## 5 Experimental Outcomes
### Outcome Statistical Validation  
Modern optimization research demands optimization results be meticulously statistically validated in order to establish the statistical significance of the demonstrated improvements. The preferred approach for validating outcomes is the use of parametric tests. However, the safe utilization of these tests needs to be established first. Three criteria need to be met: independence, normality, and homoscedasticity [49]. The first condition is fulfilled by utilizing an independent random seed for each execution. The normality condition is assessed using the outcomes of the Shapiro-Wilk test shown in Table 9 as well as through the visual observations of objective function outcome distributions shown in Figure 7.  
The resultant \(p\)-values were all less than 0.05, suggesting that the null hypothesis (H0) may be rejected. As a result, we may infer that the outcomes produced in all three simulations do not follow a normal distribution. These outcomes are further reinforced in Figure 7.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Method** & **Learning Rate** & **Min Child Weight** & **Subsample** & **Colosample** & **Max Depth** & **Gamma** \\ \hline CNN-XG-GIBSA & 0.900000 & 6 & 0.484839 & 1.000000 & 6 & 0.123762 \\ CNN-XG-BSA & 0.894472 & 10 & 0.835341 & 1.000000 & 6 & 0.00000 \\ CNN-XG-GA & 0.682788 & 5 & 0.654867 & 1.000000 & 8 & 0.439790 \\ CNN-XG-PSO & 0.293758 & 10 & 0.890094 & 1.000000 & 10 & 0.348853 \\ CNN-XG-GA & 0.873667 & 10 & 1.00000 & 1.000000 & 10 & 0.80000 \\ CNN-XG-SA & 0.900000 & 10 & 0.528148 & 0.761996 & 6 & 0.062693 \\ CNN-XG-WOGA & 0.578212 & 10 & 0.863927 & 0.915171 & 10 & 0.800000 \\ CNN-XG-COISHADE & 0.696242 & 9 & 0.589664 & 0.895006 & 8 & 0.381628 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Control parameter selections made by each metaheuristic for respective best-performing multi-class classification models.  
Figure 6: GIRSA XGBost best performing multi-class classification model.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Problem** & **GIRSA** & **RSA** & **GA** & **PSO** & **FA** & **SSA** & **WOA** & **COISHADE** \\ \hline XG-Binary & 0.032 & 0.041 & 0.046 & 0.018 & 0.021 & 0.033 & 0.035 & 0.040 \\ XG-Multi & 0.032 & 0.041 & 0.046 & 0.018 & 0.021 & 0.033 & 0.035 & 0.040 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Shapiro–Wilk normality tests.  
Parametric tests were not applicable since the normality assumption was not fulfilled. As a result, the non-parametric Wilcoxon signed-rank [50] test was used in the following stage. This test can be applied to the same data series consisting of the best values achieved in every run of each metaheuristic.  
The created algorithm is used as the control algorithm in this test, and the Wilcoxon signed-rank test was run on the specified data series. The calculated \(p\)-values in all three observed cases were less than 0.05. Considering the significance level of \(alpha=0.1\), these findings show that the introduced algorithm outperformed all competing approaches statistically significantly. Table 10 shows the overall results of the Wilcoxon signed-rank test.