## 3 Proposed RBAVO-DE for GS
### The Complete RBAVO-DE Algorithm
### Convergence Analysis

It is evident in Appendix B[57] that the proposed RBAVO-DE employing the SVM and \(k\)-NN models attained optimum convergence behavior across all benchmarks. Therefore, the convergence performance of the proposed RBAVO-DE employing the SVM and \(k\)-NN models demonstrates its capability to reach optimal outcomes promptly while maintaining an efficient equilibrium between search and exploitation. \begin{table}
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**Dataset** & **Metric** & **RBA



### Wilcoxon's Rank-Sum Test

This paper compares the fitness values achieved by the proposed RBAVO-DE and its counterparts pairwise using the Wilcoxon rank-sum test [60], which aims to determine whether there is a statistically significant difference between the different approaches. This test is a crucial tool for evaluating the success of the proposed algorithm. The Wilcoxon test is employed in hypothesis testing to compare matched data. It involves sorting the absolute differences in the outcomes of paired procedures on the \(j^{th}\) of \(N\) issues. Next, the lowest value is found by summing the positive (\(R^{+}\)) and negative (\(R^{-}\)) rankings. The null hypothesis is rejected if the resultant significance level is less than 5%, and not rejected otherwise. From examining the results of the comparison made between the RBAVO-DE and its counterparts pairwise using the Wilcoxon test, we found that all \(R^{+}\) values equal 253, all \(R^{-}\) values equal 0, and all \(p\)-values equal \(4.768\times 10^{-7}\) which are less than 0.05 (significance level of 5%). Hence, it can be concluded that the proposed RBAVO-DE employing SVM and \(k\)-NN performs better than any other algorithm in all cases. Therefore, all \(p\)-values less than 0.05 (significance level of 5%) offer compelling evidence that the outcomes of the proposed strategy are statistically significant and not just coincidental. ### Computational Complexity of the RBAVO-DE Algorithm and Various Meta-Heuristic Algorithms

#### 4.7.1 Computational Complexity of the Execution Time of the RBAVO-DE Algorithm

Each of RBAVO-DE's five core steps can be analyzed separately to determine its computational complexity. These steps include filtering features, initializing the population, boosting and amending the position, appraising the fitness function, and using DE. Then, \(\mathcal{O}_{execute\_time}(RBAVO-DE)\) can be utilized to represent the overall computational complexity of the proposed RBAVO-DE algorithm. This can be computed using the following big-O notation formulas:

\[ \begin{split}\mathcal{O}_{execute\_time}(RBAVO-DE)& =\mathcal{O}_{execute\_time}(\text{Filtering features})+\\ &\mathcal{O}_{execute\_time}(\text{Initializing population})+\\ &\mathcal{O}_{execute\_time}(\text{Boosting and amending position})+\\ &\mathcal{O}_{execute\_time}(\text{Appraising fitness function})+\\ &\mathcal{O}_{execute\_time}(\text{Incorporating DE technique}).\end{split}  \tag{27}\]

Since \(N\) determines the population size, \(G_{max}\) is the maximum number of iterations allowed, and \(D\) is the problem's dimensional space. Hence,

\(\mathcal{O}_{execute\_time}(\text{Filtering features})=\mathcal{O}_{execute\_ time}(D)\). \(\mathcal{O}_{execute\_time}(\text{Initializing population})=\mathcal{O}_{execute\_ time}(N)\). \(\mathcal{O}_{execute\_time}(\text{Boosting and amending position})=\mathcal{O}_{execute\_time}(G_{max}\times N\times D)\). \(\mathcal{O}_{execute\_time}(\text{Appraising fitness function})=\mathcal{O}_{execute\_ time}(G_{max}\times N)\). \(\mathcal{O}_{execute\_time}(\text{Incorporating DE technique})=\mathcal{O}_{execute\_ time}(N\times D)\). For that,

\[ \begin{split}\mathcal{O}_{execute\_time}(RBAVO-DE)& =\mathcal{O}_{execute\_time}(D)+\\ &\mathcal{O}_{execute\_time}(N)+\mathcal{O}_{execute\_time}(G_{max} \times N\times D)+\\ &\mathcal{O}_{execute\_time}(G_{max}\times N)+\mathcal{O}_{execute\_time}(N\times D)=\\ &\mathcal{O}_{execute\_time}(G_{max}\times N\times D).\end{split}