## 4 Test Experiments and Discussion of DMMAEO
### Comparative Analysis Between DMMAEO and Other Algorithms  
The previous subsection validates the effectiveness of the three enhancement mechanisms, and the proposed DMMAEO emerges as the top performer within diverse EO variants. For further analyzing the superiority of DMMAEO, this subsection conducts a comparative study between the DMMAEO and several recent promising algorithms (EO [11], PSO [8], GWO [5], HHO [6], SMA [7], MPSO [36], MELGWO [37], LWMEO [20], and EBOwithCMAR [38]) on the 58 test functions. These compared algorithms consists of three different categories: the recently established algorithm (EO, PSO, GWO, HHO, and SMA), the improved algorithm (MPSO, MELGWO, and LWMEO), and the top algorithm (EBOwithCMAR). The detailed parameters for the above compared algorithms are set according to the corresponding original literature. The comparison results of Ave., Std., Wilcoxon signed rank test, and Friedman test are listed in Tables 7-12. Similar to the previous subsection, these results are also obtained by conducting each algorithm with 30 independent experiments across each test function. And the top-performing method and best results obtained from the comparative study within these tables are highlighted in bold as well. \begin{table}
\begin{tabular}{r c c c c c c} \hline \hline \multicolumn{1}{c}{**Function**} & \multicolumn{1}{c}{**EO**} & **PSO** & **GWO** & **HHO** & **SMA** \\ \hline \multirow{10}{*}{Unimodal} & TF1 & Ave. & \(4.297\times 10^{-41}\) & \(3.171\times 10^{-5}\) & \(5.950\times 10^{-28}\) & \(1.055\times 10^{-102}\) & \(0.000\times 10^{0}\) \\  & Std. & \(7.488\times 10^{-41}\) & \(1.480\times 10^{-5}\) & \(4.296\times 10^{-28}\) & \(3.281\times 10^{-102}\) & \(0.000\times 10^{0}\) \\  & TF2 & Ave. & \(1.494\times 10^{-23}\) & \(6.739\times 10^{-4}\) & \(6.610\times 10^{-17}\) & \(5.888\times 10^{-53}\) & \(1.332\times 10^{-167}\) \\  & Std. & \(2.772\times 10^{-23}\) & \(2.916\times 10^{-4}\) & \(2.231\times 10^{-17}\) & \(1.196\times 10^{-52}\) & \(0.000\times 10^{0}\) \\  & TF3 & Ave. & \(9.458\times 10^{-9}\) & \(3.512\times 10^{2}\) & \(2.230\times 10^{-6}\) & \(3.215\times 10^{-83}\) & \(0.000\times 10^{0}\) \\  & Std. & \(3.193\times 10^{-8}\) & \(9.412\times 10^{1}\) & \(2.400\times 10^{-6}\) & \(6.979\times 10^{-83}\) & \(0.000\times 10^{0}\) \\  & TF4 & Ave. & \(3.885\times 10^{-10}\) & \(3.178\times 10^{0}\) & \(4.708\times 10^{-7}\) & \(3.018\times 10^{-52}\) & \(5.280\times 10^{-166}\) \\  & Std. & \(5.952\times 10^{-10}\) & \(4.759\times 10^{-1}\) & \(1.851\times 10^{-7}\) & \(7.690\times 10^{-52}\) & \(0.000\times 10^{0}\) \\  & TF5 & Ave. & \(2.544\times 10^{1}\) & \(5.636\times 10^{1}\) & \(2.702\times 10^{1}\) & \(\mathbf{3.147\times 10^{-3}}\) & \(7.350\times 10^{0}\) \\  & Std. & \(1.393\times 10^{-1}\) & \(2.653\times 10^{1}\) & \(4.477\times 10^{-1}\) & \(2.450\times 10^{-3}\) & \(1.057\times 10^{1}\) \\  & TF6 & Ave. & \(1.262\times 10^{-5}\) & \(2.921\times 10^{-5}\) & \(7.441\times 10^{-1}\) & \(6.537\times 10^{-5}\) & \(6.706\times 10^{-3}\) \\  & Std. & \(7.772\times 10^{-6}\) & \(2.488\times 10^{-5}\) & \(1.697\times 10^{-1}\) & \(6.042\times 10^{-5}\) & \(1.946\times 10^{-3}\) \\  & TF7 & Ave. & \(1.633\times 10^{-3}\) & \(1.752\times 10^{-2}\) & \(1.836\times 10^{-3}\) & \(8.986\times 10^{-5}\) & \(2.236\times 10^{-4}\) \\  & Std. & \(6.363\times 10^{-4}\) & \(3.559\times 10^{-3}\) & \(5.905\times 10^{-4}\) & \(5.694\times 10^{-5}\) & \(1.076\times 10^{-4}\) \\ \hline \multicolumn{1}{c}{**Function**} & \multicolumn{1}{c}{**MPSO**} & **MELGWO** & **LWMEO** & **EBOwithCMAR** & **DMMAEO** \\ \hline \multirow{10}{*}{TF2} & TF1 & Ave. & \(5.360\times 10^{-29}\) & \(2.068\times 10^{-57}\) & \(1.182\times 10^{-97}\) & \(1.213\times 10^{-15}\) & \(\mathbf{0.000\times 10^{0}}\) \\  & Std.