# Improved Binary Grey Wolf Optimization Approaches for Feature Selection Optimization
## 7 Simulation Results
IBGWO4-S was negatively affected by applying the S-shaped TF relative to the other three proposed approaches; however, it achieved better mean and overall ranks relative to the original BGWO-S and BPSO-S approaches. Figure 8: Evaluation of the proposed approaches based on S-shaped TF in terms of AFV. Figure 9: Statistical analysis of the proposed approaches based on S-shaped TF. Figures 8 and 9 summarize the findings in terms of AFV, which is a combination of the classification error and the number of selected features. Note that it is required to minimize the AFV value to improve the performance of the proposed optimizer. According to the results, IBGWO3-S achieved an average AFV value of 0.1 across all datasets. This optimizer provided the fittest outcomes when compared with all other optimizers, including the original BGWO-S and BPSO-S optimizers. This means that this approach was able to provide the most accurate balance between the minimum possible classification error and the minimum possible number of selected features in all datasets. Using the S-shaped TF negatively affected the usage of the IBGWO4-S optimizer approach in terms of the AFV metric. Figure 10 shows the evaluation results of the proposed FS optimizers based on the S-shaped TF in terms of the ACT. As expected, the figure shows that the most complicated approach, i.e., IBGWO4-S, had the most ACT, followed by IBGWO3-S and IBGWO2-S. The two latter approaches were less complex in the ranking process of the different solutions that were investigated in each iteration when compared to IBGWO4-S. This difference was more apparent for the 11_Tumers and 14_Tumers datasets than for other datasets. The reason for this was that, as shown previously in Table 1, these two datasets contained the largest number of instances, features, and classes relative to other datasets. This normally increased the ACT of IBGWO4-S relative to the other two approaches. The original BPSO-S and BGWO-S had lower ACT than the three proposed approaches since the three proposed approaches were a hybrid of the former two approaches. Figures 11 and 12 show the convergence curves for all FS optimizers based on the S-shaped TF over all iterations. IBGWO3-S had the best performance because other approaches converged early and then became stuck at the local optima. IBGWO3-S exhibited good behavior and obtained the lowest fitness values for most of the datasets. Since the fitness value is the ratio between the number of selected features to the overall features in addition to the classification error, as shown in Equation (15), the solution with the least ratio and the smallest error is the fittest. The curves of the fitness values clarify that IBGWO3-S was the best optimizer based on the S-shaped TF. This means that IBGWO3-S had a high tuning ability for local and global searches, which allowed it to achieve the global optimal solution. Moreover, it had a high ability to escape the area of local optima and search for the most promising area until it found the best global solution. Figure 10: Evaluation of the proposed approaches based on S-shaped TF in terms of ACT. Figure 11: Convergence curves for all approaches based on S-shaped TFs (Part 1 of the datasets). 2. Evaluating the proposed approaches based on the V-shaped TF  
The proposed approaches based on the V-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 13-15, respectively. Figure 16 shows a statistical analysis of the proposed approaches based on the V-shaped TF in terms of the same three evaluation metrics. Figure 12: Convergence curves for all approaches based on S-shaped TFs (Part 2 of the datasets). Figure 13: Evaluation of the proposed approaches based on V-shaped TF in terms of ACA. Figure 16: Statistical analysis of the proposed approaches based on V-shaped TF. Figure 14: Evaluation of the proposed approaches based on V-shaped TF in terms of ASF.