# Dynamic Heterogeneous Search-Mutation Structure-Based Equilibrium Optimizer
## 4 Numerical Experiments and Discussion for DHSMEO
### Comparative Test of DHSMEO and Other Algorithms
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Problem** & **EO** & **RSA** & **SMA** & **HGS** & **DMMAEO** \\ \hline Unimodal & BF1 & Avg & \(4.572\times 10^{-41}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(2.548\times 10^{-156}\) & \(0.000\times 10^{0}\) \\  & Std & \(4.015\times 10^{-41}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(1.390\times 10^{-155}\) & \(0.000\times 10^{-08}\) \\  & BP2 & Avg & \(9.844\times 10^{-24}\) & \(0.000\times 10^{0}\) & \(6.661\times 10^{-168}\) & \(9.350\times 10^{-88}\) & \(3.361\times 10^{-88}\) \\  & Std & \(9.957\times 10^{-24}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(2.850\times 10^{-87}\) & \(0.000\times 10^{0}\) \\  & BF3 & Avg & \(9.900\times 10^{-9}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(7.709\times 10^{-69}\) & \(0.000\times 10^{0}\) \\  & Std & \(3.708\times 10^{-8}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(3.435\times 10^{-68}\) & \(0.000\times 10^{0}\) \\  & BF4 & Avg & \(2.767\times 10^{-10}\) & \(0.000\times 10^{0}\) & \(3.823\times 10^{-166}\) & \(4.178\times 10^{-67}\) & \(6.520\times 10^{-366}\) \\  & Std & \(2.546\times 10^{-10}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(1.928\times 10^{-66}\) & \(0.000\times 10^{0}\) \\  & BF5 & Avg & \(2.544\times 10^{1}\) & \(1.789\times 10^{1}\) & \(5.019\times 10^{0}\) & \(2.268\times 10^{1}\) & \(2.472\times 10^{1}\) \\  & Std & \(1.159\times 10^{-1}\) & \(1.402\times 10^{1}\) & \(8.022\times 10^{0}\) & \(7.682\times 10^{0}\) & \(1.368\times 10^{-1}\) \\  & BF6 & Avg & \(1.008\times 10^{-5}\) & \(7.126\times 10^{0}\) & \(6.146\times 10^{-3}\) & \(5.622\times 10^{-6}\) & \(1.541\times 10^{-6}\) \\  & Std & \(3.830\times 10^{-6}\) & \(1.288\times 10^{-1}\) & \(1.718\times 10^{-3}\) & \(4.135\times 10^{-6}\) & \(7.254\times 10^{-7}\) \\  & BF7 & Avg & \(1.452\times 10^{-3}\) & \(1.289\times 10^{-4}\) & \(2.243\times 10^{-4}\) & \(8.059\times 10^{-4}\) & \(4.766\times 10^{-5}\) \\  & Std & \(4.282\times 10^{-4}\) & \(7.633\times 10^{-5}\) & \(1.223\times 10^{-4}\) & \(7.635\times 10^{-4}\) & \(2.450\times 10^{-5}\) \\ \hline  & **Problem** & **DEEO** & **HRSA** & **ESMA** & **AOAHGS** & **DHSMEO** \\ \hline BF1 & Avg & \(9.675\times 10^{-22}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std & \(6.645\times 10^{-22}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & BP2 & Avg & \(2.458\times 10^{-13}\) & \(0.000\times 10^{0}\) & \(4.209\times 10^{-236}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std & \(8.407\times 10^{-14}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\ BF3 & Avg & \(4.145\times 10^{-3}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(4.010\times 10^{-158}\) & \(0.000\times 10^{0}\) \\  & Std & \(4.934\times 10^{-3}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(1.512\times 10^{-134}\) & \(0.000\times 10^{0}\) \\  & BF4 & Avg & \(2.920\times 10^{-5}\) & \(0.000\times 10^{0}\) & \(6.917\times 10^{-323}\) & \(1.241\times 10^{-66}\) & \(0.000\times 10^{0}\) \\  & Std & \(1.486\times 10^{-5}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(2.928\times 10^{-66}\) & \(0.000\times 10^{0}\) \\  & BF5 & Avg & \(2.555\times 10^{1}\) & \(2.896\times 10^{1}\) & \(**4.277\times 10^{-1}\)** & \(2.282\times 10^{1}\) & \(2.507\times 10^{1}\) \\  & Std & \(1.631\times 10^{-1}\) & \(6.764\times 10^{-2}\) & \(3.179\times 10^{-1}\) & \(1.035\times 10^{1}\) & \(7.996\times 10^{-2}\) \\  & BF6 & Avg & \(1.592\times 10^{-5}\) & \(4.328\times 10^{0}\) & \(1.526\times 10^{-3}\) & \(1.372\times 10^{-4}\) & \(4.816\times 10^{-6}\) \\  & Std & \(7.366\times 10^{-6}\) & \(1.385\times 10^{0}\) & \(5.754\times 10^{-4}\) & \(1.453\times 10^{-4}\) & \(1.465\times 10^{-6}\) \\  & BF7 & Avg & \(2.507\times 10^{-3}\) & \(1.165\times 10^{-4}\) & \(7.383\times 10^{-5}\) & \(5.294\times 10^{-5}\) & \(\bf{3.824\times 10^{-5}}\) \\  & Std & \(6.013\times 10^{-4}\) & \(8.014\times 10^{-5}\) & \(4.497\times 10^{-5}\) & \(2.400\times 10^{-5}\) & \(2.492\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table}