# Improved Binary Grey Wolf Optimization Approaches for Feature Selection Optimization
## 7 Simulation Results
The authors also plan to compare the proposed approaches with a set of advanced metaheuristic methods like the work proposed in [51; 52; 58; 59] and other works that combine GWO with PSO. Such work can be compared with our approaches in a future extension of this work. Figure 8:3 Convergence curves for all approaches based on V-shaped TFs (Part 2 of the datasets). Figure 20 shows a statistical analysis of the comparison between IBGWO3-S and IBGWO4-V on one side and the eight selected state-of-the-art metaheuristic-based FS optimizers on the other side. This comparison was made in terms of the same three evaluation metrics, i.e., ACA, ASF, and AFV. Figure 20 shows the mean and overall ranks of each approach across all datasets under consideration. The rank was generally a number from 1 to 10 since there were ten approaches compared against each other, where 10 means the highest-ranked approach. Additionally, Figure 20 shows the number of datasets in which each approach obtained the best rank. Figure 20 shows that IBGWO4-V achieved the best ACA results in nine datasets. The mean and overall rank values showed the superiority of IBGWO4-V over other optimizers, followed by IBGWO3-S. In terms of ASF, IBGWO4-V also outperformed other optimizers in all datasets. Additionally, the mean and overall rank ASF results showed that IBGWO4-V attained the best rank compared to other optimizers, followed by IBGWO3-S. In terms of AFV, the figure shows the superiority of IBGWO4-V in seven datasets. The mean and overall rank ASF results revealed that IBGWO4-V and IBGWO3-S also outperformed other optimizers. This confirms the potential of these two proposed approaches to jump out of the areas that contain the local optima and orient themselves towards the most promising area of relevant features. Figures 21 and 22 show the convergence curves for all ten optimizers over all iterations. The two figures illustrate that IBGWO4-V outperformed other optimizers in order of fitness values. Convergence curves reveal the ability of this optimizer to avoid local optima and immature convergence. If an optimizer cannot make a stable trade-off between exploration and exploitation, then it will converge to local optima, which leads to immature convergence. Figure 8:4 Convergence curves for IBGWO4-V and eight well-known FS optimizers (Part 1 of the datasets). Figures 23-26 show the results of the comparisons of IBGWO3-S and IBGWO4-V with the two recent FS optimizers, i.e., HTGWPS-S1 and HTGWPS-V1, from the literature. The four figures show comparisons in terms of the four previously described evaluation metrics, i.e., ACA, ASF, AFV, and ACT, respectively. Figure 8:5 Comparison of the two best-performing proposed approaches with a recent metaheuristic (HTGWPS) in terms of ACA. Figure 8:6 Convergence curves for IBGWO4-V and eight well-known FS optimizers (Part 2 of the datasets). achieved the lowest ASF in six datasets. Figure 25 shows that IBGWO4-V achieved the lowest AFV in six datasets. Finally, Figure 26 shows that IBGWO3-S and IBGWO4-V had the lowest ACT in three and four datasets, respectively. In general, IBGWO4 obtained better results than HTGWPS because the latter was based on selecting only one of three optimizers, i.e., BGWO, BPSO, or TS. On the contrary, IBGWO applied both BGWO and BPSO in each iteration with a ranking process among all solutions obtained from both optimizers. This enhanced the results obtained from IBGWO when compared with HTGWPS. In this section, the computational complexity of the proposed approaches is analyzed and presented. Table 3 shows the computational complexity of the proposed approaches. The complexity was analyzed by computing the estimated total number of iterations for each approach. Moreover, a Big-O analysis in terms of the maximum number of iterations (T) and the population size (P) is presented.