## 3 Experimental Results and Discussion
### Statistical Test  
It is suggested that not only mean and standard deviation comparisons but more evaluation metrics should be used to assess the effectiveness of the metaheuristic algorithms [51]. The use of statistical tests such as the Friedman test and Wilcoxon rank-sum test are advised as effective evaluation metrics to compare the performance of different algorithms.  
The significance threshold for the Wilcoxon rank-sum test was set at 0.05. The approach was deemed statistically better, when \(p<0.05\). Table 6 displayed the Wilcoxon rank-sum test findings with the notation \"\(+/-\)\(=\)\" denoting whether the recommended approach was superior to, inferior to, or equal to the compared approach [52]. According to Table 6, GSLEO-AEFA always provides R+ values that are greater than R\(-\) values. Additionally, Table 6 reveals that the \(p\) values of the six algorithms are less than 0.05, indicating that GSLEO-AEFA is superior to the others. The + value of GSLEO-AEFA increased as the dimension increased from 50 to 100, as shown in Table 6. This indicates that the GSLEO-AEFA algorithm performs better than other algorithms, as the dimension increases. The results show that GSLEO-AEFA has higher level of solution accuracy.  
\begin{table}
\begin{tabular}{l l c c c c c c} \hline \hline
**Dimension** & **Case** & \(-\) & **+** & \(=\) & **R\(-\)** & **R\(+\)** & \(p\)**-Value** \\ \hline
30 & GSLEO-AEFA vs. AEEA & 0 & 19 & 4 & 0 & 190 & \(1.32\times 10^{-4}\) \\  & GSLEO-AEFA vs. PSO & 0 & 19 & 4 & 0 & 190 & \(1.32\times 10^{-4}\) \\  & GSLEO-AEFA vs. DE & 1 & 17 & 5 & 6 & 165 & \(5.35\times 10^{-4}\) \\  & GSLEO-AEFA vs. JAVA & 0 & 21 & 2 & 0 & 231 & \(6.00\times 10^{-5}\) \\  & GSLEO-AEFA vs. SCA & 0 & 20 & 3 & 0 & 210 & \(8.90\times 10^{-5}\) \\  & GSLEO-AEFA vs. CS & 2 & 13 & 8 & 19 & 101 & \(1.99\times 10^{-2}\) \\ \hline
50 & GSLEO-AEFA vs. AEEA & 0 & 13 & 0 & 0 & 91 & \(1.32\times 10^{-4}\) \\  & GSLEO-AEFA vs. PSO & 2 & 11 & 0 & 7 & 84 & \(1.32\times 10^{-4}\) \\  & GSLEO-AEFA vs. DE & 1 & 12 & 0 & 7 & 87 & \(5.35\times 10^{-4}\) \\  & GSLEO-AEFA vs. JAVA & 0 & 13 & 0 & 0 & 91 & \(6.00\times 10^{-5}\) \\  & GSLEO-AEFA vs. SCA & 0 & 13 & 0 & 0 & 91 & \(8.90\times 10^{-5}\) \\  & GSLEO-AEFA vs. CS & 1 & 12 & 0 & 12 & 79 & \(1.99\times 10^{-2}\) \\ \hline
100 & GSLEO-AEFA vs. AEEA & 0 & 13 & 0 & 0 & 91 & \(1.47\times 10^{-3}\) \\  & GSLEO-AEFA vs. PSO & 0 & 13 & 0 & 0 & 91 & \(1.47\times 10^{-3}\) \\  & GSLEO-AEFA vs. DE & 0 & 13 & 0 & 0 & 91 & \(1.47\times 10^{-3}\) \\  & GSLEO-AEFA vs. JAVA & 0 & 13 & 0 & 0 & 91 & \(1.47\times 10^{-3}\) \\  & GSLEO-AEFA vs. SCA & 0 & 13 & 0 & 0 & 91 & \(1.47\times 10^{-3}\) \\  & GSLEO-AEFA vs. CS & 0 & 13 & 0 & 0 & 91 & \(1.47\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Wilcoxon test analysis results.  
Figure 4: Convergence trajectory graphs for all studied benchmark functions F1–F23.  
The validity of the experiments is evaluated using the Friedman test by contrasting the proposed GSLEO-AEFA with other algorithms. The Friedman test is one of the widely used statistical tests which is used to determine whether more than one techniques' outputs differ significantly [53]. The outcomes of the Friedman tests are presented in Table 7. The technique that obtains the lowest rank is the most efficient according to Friedman test. In each of the various scenarios, the suggested GSLEO-AEFA is always rated first. Table 7 shows the results for the 30, 50 and 100 dimensions. The GSLEO-AEFA outperforms other algorithms in terms of competitiveness.  
In conclusion, AEFA-CSR is more competitive than innovative algorithms such as SCA and CS as well as traditional algorithms such as DE and PSO. The greater accomplishments of GSLEO-AEFA can be attributed to the newly implemented strategies. The LEO solution strategy makes the local optimal escape mechanism better and the GM based SRL makes the population more diversified. As a result, when the two methods are combined, the capacity of GSLEO-AEFA to solve multimodal and unimodal functions is significantly improved.