# Dynamic Heterogeneous Search-Mutation Structure-Based Equilibrium Optimizer
## 4 Numerical Experiments and Discussion for DHSMEO
### Impacts of Improvement Strategies on EO
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Problem** & \multicolumn{2}{c}{**Dim 30**} & \multicolumn{2}{c}{**Dim 50**} & \multicolumn{2}{c}{**Dim 100**} \\  & & **DHSMEO** & **EO** & **DHSMEO** & **EO** & **DHSMEO** & **EO** \\ \hline BF1 & Avg & \(0.000\times 10^{0}\) & \(4.572\times 10^{-41}\) & \(0.000\times 10^{0}\) & \(1.702\times 10^{-34}\) & \(0.000\times 10^{0}\) & \(4.648\times 10^{-29}\) \\  & Std & \(0.000\times 10^{0}\) & \(4.015\times 10^{-41}\) & \(0.000\times 10^{0}\) & \(2.181\times 10^{-34}\) & \(0.000\times 10^{0}\) & \(4.544\times 10^{-29}\) \\ BF2 & Avg & \(0.000\times 10^{0}\) & \(9.844\times 10^{-24}\) & \(0.000\times 10^{0}\) & \(2.076\times 10^{-20}\) & \(0.000\times 10^{0}\) & \(1.910\times 10^{-17}\) \\  & Std & \(0.000\times 10^{0}\) & \(9.957\times 10^{-24}\) & \(0.000\times 10^{0}\) & \(1.302\times 10^{-20}\) & \(0.000\times 10^{0}\) & \(5.657\times 10^{-18}\) \\ BF3 & Avg & \(0.000\times 10^{0}\) & \(9.900\times 10^{-9}\) & \(0.000\times 10^{0}\) & \(3.827\times 10^{-4}\) & \(0.000\times 10^{0}\) & \(5.299\times 10^{0}\) \\  & Std & \(0.000\times 10^{0}\) & \(3.708\times 10^{-8}\) & \(0.000\times 10^{0}\) & \(6.177\times 10^{-4}\) & \(0.000\times 10^{0}\) & \(6.781\times 10^{0}\) \\ BF4 & Avg & \(0.000\times 10^{0}\) & \(2.767\times 10^{-10}\) & \(0.000\times 10^{0}\) & \(5.724\times 10^{-7}\) & \(0.000\times 10^{0}\) & \(5.523\times 10^{-3}\) \\  & Std & \(0.000\times 10^{0}\) & \(2.546\times 10^{-10}\) & \(0.000\times 10^{0}\) & \(5.211\times 10^{-7}\) & \(0.000\times 10^{0}\) & \(1.514\times 10^{-2}\) \\ BF5 & Avg & \(2.507\times 10^{1}\) & \(2.544\times 10^{1}\) & \(4.529\times 10^{1}\) & \(4.578\times 10^{1}\) & \(9.568\times 10^{1}\) & \(9.647\times 10^{1}\) \\  & Std & \(7.996\times 10^{-2}\) & \(1.159\times 10^{-1}\) & \(6.652\times 10^{-2}\) & \(3.041\times 10^{-1}\) & \(5.859\times 10^{-2}\) & \(7.927\times 10^{-1}\) \\ BF6 & Avg & \(4.816\times 10^{-6}\) & \(1.008\times 10^{-5}\) & \(1.108\times 10^{-3}\) & \(9.593\times 10^{-2}\) & \(3.085\times 10^{0}\) & \(4.277\times 10^{0}\) \\  & Std & \(1.465\times 10^{-6}\) & \(3.830\times 10^{-6}\) & \(2.778\times 10^{-4}\) & \(1.328\times 10^{-1}\) & \(4.381\times 10^{-1}\) & \(4.340\times 10^{-1}\) \\ BF7 & Avg & \(3.824\times 10^{-5}\) & \(1.452\times 10^{-3}\) & \(6.153\times 10^{-5}\) & \(2.239\times 10^{-3}\) & \(6.579\times 10^{-5}\) & \(2.754\times 10^{-3}\) \\  & Std & \(2.492\times 10^{-5}\) & \(4.282\times 10^{-4}\) & \(2.223\times 10^{-5}\) & \(9.034\times 10^{-4}\) & \(2.654\times 10^{-5}\) & \(7.464\times 10^{-4}\) \\ BF8 & Avg & \(-9.801\times 10^{3}\) & \(-8.650\times 10^{3}\) & \(-1.546\times 10^{4}\) & \(-1.388\times 10^{4}\) & \(-2.723\times 10^{4}\) & \(-2.520\times 10^{4}\) \\  & Std & \(3.772\times 10^{2}\) & \(4.107\times 10^{2}\) & \(4.761\times 10^{2}\) & \(6.592\times 10^{2}\) & \(8.470\times 10^{2}\) & \(8.239\times 10^{2}\) \\ BF9 & Avg & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\ BF10 & Avg & \(8.882\times 10^{-16}\) & \(9.652\times 10^{-15}\) & \(8.882\times 10^{-16}\) & \(1.806\times 10^{-14}\) & \(8.882\times 10^{-16}\) & \(3.724\times 10^{-14}\) \\  & Std & \(0.000\times 10^{0}\) & \(3.057\times 10^{-15}\) & \(0.000\times 10^{0}\) & \(3.501\times 10^{-15}\) & \(0.000\times 10^{0}\) & \(4.444\times 10^{-15}\) \\ BF11 & Avg & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\ BF12 & Avg & \(2.716\times 10^{-7}\) & \(1.072\times 10^{-6}\) & \(4.008\times 10 The comparative results from Tables 5-8 show that EO, DAEO, HUEO, and LREO achieve the best results with 6, 7, 11, and 7 out of the 39 typical benchmark functions, respectively.