# Dynamic Heterogeneous Search-Mutation Structure-Based Equilibrium Optimizer
## 4 Numerical Experiments and Discussion for DHSMEO
### Scalability Analysis
Consequently, the results of  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Problem** & \(\mathbf{R_{\rm a}=0.4}\) & \(\mathbf{R_{\rm a}=0.5}\) & \(\mathbf{R_{\rm a}=0.6}\) & \(\mathbf{R_{\rm a}=0.7}\) & \(\mathbf{R_{\rm a}=0.8}\) \\ \hline BF1 & Avg & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\ BF2 & Avg & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\ BF3 & Avg & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\ BF4 & Avg & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\ BF5 & Avg & \(2.598\times 10^{1}\) & \(2.566\times 10^{1}\) & \(2.543\times 10^{1}\) & \(2.557\times 10^{1}\) & \(2.507\times 10^{1}\) \\  & Std & \(1.211\times 10^{-1}\) & \(1.702\times 10^{-1}\) & \(1.554\times 10^{-1}\) & \(1.352\times 10^{-1}\) & \(7.996\times 10^{-2}\) \\ BF6 & Avg & \(8.738\times 10^{-3}\) & \(9.859\times 10^{-5}\) & \(7.782\times 10^{-5}\) & \(3.218\times 10^{-5}\) & \(4.816\times 10^{-6}\) \\  & Std & \(4.488\times 10^{-2}\) & \(3.910\times 10^{-5}\) & \(2.989\times 10^{-5}\) & \(1.686\times 10^{-5}\) & \(1.465\times 10^{-6}\) \\ BF7 & Avg & \(1.135\times 10^{-4}\) & \(4.445\times 10^{-5}\) & \(1.092\times 10^{-4}\) & \(1.663\times 10^{-4}\) & \(3.824\times 10^{-5}\) \\  & Std & \(5.620\times 10^{-5}\) & \(2.503\times 10^{-5}\) & \(5.218\times 10^{-5}\) & \(9.145\times 10^{-5}\) & \(2.492\times 10^{-5}\) \\ BF8 & Avg & \(-8.322\times 10^{3}\) & \(-8.900\times 10^{3}\) & \(-9.396\times 10^{3}\) & \(-8.984\times 10^{3}\) & \(-9.801\times 10^{3}\) \\  & Std & \(3.790\times 10^{2}\) & \(3.876\times 10^{2}\) & \(3.383\times 10^{2}\) & \(3.283\times 10^{2}\) & \(3.772\times 10^{2}\) \\ BF9 & Avg & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\ BF10 & Avg & \(8.882\times 10^{-16}\) & \(8.882\times 10^{-16}\) & \(8.882\times 10^{-16}\) & \(8.882\times 10^{-16}\) & \(8.882\times 10^{-16}\) \\  & Std & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\ BF11 & Avg & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\  & Std & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) & \(0.000\times 10^{0}\) \\ BF12 & Avg & \(6.914\times 10^{-5}\) & \(1.191\times 10^{-5}\) & \(5.708\times 10^{-6}\) & \(1.854\times 10^{-6}\) & \(2.716\times 10^{-7}\) \\  & Std & \(4.101\times 10^{-5}\) & \(4.051\times 10^{-6}\) & \(1.840\times 10^{-6}\) & \(8.766\times 10^{-7}\) & \(6.933\times 10^{-8}\) \\ BF13 & Avg & \(2.246\times 10^{0}\) & \(1.752\times 10^{0}\) & \(1.822\times 10^{0}\) & \(1.208\times 10^{0}\) & \(5.501\times 10^{-1}\) \\  & Std & \(1.037\times 10^{-1}\) & \(2.599\times 10^{-1}\) & \(1.469\times 10^{-1}\) & \(3.097\times 10^{-1}\) & \(2.201\times 10^{-1}\) \\  & Friedman mean rank & 3.846 & 3.231 & 2.  
scalability analysis indicate that DHSMEO performs superior stability in the optimization performance compared to EO as the dimensionality increases.