# Improved Binary Grey Wolf Optimization Approaches for Feature Selection Optimization
## 7 Simulation Results  
A set of comparisons are introduced in this section to evaluate the performance of the proposed approaches. Firstly, the evaluation results of the proposed approaches based on the S-shaped TF are compared with the original BGWO and BPSO algorithms. Secondly, the results of the proposed approaches based on the V-shaped TF are compared with the original \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Maximum number of iterations (T) & 100 \\ \hline Number of runs (R) & 30 \\ \hline The weight \(v\) in Equation (15) & 0.99 [41, 71] \\ \hline Population size (P) & 10 \\ \hline Vector A & Decreased linearly in the range \([-2,2]\)[15, 16] \\ (GWO algorithm input parameter) & \\ \hline Vector a & Reduced linearly from 2 to 0 [15, 16] \\ (GWO algorithm input parameter) & \\ \hline Vector C & \\ (GWO algorithm input parameter) & Random value between 0 and 2 [15, 16] \\ \hline c1, c2 (PSO algorithm input parameters) & 2 for each of the two parameters [75] \\ \hline K for KNN & 5 [76] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of parameters used in simulations. BGWO and BPSO algorithms. Finally, the comparisons of the best proposed approaches for S-shaped and V-shaped TFs are presented as follows. A comparative study was performed with eight state-of-the-art FS optimizers and another comparative study was performed with a recent hybrid FS optimizer that combined the BGWO and BPSO algorithms. The classification accuracy of the proposed approaches was measured using the KNN classifier [72]. KNN is one of the most widely used classifiers and is employed to evaluate and compare the performance of different feature selection algorithms [12]. This is due to its simplicity, ease of implementation, and low computational complexity when compared with other classifiers. The authors would like to note that other common classifiers can also be employed but are deferred to a future extension of this work. Evaluating the proposed approaches based on the S-shaped TF  
The proposed approaches based on the S-shaped TF were compared against the original BGWO and BPSO algorithms. These comparisons are illustrated in terms of ACA, ASF, and AFV, as shown in Figures 6-8, respectively. Figure 9 shows a statistical analysis of the proposed approaches based on the S-shaped TF in terms of the same three evaluation metrics. This figure shows the mean and overall ranks of each approach across all datasets under consideration. The rank is generally a number from 1 to 6 since there are six approaches compared against each other, where 6 indicates the highest-ranked approach. Additionally, Figure 9 shows the number of datasets in which each approach  
According to the ACA evaluation results shown in Figures 6 and 9, IBGWO3-S exceeded other approaches in five datasets. IBGWO3-S achieved an average ACA value of 0.9 across all datasets. IBGWO4-S yielded the best performance in two datasets. It was expected that the IBGWO3-S and IBGWO4-S optimization approaches would result in the best solutions. The reason for this was that the IBGWO3-S approach took into consideration in each iteration the fittest of all populations that resulted from applying BGWO alone and from applying BGWO followed by BPSO. Also, IBGWO4-S added to this ranking process the initial population that resulted from the previous iteration. However, using the S-shaped TF was found to negatively affect the results of IBGWO4-S relative to the results of IBGWO3-S. In general, all proposed approaches were found to outperform the original BGWO-S and BPSO-S since the hybrid approaches combined the exploration and exploitation properties of both approaches. Figure 7 shows that IBGWO1-S, IBGWO2-S, and IBGWO3-S achieved the best ASF results by selecting the fewest number of features in most of the datasets. As shown in Figure 8, the mean and overall ranks show that IBGWOI-S, IBGWO2-S, and IBGWO3-S achieved the best ranks and outperformed other approaches in terms of selecting the most suitable features.