & 3 \\ \(f_{2}\) & 200 & 20 & 2 & 2 & 0.0001 & 0.9 & 1 \\ \(f_{3}\) & 100 & 50 & 0.2 & 0.3 & 0.5 & 0.9 & 0.7 \\ \(f_{4}\) & 50 & 10 & 0.4 & 0.4 & 0.2 & 0.9 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters setting.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Iterations** &
\begin{tabular}{c} **The Error of the** \\ **Minimum Value of ‘f1’** \\ \end{tabular} & **Run Time (s)** \\ \hline
10 & \(8.0748\times 10^{-12}\) & 0.0202 \\
20 & \(1.1816\times 10^{-23}\) & 0.0246 \\
50 & \(7.7729\times 10^{-70}\) & 0.0511 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The sensitivity analysis of the iterations.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Function** & **G-BAPSO** & **G-PSO** & **PSO** & **Bat** & **FOA** \\ \hline \(f_{1}\) & \(\mathbf{1.1816\times 10^{-23}}\) & \(2.6410\times 10^{-23}\) & \(5.4593\times 10^{-6}\) & \(4.0801\times 10^{-3}\) & \(1.2026\times 10^{-2}\) \\ \(f_{2}\) & \(\mathbf{2.3441\times 10^{-15}}\) & \(3.1405\times 10^{-15}\) & \(2.8753\times 10^{-15}\) & \(5.0260\times 10^{-3}\) & \(2.2302\times 10^{-3}\) \\ \(f_{3}\) & \(\mathbf{0}\) & 0 & \(1.3776\times 10^{-13}\) & \(9.3501\times 10^{-5}\) & \(0.0114\times 10^{-2}\) \\ \(f_{4}\) & \(\mathbf{6.8003\times 10^{-6}}\) & \(7.9036\times 10^{-6}\) & \(3.2363\times 10^{-5}\) & \(3.9358\times 10^{-3}\) & \(1.8720\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: The average error of the optimal solution in 200 experiments.  
features including power factor, load current, synchronous motor excitation current change, and power factor error. There are 557 groups of samples, where 400 samples are used as the training set and 157 samples are used as the test set.  
Dataset 3 is the Banknote authentication dataset in the UCI database, which is extracted from images of samples of real and counterfeit bills. The task is to verify the authenticity of bills (classification). The data contains 4 input features (the variance, the skewness, the curtosis, and the entropy of the image), and the output corresponding to each group of input features is the banknote category (true or false). The dataset has 1372 samples, where 1038 samples are used for training and 334 samples are used for testing.  
Dataset 4 is the Iris dataset in the UCI database. There are three categories of Iris, and the task is to identify the iris category based on four input attributes including the length and width of calyx, and the length and width of the petal. The dataset contains 150 groups of samples, of which each category contains 50 groups of samples. where 120 groups of samples are used for training and 30 groups of samples are used for testing.  
Table 6 shows the relevant information of the four datasets.