## 4 Test Experiments and Discussion of DMMAEO
### Comparative Analysis Between DMMAEO and Other Algorithms
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Function** & \multicolumn{2}{c}{**EO**} & **PSO** & **GWO** & **HHO** & **SMA** \\ \hline \multirow{8}{*}{Multimodal (High dimension)} & TF8 & Ave. & \(-8.586\times 10^{3}\) & \(-6.805\times 10^{3}\) & \(-6.438\times 10^{3}\) & \(-\mathbf{1.257\times 10^{4}}\) & \(-1.257\times 10^{4}\) \\  & Std. & \(3.178\times 10^{2}\) & \(3.917\times 10^{2}\) & \(4.074\times 10^{2}\) & \(3.047\times 10^{-1}\) & \(2.828\times 10^{-1}\) \\  & TP9 & Ave. & \(0.000\times 10^{0}\) & \(4.232\times 10^{1}\) & \(1.052\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std. & \(0.000\times 10^{0}\) & \(6.936\times 10^{0}\) & \(1.812\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & TF10 & Ave. & \(1.036\times 10^{-14}\) & \(1.635\times 10^{-3}\) & \(1.011\times 10^{-13}\) & \(8.882\times 10^{-16}\) & \(8.882\times 10^{-16}\) \\  & Std. & \(3.407\times 10^{-15}\) & \(6.152\times 10^{-4}\) & \(8.418\times 10^{-15}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & TF11 & Ave. & \(0.000\times 10^{0}\) & \(6.514\times 10^{-3}\) & \(1.221\times 10^{-16}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std. & \(0.000\times 10^{0}\) & \(7.262\times 10^{-3}\) & \(6.689\times 10^{-16}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & TF12 & Ave. & \(8.485\times 10^{-7}\) & \(6.914\times 10^{-3}\) & \(4.040\times 10^{-2}\) & \(1.732\times 10^{-6}\) & \(4.822\times 10^{-3}\) \\  & Std. & \(6.308\times 10^{-7}\) & \(2.630\times 10^{-2}\) & \(9.126\times 10^{-3}\) & \(1.281\times 10^{-6}\) & \(4.203\times 10^{-3}\) \\  & TF13 & Ave. & \(5.441\times 10^{-2}\) & \(1.487\times 10^{-3}\) & \(6.283\times 10^{-1}\) & \(3.768\times 10^{-8}\) & \(5.160\times 10^{-3}\) \\  & Std. & \(5.411\times 10^{-2}\) & \(3.791\times 10^{-3}\) & \(1.242\times 10^{-1}\) & \(2.960\times 10^{-5}\) & \(3.333\times 10^{-3}\) \\ \hline \multicolumn{2}{c}{**Function**} & \multicolumn{2}{c}{**MPSO**} & **MELGWO** & **LWMEO** & **EBOwithCMAR** & **DMMAEO** \\ \hline \multirow{8}{*}{TF9} & TF8 & Ave. & \(-8.852\times 10^{3}\) & \(-8.772\times 10^{3}\) & \(-7.317\times 10^{3}\) & \(-1.185\times 10^{4}\) & \(-9.152\times 10^{3}\) \\  & Std. & \(2.880\times 10^{2}\) & \(2.126\times 10^{2}\) & \(6.336\times 10^{2}\) & \(1.649\times 10^{2}\) & \(7.372\times 10^{2}\) \\  & TP9 & Ave. & \(2.312\times 10^{0}\) & \(0.000\times 10^{0}\) & \(2.421\times 10^{0}\) & \(5.207\times 10^{0}\) & \(\mathbf{0.000\times 10^{0}}\) \\  & Std. & \(3.227\times 10^{0}\) & \(0.000\times 10^{0}\) & \(4.493\times 10^{0}\) & \(1.785\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & TF10 & Ave. & \(4.441\times 10^{-15}\) & \(7.638\times 10^{-15}\) & \(4.441\times 10^{-15}\) & \(4.374\times 10^{-1}\) & \(8.882\times 10^{-16}\) \\  & Std. & \(0.000\times 10^{0}\) & \(1.084\times 10^{-15}\) & \(0.000\times 10^{0}\) & \(9.810\times 10^{-1}\) & \(0.000\times 10^{0}\) \\  & TF11 & Ave. & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(2.216\times 10^{-3}\) & \(0.000\times 10^{0}\) \\  & Std. & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(5.184\times 10^{-3}\) & \(0.000\times 10^{0}\) \\  & TF12 & Ave. & \(1.574\times 10^{-1}\) & \(4.506\times 10^{-3}\) & \(2.384\times 10^{-2}\) & \(1.071\times 10^{-1}\) & \(1.080\times 10^{-7}\) \\  & Std. & \(1.281\times 10^{-1}\) & \(3.391\times 10^{-3}\) & \(9.734\times 10^{-3}\) & \(1.374\times 10^{-1}\) & \(4.348\times 10^{-8}\) \\  & TF13 & Ave. & \(6.741\times 10^{-1}\) & \(1.729\times 10^{-1}\) & \(9.883\times 10^{-1}\) & \(1.831\times 10^{-3}\) & \(3.486\times 10^{-1}\) \\  & Std. & \(6.155\times 10^{-1}\) & \(1.009\times 10^{-1}\) & \(2.499\times 10^{-1}\) & \(4.165\times 10^{-3}\) & \(2.149\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results for DMMAEO and several recent promising algorithms multimodal test functions with high dimensions.