## 4 Test Experiments and Discussion of DMMAEO
### Diversity Comparison Analysis  
Diversity is used as a measurement for the distribution of population particles, which plays an important role in forming diverse population during the search process. According to [41], population diversity is measured through \(Div\), which is calculated by  
\[\bar{P}_{j}=\frac{1}{N}\sum_{j=1}^{N}P_{i,j},i=1,2,3,\ldots,N,j=1,2,3,\ldots,D, \tag{20}\]  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Function**} & \multicolumn{3}{c}{**Dimension = 30**} & \multicolumn{3}{c}{**Dimension = 50**} & \multicolumn{3}{c}{**Dimension = 100**} \\  & **DMMAEO** & **EO** & **DMMAEO** & **EO** & **DMMAEO** & **EO** \\ \hline TF1 & Ave. & \(0.000\times 10^{0}\) & \(4.297\times 10^{-41}\) & \(0.000\times 10^{0}\) & \(1.772\times 10^{-34}\) & \(0.000\times 10^{0}\) & \(3.421\times 10^{-29}\) \\  & Std. & \(0.000\times 10^{0}\) & \(7.488\times 10^{-41}\) & \(0.000\times 10^{0}\) & \(2.678\times 10^{-34}\) & \(0.000\times 10^{0}\) & \(3.803\times 10^{-29}\) \\ TF2 & Ave. & \(2.614\times 10^{-308}\) & \(1.494\times 10^{-23}\) & \(3.144\times 10^{-308}\) & \(1.800\times 10^{-20}\) & \(3.287\times 10^{-307}\) & \(2.063\times 10^{-17}\) \\  & Std. & \(0.000\times 10^{0}\) & \(2.772\times 10^{-23}\) & \(0.000\times 10^{0}\) & \(1.036\times 10^{-20}\) & \(0.000\times 10^{0}\) & \(1.121\times 10^{-17}\) \\ TF3 & Ave. & \(0.000\times 10^{0}\) & \(9.458\times 10^{-9}\) & \(0.000\times 10^{0}\) & \(5.864\times 10^{-4}\) & \(0.000\times 10^{0}\) & \(3.993\times 10^{0}\) \\  & Std. & \(0.000\times 10^{0}\) & \(3.193\times 10^{-8}\) & \(0.000\times 10^{0}\) & \(1.811\times 10^{-3}\) & \(0.000\times 10^{0}\) & \(5.456\times 10^{0}\) \\ TF4 & Ave. & \(2.164\times 10^{-304}\) & \(3.885\times 10^{-10}\) & \(7.719\times 10^{-304}\) & \(5.980\times 10^{-7}\) & \(6.794\times 10^{-302}\) & \(1.903\times 10^{-3}\) \\  & Std. & \(0.000\times 10^{0}\) & \(5.952\times 10^{-10}\) & \(0.000\times 10^{0}\) & \(5.584\times 10^{-7}\) & \(0.000\times 10^{0}\) & \(2.835\times 10^{-3}\) \\ TF5 & Ave. & \(2.469\times 10^{1}\) & \(2.544\times 10^{1}\) & \(4.491\times 10^{1}\) & \(4.580\times 10^{1}\) & \(9.519\times 10^{1}\) & \(9.711\times 10^{1}\) \\  & Std. & \(1.189\times 10^{-1}\) & \(1.393\times 10^{-1}\) & \(8.788\times 10^{-2}\) & \(2.348\times 10^{-1}\) & \(3.512\times 10^{-1}\) & \(8.106\times 10^{-1}\) \\ TF6 & Ave. & \(1.437\times 10^{-6}\) & \(1.262\times 10^{-5}\) & \(4.242\times 10^{-4}\) & \(1.370\times 10^{-1}\) & \(2.427\times 10^{0}\) & \(4.307\times 10^{0}\) \\  & Std. & \(5.836\times 10^{-7}\) & \(7.772\times 10^{-6}\) & \(1.308\times 10^{-4}\) & \(1.352\times 10^{-1}\) & \(3.695\times 10^{-1}\) & \(4.265\times 10^{-1}\) \\ TF7 & Ave. & \(4.582\times 10^{-5}\) & \(1.633\times 10^{-3}\) & \(5.162\times 10^{-5}\) & \(1.876\times 10^{-3}\) & \(6.143\times 10^{-5}\) & \(2.778\times 10^{-3}\) \\  & Std. & \(3.313\times 10^{-5}\) & \(6.363\times 10^{-4}\) & \(2.747\times 10^{-5}\) & \(4.980\times 10^{-4}\) & \(2.983\times 10^{-5}\) & \(5.771\times 10^{-4}\) \\ TF8 & Ave. & \(-9.152\times 10^{3}\) & \(-8.586\times 10^{3}\) & \(-1.410\times 10^{4}\) & \(-1.392\times 10^{4}\) & \(-2.489\times 10^{4}\) & \(-2.481\times 10^{4}\) \\  & Std. & \(7.372\times 10^{2}\) & \(3.178\times 10^{2}\) & \(1.057\times 10^{3}\) & \(5.269\times 10^{2}\) & \(2.407\times 10^{3}\) & \(1.220\times 10^{3}\) \\ TF9 & Ave. & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std. & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\ TF10 & Ave. & \(8.882\times 10^{-16}\) & \(1.036\times 10^{-14}\) & \(8.882\times 10^{-16}\) & \(1.699\times 10^{-14}\) & \(8.882\times 10^{-16}\) & \(3.713\times 10^{-14}\) \\  & Std.