# 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** & \multicolumn{2}{c}{**EO**} & **RSA** & **SMA** & **HGS** & **DMMAEO** \\ \hline Multimodal (Fixed-dimension) & BF14 & Avg & \(9.980\times 10^{-1}\) & \(4.388\times 10^{0}\) & \(9.980\times 10^{-1}\) & \(1.649\times 10^{0}\) & \(9.980\times 10^{-1}\) \\  & Std & \(2.102\times 10^{-16}\) & \(2.478\times 10^{0}\) & \(2.778\times 10^{-13}\) & \(2.478\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & BF15 & Avg & \(8.438\times 10^{-3}\) & \(1.437\times 10^{-3}\) & \(6.404\times 10^{-4}\) & \(7.562\times 10^{-4}\) & \(3.082\times 10^{-4}\) \\  & Std & \(9.907\times 10^{-3}\) & \(3.653\times 10^{-4}\) & \(1.557\times 10^{-4}\) & \(1.171\times 10^{-4}\) & \(1.392\times 10^{-6}\) \\  & BF16 & Avg & \(-1.032\times 10^{0}\) & \(-1.031\times 10^{0}\) & \(-1.032\times 10^{0}\) & \(-1.032\times 10^{0}\) & \(-1.032\times 10^{0}\) \\  & Std & \(5.758\times 10^{-16}\) & \(5.912\times 10^{-4}\) & \(4.390\times 10^{-10}\) & \(6.649\times 10^{-16}\) & \(6.775\times 10^{-16}\) \\  & BF17 & Avg & \(3.979\times 10^{-1}\) & \(4.181\times 10^{-1}\) & \(3.979\times 10^{-1}\) & \(3.979\times 10^{-1}\) & \(3.979\times 10^{-1}\) \\  & Std & \(0.000\times 10^{0}\) & \(1.487\times 10^{-2}\) & \(1.260\times 10^{-8}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & BF18 & Avg & \(3.000\times 10^{0}\) & \(3.000\times 10^{0}\) & \(3.000\times 10^{0}\) & \(3.000\times 10^{0}\) & \(3.000\times 10^{0}\) \\  & Std & \(1.259\times 10^{-15}\) & \(4.144\times 10^{-4}\) & \(2.345\times 10^{-10}\) & \(1.932\times 10^{-15}\) & \(1.688\times 10^{-15}\) \\  & BF19 & Avg & \(-3.863\times 10^{0}\) & \(-3.799\times 10^{-2}\) & \(-3.863\times 10^{0}\) & \(-3.863\times 10^{0}\) & \(-3.863\times 10^{0}\) \\  & Std & \(2.464\times 10^{-15}\) & \(3.499\times 10^{-2}\) & \(1.519\times 10^{-7}\) & \(2.710\times 10^{-15}\) & \(2.710\times 10^{-15}\) \\  & BF20 & Avg & \(-3.231\times 10^{0}\) & \(-2.611\times 10^{0}\) & \(-3.207\times 10^{0}\) & \(-3.246\times 10^{0}\) & \(-3.322\times 10^{0}\) \\  & Std & \(5.126\times 10^{-2}\) & \(2.646\times 10^{-1}\) & \(2.176\times 10^{-2}\) & \(6.493\times 10^{-2}\) & \(1.424\times 10^{-15}\) \\  & BF21 & Avg & \(-8.287\times 10^{0}\) & \(-5.055\times 10^{0}\) & \(-1.015\times 10^{1}\) & \(-9.643\times 10^{0}\) & \(-1.015\times 10^{1}\) \\  & Std & \(2.495\times 10^{0}\) & \(1.322\times 10^{-7}\) & \(1.542\times 10^{-4}\) & \(1.556\times 10^{0}\) & \(6.643\times 10^{-6}\) \\  & Br22 & Avg & \(-9.694\times 10^{0}\) & \(-5.088\times 10^{0}\) & \(-1.040\times 10^{1}\) & \(-1.023\times 10^{0}\) & \(-1.040\times 10^{1}\) \\  & Std & \(1.838\times 10^{0}\) & \(4.401\times 10^{-7}\) & \(1.331\times 10^{-4}\) & \(9.704\times 10^{-1}\) & \(4.211\times 10^{-6}\) \\  & BF23 & Avg & \(-9.455\times 10^{0}\) & \(-5.128\times 10^{0}\) & \(-1.054\times 10^{1}\) & \(-9.996\times 10^{0}\) & \(-1.054\times 10^{1}\) \\  & Std & \(2.200\times 10^{0}\) & \(9.763\times 10^{-7}\) & \(9.975\times 10^{-5}\) & \(1.650\times 10^{0}\) & \(6.669\times 10^{-8}\) \\ \hline  & **Problem** & \multicolumn{2}{c}{**DEEO**} & **HRSA** & **ESMA** & **AAOHGS** & **DHSMEO** \\ \hline BF14 & Avg & \(9.980\times 10^{-1}\) & \(2.177\times 10^{0}\) & \(9.980\times 10^{-1}\) & \(2.366\times 10^{0}\) & \(9.980\times 10^{-1}\) \\  & Std & \(0.000\times 10^{0}\) & \(8.259\times 10^{-1}\) & \(6.438\times 10^{-14}\) & \(3.369\times 10^{0}\) & \(0.000\times 10^{0}\) \\ BF15 & Avg & \(\mathbf{3.075\times 10^{-4}}\) & \(5.639\times 10^{-4}\) & \(4.262\times 10^{-4}\) & \(3.415\times 10^{-4}\) & \(3.080\times 10^{-4}\) \\  & Std & \(6.066\times 10^{-12}\) & \(1.199\times 10^{-4}\) & \(7.580\times 10^{-5}\) & \(6.548\times 10^{-5}\) & \(5.783\times 10^{-7}\) \\ BF16 & Avg & \(-1.032\times 10^{0}\) & \(-1.032\times 10^{0}\) & \(-1.032\times 10^{0}\) & \(-1.032\times 10^{0}\) & \(-1.032\times 10^{0}\) \\  & Std & \(6.775\times 10^{-16}\) & \(1.851\times 10^{-5}\) & \(3.025\times 10^{-10}\) & \(2.831\times 10^{-12}\) & \(6.775\times 10^{-16}\) \\ BF17 & Avg & \(3.979\times 10^{-1}\) & \(3.979\times 10^{-1}\) & \(3.979\times 10^{-1}\) & \(3.979\times 10^{-1}\) & \(3.979\times 10^{-1}\) \\  & Std & \(0.