# Dynamic Heterogeneous Search-Mutation Structure-Based Equilibrium Optimizer
## 4 Numerical Experiments and Discussion for DHSMEO
### Impacts of Improvement Strategies on EO
In contrast, DHSMEO achieves the best performance in 38 of 39 benchmark functions and exhibits superior optimization performance compared to EO, DAEO, HUEO, and LREO. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Problem** & & **EO** & **DAEO** & **HUEO** & **LREO** & **DHSMEO** \\ \hline Multimodal & BF8 & Avg & \(-8.650\times 10^{3}\) & \(9.980\times 10^{-1}\) & \(9.980\times 10^{-1}\) & \(9.980\times 10^{-1}\) & \(\mathbf{9.980\times 10^{-1}}\) \\ (High & Std & \(2.102\times 10^{-16}\) & \(2.369\times 10^{-16}\) & \(1.649\times 10^{-16}\) & \(1.749\times 10^{-16}\) & \(0.000\times 10^{0}\) \\ dimension) & BF15 & Avg & \(8.438\times 10^{-3}\) & \(1.811\times 10^{-3}\) & \(3.436\times 10^{-4}\) & \(3.920\times 10^{-3}\) & \(\mathbf{3.080\times 10^{-4}}\) \\  & Std & \(9.907\times 10^{-3}\) & \(5.057\times 10^{-3}\) & \(5.582\times 10^{-5}\) & \(7.492\times 10^{-3}\) & \(5.783\times 10^{-7}\) \\  & BF16 & Avg & \(-1.032\times 10^{-10}\) & \(-1.032\times 10^{0}\) & \(-1.032\times 10^{0}\) & \(-1.032\times 10^{0}\) & \(-1.032\times 10^{0}\) \\  & Std & \(5.758\times 10^{-16}\) & \(5.296\times 10^{-16}\) & \(5.216\times 10^{-16}\) & \(5.133\times 10^{-16}\) & \(6.775\times 10^{-16}\) \\  & BF17 & Avg & \(3.979\times 10^{-1}\) & \(3.979\times 10^{-1}\) & \(3.979\times 10^{-1}\) & \(3.979\times 10^{-1}\) & \(\mathbf{3.979\times 10^{-1}}\) \\  & Std & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(\mathbf{0.000\times 10^{0}}\) \\  & SF18 & Avg & \(3.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & SF19 & Avg & \(-3.863\times 10^{0}\) & \(-3.863\times 10^{0}\) & \(-3.863\times 10^{0}\) & \(-3.863\times 10^{0}\) & \(-\mathbf{3.863\times 10^{0}}\) \\  & SF20 & Avg & \(-3.231\times 10^{0}\) & \(-3.306\times 10^{0}\) & \(-3.258\times 10^{-5}\) & \(-3.286\times 10^{0}\) & \(-3.322\times 10^{0}\) \\  & Std & \(5.126\times 10^{-2}\) & \(4.111\times 10^{-2}\) & \(5.992\times 10^{-2}\) & \(5.542\times 10^{-2}\) & \(1.355\times 10^{-15}\) \\  & BF21 & Avg & \(-8.287\times 10^{0}\) & \(-9.478\times 10^{0}\) & \(-5.055\times 10^{0}\) & \(-1.015\times 10^{0}\) & \(\mathbf{-1.015\times 10^{0}}\) \\  & Std & \(2.495\times 10^{0}\) & \(1.751\times 10^{0}\) & \(1.565\times 10^{-15}\) & \(6.218\times 10^{-6}\) & \(5.637\times 10^{-15}\) \\  & BF22 & Avg & \(-9.694\times 10^{0}\) & \(-9.874\times 10^{0}\) & \(-5.619\times 10^{0}\) & \(-1.040\times 10^{0}\) & \(\mathbf{-1.040\times 10^{0}}\) \\  & Std & \(1.838\times 10^{0}\) & \(1.613\times 10^{0}\) & \(1.622\times 10^{0}\) & \(4.850\times 10^{-5}\) & \(5.713\times 10^{-16}\) \\ BF23 & Avg & \(-9.455\times 10^{0}\) & \(-1.027\times 10^{1}\) & \(-6.304\times 10^{0}\) & \(-1.054\times 10^{0}\) & \(\mathbf{-1.054\times 10^{0}}\) \\  & Std & \(2.200\times 10^{0}\) & \(1.482\times 10^{0}\) & \(2.397\times 10^{0}\) & \(4.205\times 10^{-5}\) & \(2.618\times 10^{-5}\) \\ \hline \end{tabular}
\end{table} 
Table 6: Test results of different improvement strategies in multimodal benchmark functions with high dimension.