## 3 Proposed IBFO-KELM Model
We recorded the average (Ave) and standard deviation (Std) for each benchmark problem. Table 3 shows the detailed statistical results for the nine multidimensional benchmark functions when dimension =2 for different algorithms (PSO, BA, BFO, IBFO), respectively. Based on the results in Table 3, IBFO can provide very competitive results. According to the statistical result of \(f_{1}\)-\(f_{9}\), it can be seen that IBFO has better searching ability and is more stable, which means that it also has better robustness. According to the performance of \(f_{1}\)-\(f_{9}\) in Figure 2, it is obvious that although the proposed IBFO can converge slowly in the early stages in some functions, the final result is optimal as the number of iterations increases. \begin{table} \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**Methods**} \\ \hline \multicolumn{2}{c}{**PSO**} & \multicolumn{2}{c}{**BA**} & \multicolumn{2}{c}{**BFO**} & \multicolumn{2}{c}{**IBFO**} & \multicolumn{2}{c}{**IBFO**} \\ \cline{2-9}  & **Ave** & **Std** & **Ave** & **Std** & **Ave** & **Std** & **Ave** & **Std** \\ \hline \(f_{1}\) & 0.0185 & 0.0097 & 0.0113 & 0.0053 & 0.0075 & 0.0042 & 0.0057 & 0.0031 \\ \(f_{2}\) & 0.0006 & 0.0005 & 0.0001 & 0.0001 & \(4.07\times 10^{-5}\) & \(4.76\times 10^{-5}\) & \(2.83\times 10^{-5}\) & \(4.83\times 10^{-5}\) \\ \(f_{3}\) & 0.0135 & 0.0079 & 0.0095 & 0.0045 & 0.2072 & 1.1059 & 0.0046 & 0.0029 \\ \(f_{4}\) & 0.0003 & 0.0003 & \(9.88\times 10^{-5}\) & 0.0001 & \(5.11\times 10^{-5}\) & 0.0001 & \(3.13\times 10^{-5}\) & \(3.76\times 10^{-5}\) \\ \(f_{5}\) & 0.0070 & 0.0045 & 0.0020 & 0.0016 & 0.00045 & 0.0003 & 0.0004 & 0.0003 \\ \(f_{6}\) & \(-793.55\) & 65.4056 & \(-763.56\) & 77.9863 & \(-720.08\) & 76.2664 & \(-797.41\) & 56.1899 \\ \(f_{7}\) & 1.9873 & 1.5529 & 2.8100 & 1.9357 & 1.7915 & 1.0204 & 1.3947 & 0.8472 \\ \(f_{8}\) & 0.0012 & 0.0002 & 0.0081 & 0.0095 & 0.0007 & 0.0002 & 0.0007 & 0.0002 \\ \(f_{9}\) & \(-5.1904\) & 1.9864 & \(-5.8112\) & 3.1206 & \(-10.3323\) & 0.9752 & \(-10.5104\) & 0.0135 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of testing nine multidimensional benchmark functions. Figure 2: _Cont._

### Results of the Somatization Disorder Diagnosis

Previous studies have shown that the chemotaxis step size of the bacterial optimization algorithm plays an important role in the search ability of bacteria. Thus this paper first analyzed and studied the influence of this on the performance of IBPG-KELM. Table 4 shows that the IBPG-KELM obtained the classification results in the psychological correction data under different chemotaxis step sizes. The data shown in the table mainly consist of mean and variance. As can be seen from the table, when the chemotaxis step size value is 0.5, the IBPG-KELM model achieved the best results with 96.97% classification accuracy, 0.9243 MCC, 97.29% sensitivity and 96.00% specificity. In addition, the variance of the model on the ACC index is the smallest when the value is 0.15, which indicates that the model has the most stable performance at this value. Therefore, in the follow-up experiment, we will take the chemotaxis step size value of 0.15 as the experimental parameter. In order to verify the effectiveness of the proposed method, we proposed a comparison study with four other efficient machine learning models, namely Grid-KELM, BFO-KELM, GA-KELM and PSO-KELM. The comparison of the five methods in terms of the average ACC, MCC, sensitivity, and specificity is shown in Table 5. As shown, the IBPG-KELM had the highest ACC among the five methods. IBPG-KELM yielded average results of 96.97% ACC, 0.9243 MCC, 97.29% sensitivity, and 96.00% specificity. BFO-KELM yielded an ACC of 93.29%, 0.8280 MCC, sensitivity of 95.86%, and specificity of 85.50%. The PSO-KELM yielded an ACC of 92.82%, 0.8056 MCC, sensitivity of 96.57%,