## 3 Proposed IBFO-KELM Model
The IBFO-KELM, BFO-KELM, PSO-KELM, GA-KELM, and Grid-KELM models were implemented in the MATLAB platform. The technique used by [PERSON] (available online: [[http://www3.ntu.edu.sg/home/egbhuang](http://www3.ntu.edu.sg/home/egbhuang)]([http://www3.ntu.edu.sg/home/egbhuang](http://www3.ntu.edu.sg/home/egbhuang)), 17 January 2018) was used for the KELM classification. The data was scaled into a range of [\(-\)1, 1] before each classification was conducted. The search ranges of the penalty parameter \(C\) and kernel bandwidth \(\gamma\) in \(K(x,x_{i})=\exp(-\gamma\|x-x_{i}\|^{2})\) were defined as \(C\in\{2^{-5},\,2^{-3},\,\ldots,\,2^{15}\}\) and \(\gamma\in\{2^{-15},\,2^{-13},\,\ldots,\,2^{5}\}\). A population swarm size of eight, chemotactic step number of five, swimming length of four, reproduction step number of five, elimination-dispersal event number of two, and elimination-dispersal probability of 0.25 were selected for BFO-KELM and IBFO-KELM. The chemotaxis step value was established through trial and error, as shown in the experimental results section. For PSO, the maximum velocity was set to about 60% of the dynamic range of the variable on each dimension for the continuous type of dimensions. The two acceleration coefficients \(c_{1}\) and \(c_{2}\) were set as 2.05, the inertia weight was set to one.In order to determine the validity and accuracy of the results, the \(k\)-fold CV [38] was used to evaluate the classification performance of the model. A nested stratified 10-fold CV, which has been widely used in previous research, was used for the purposes of this study [39]. The classification performance evaluation was conducted in the outer loop. Since a 10-fold CV was used in the outer loop, the classifiers were evaluated in one independent fold of data, and the other nine folds of data were left for training. The parameter optimization process was \begin{table}
\begin{tabular}{c c} \hline
**Feature** & **Description** \\ \hline F1 & Headache \\ F2 & Dizzy or fainted \\ F3 & Chest pain \\ F4 & Low back pain \\ F5 & Nausea or upset stomach \\ F6 & Muscle soreness \\ F7 & Having breathe difficulty \\ F8 & A series of chills or fever \\ F9 & Body tinging or prickling \\ F10 & The throat is infarcted \\ F11 & Feeling that part of the body is weak \\ F12 & Feeling the weight of your hands or feet \\ F13 & Somalization severity \\ \hline \end{tabular}
\end{table} 
Table 1: Description of the somatization disorder data. performed in the inner loop. Since a five-fold CV was used in the inner loop, the IBFO-KELM searched for the optimal values of \(C\) and \(\gamma\) in the remaining nine folds of data. The nine folds of data were further split into one fold of data for the performance evaluation, and four folds of data were left for training. To evaluate the proposed method, commonly used evaluation criteria such as classification accuracy (ACC), sensitivity, specificity and Matthews correlation coefficients (MCC) were analyzed. ## 5 Experimental Results and Discussion

### Benchmark Function Validation

In order to test the performance of the proposed algorithm IBFO, nine multidimensional benchmark functions, as shown in Table 2, were used. This paper selected nine multidimensional benchmark functions for the experiment to illustrate the effectiveness of the proposed IBFO algorithm. The nine benchmark functions are made up of five unimodal (\(f_{1}\)-\(f_{5}\)) benchmark functions, one multimodal (\(f_{6}\)) benchmark functions and three fixed-dimension multimodal (\(f_{7}\)-\(f_{9}\)) benchmark functions. Moreover, the performance of the IBFO is also compared with the PSO, Bat algorithm (BA) and conventional BFO. As mentioned in the literature, the proposed IBFO has superior results for these benchmark functions compared to the PSO, BA and original BFO. A total of 30 independent runs of the four algorithms were performed on each benchmark function. The maximum number of iterations and population size for all algorithms were set to 600 and 50, respectively.