## 4 Test Experiments and Discussion of DMMAEO
### Comparative Analysis Between DMMAEO and Other Algorithms
& \(1.707\times 10^{2}\) & \(1.281\times 10^{2}\) & \(1.113\times 10^{3}\) & \(2.967\times 10^{3}\) & \(1.079\times 10^{2}\) \\ TF51 & Ave. & \(2.621\times 10^{3}\) & \(2.623\times 10^{3}\) & \(2.625\times 10^{3}\) & \(2.694\times 10^{3}\) & \(2.625\times 10^{3}\) \\  & Std. & \(4.823\times 10^{3}\) & \(6.040\times 10^{3}\) & \(8.172\times 10^{3}\) & \(2.092\times 10^{3}\) & \(3.983\times 10^{3}\) \\ TF52 & Ave. & \(2.747\times 10^{3}\) & \(2.757\times 10^{3}\) & \(2.762\times 10^{3}\) & \(2.840\times 10^{3}\) & \(2.763\times 10^{3}\) \\  & Std. & \(6.378\times 10^{3}\) & \(9.590\times 10^{3}\) & \(7.262\times 10^{3}\) & \(2.643\times 10^{3}\) & \(6.386\times 10^{0}\) \\ TF53 & Ave. & \(2.946\times 10^{3}\) & \(2.939\times 10^{3}\) & \(2.946\times 10^{3}\) & \(2.947\times 10^{3}\) & \(2.946\times 10^{3}\) \\  & Std. & \(1.799\times 10^{3}\) & \(1.267\times 10^{3}\) & \(3.934\times 10^{3}\) & \(9.244\times 10^{3}\) & \(1.808\times 10^{3}\) \\ TF54 & Ave. & \(3.072\times 10^{3}\) & \(2.936\times 10^{3}\) & \(3.142\times 10^{3}\) & \(3.962\times 10^{3}\) & \(3.396\times 10^{3 Tables 7-11 present the results of Ave. and Std. for the compared algorithms across 58 test functions (TF1-TF58). According to the results in Tables 7-11, the DMMAEO captures the best results on TF1-TF4, TF7, TF9-TF12, TF14, TF16, TF17, TF19-TF21, TF23-TF25, TF28, TF44, TF49, TF50, and TF52-TF57. Regarding other test functions, the DMMAEO also shows competitive optimization capability. Hence, the DMMAEO shows better performance on most test functions compared to other algorithms. This means that the DMMAEO performs better in the comprehensive optimization ability, and especially has advantages in the balancing ability between exploration and exploitation. In addition, Figure 4 presents convergence curves for the algorithms involved in the comparative study on nine test functions. According to the illustrated results given by Figure 4, the DMMAEO exhibits superior convergence speed and accuracy than other compared algorithms. In the meantime, the results of the Friedman test and Wilcoxon signed rank test obtained from across 58 test functions are given in Table 12, which are employed to assess \begin{table}
\begin{tabular}{l c c c c c} \hline  & **EO** & **PSO** & **GWO** & **HHO** & **SMA** \\ \hline [PERSON] mean rank & 5.474 & 6.931 & 7.483 & 7.741 & 6.017 \\ Final rank & 6 & 8 & 9 & 10 & 7 \\
1/0/\(-\)1 & 46, 6, 6 & 49, 3, 6 & 56, 0, 2 & 52, 3, 3 & 49, 5, 4 \\ \hline  & **MPSO** & **MELGWO** & **LWMEO** & **EBOwithCMAR** & **DMMAEO** \\ \hline [PERSON] mean rank & 4.897 & 5.379 & 5.310 & 3.422 & **2.345** \\ Final rank & 3 & 5 & 4 & 2 & 1 \\
1/0/\(-\)1 & 47, 2, 9 & 54, 2, 2 & 48, 5, 5 & 28, 4, 26 & \(\sim\) \\ \hline \end{tabular}  
* The best comparative results are presented in bold.  
\end{table} 
Table 12: Non-parametric test results for DMMAEO and several recent promising algorithms across 58 test functions. the statistical significance for the superiority of D MMAEO. As per the Wilcoxon signed rank test results expressed as '1/0/\(-\)1', Table 12 shows that the D MMAEO exhibits superior optimization capability over EO, PSO, GWO, HHO, SMA, MPSO, MELGOV, LWMEO, and EBOwithCMAR across 46, 49, 56, 52, 49, 47, 54, 48, and 28 functions, respectively. This result denotes that the D MMAEO has significant superiority on most test functions compared to other algorithms. According to the Friedman test results given by Table 12, the D MMAEO holds the top rank. It is worth noting that the top algorithm EBOwithCMAR achieves high optimization performance through a complex mechanism, while D MMAEO still exhibits competitive optimization performance compared to EBOwithCMAR. Thus, the D MMAEO performs the strongest overall optimization capability within the algorithms involved in the comparative study from a statistical perspective.