## 5 Results and Discussion
### Parameter Estimation Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithms** & **SSE** & **AE** & **MAE** & **MSE** & **RMSE** \\ \hline \multirow{4}{*}{**GSA**} & **Minimum** & \(1.03\times 10^{-5}\) & \(3.27\times 10^{-3}\) & \(1.66\times 10^{-4}\) & \(5.15\times 10^{-7}\) & \(7.41\times 10^{-4}\) \\  & **Maximum** & \(7.71\times 10^{-5}\) & \(8.70\times 10^{-3}\) & \(4.33\times 10^{-4}\) & \(3.86\times 10^{-6}\) & \(1.98\times 10^{-3}\) \\  & **Mean** & \(3.18\times 10^{-5}\) & \(5.64\times 10^{-3}\) & \(2.81\times 10^{-4}\) & \(1.59\times 10^{-6}\) & \(1.22\times 10^{-3}\) \\  & **Standard deviation** & \(1.93\times 10^{-5}\) & \(4.31\times 10^{-3}\) & \(2.20\times 10^{-4}\) & \(9.65\times 10^{-7}\) & \(9.92\times 10^{-4}\) \\ \hline \multirow{4}{*}{**MVO**} & **Minimum** & \(1.09\times 10^{-5}\) & \(3.33\times 10^{-3}\) & \(1.05\times 10^{-4}\) & \(5.45\times 10^{-7}\) & \(7.76\times 10^{-3}\) \\  & **Maximum** & \(8.25\times 10^{-5}\) & \(9.07\times 10^{-3}\) & \(4.14\times 10^{-4}\) & \(4.13\times 10^{-6}\) & \(2.02\times 10^{-3}\) \\  & **Mean** & \(3.66\times 10^{-5}\) & \(6.01\times 10^{-3}\) & \(3.62\times 10^{-4}\) & \(1.83\times 10^{-6}\) & \(1.36\times 10^{-3}\) \\  & **Standard deviation** & \(2.28\times 10^{-5}\) & \(4.74\times 10^{-3}\) & \(2.15\times 10^{-4}\) & \(1.14\times 10^{-6}\) & \(1.08\times 10^{-3}\) \\ \hline \multirow{4}{*}{**PSO**} & **Minimum** & \(3.81\times 10^{-2}\) & \(1.95\times 10^{-1}\) & \(9.7\times 10^{-3}\) & \(1.9\times 10^{-3}\) & \(4.36\times 10^{-2}\) \\  & **Maximum** & \(8.74\times 10^{-1}\) & \(9.35\times 10^{-1}\) & \(4.67\times 10^{-2}\) & \(4.37\times 10^{-2}\) & \(2.09\times 10^{-1}\) \\  & **Mean** & \(4.14\times 10^{-1}\) & \(6.43\times 10^{-1}\) & \(3.21\times 10^{-2}\) & \(2.07\times 10^{-2}\) & \(1.43\times 10^{-1}\) \\  & **Standard deviation** & \(2.63\times 10^{-1}\) & \(5.13\times 10^{-1}\) & \(2.56\times 10^{-2}\) & \(1.31\times 10^{-2}\) & \(1.11\times 10^{-1}\) \\ \hline \multirow{4}{*}{**SCA**} & **Minimum** & \(1.42\times 10^{-3}\) & \(3.76\times 10^{-2}\) & \(1.8\times 10^{-3}\) & \(7.10\times 10^{-5}\) & \(8.4\times 10^{-3}\) \\  & **Maximum** & \(1.40\times 10^{-1}\) & \(3.74\times 10^{-1}\) & \(1.87\times 10^{-2}\) & \(7.70\times 10^{-3}\) & \(8.37\times 10^{-2}\) \\  & **Mean** & \(4.0\times 10^{-2}\) & \(2.0\times 10^{-1}\) & \(1.0\times 10^{-2}\) & \(2.0\times 10^{-3}\) & \(4.47\times 10^{-2}\) \\  & **Standard deviation** & \(3.20\times 10^{-2}\) & \(1.80\times 10^{-1}\) & \(9.0\times 10^{-3}\) & \(1.6\times 10^{-3}\) & \(4.04\times 10^{-2}\) \\ \hline \multirow{4}{*}{**HBO**} & **Minimum** & \(1.1\times 10^{-3}\) & \(3.34\times 10^{-2}\) & \(1.6\times 10^{-3}\) & \(5.6\times 10^{-5}\) & \(7.4\times 10^{-3}\) \\  & **Maximum** & \(7.5\times 10^{-3}\) & \(8.65\times 10^{-2}\) & \(4.3\times 10^{-3}\) & \(3.7\times 10^{-4}\) & \(1.93\times 10^{-2}\) \\  & **Mean** & \(3.4\times 10^{-3}\) & \(5.86\times 10^{-2}\) & \(2.9\times 10^{-3}\) & \(1.7\times 10^{-4}\) & \(1.31\times 10^{-2}\) \\  & **Standard deviation** & \(1.9\times 10^{-3}\) & \(4.41\times 10^{-2}\) & \(2.2\times 10^{-3}\) & \(9.70\times 10^{-5}\) & \(9.8\times 10^{-3}\) \\ \hline \multirow{4}{*}{**PO**} & **Minimum** & \(1.0\times 10^{-3}\) & \(3.27\times 10^{-2}\) & \(1.6\times 10^{-3}\) & \(5.35\times 10^{-5}\) & \(7.3\times 10^{-3}\) \\  & **Maximum** & \(1.24\times 10^{-2}\) & \(1.11\times 10^{-1}\) & \(5.5\times 10^{-3}\) & \(6.2\times 10^{-4}\) & \(2.49\times 10^{-2}\) \\  & **Mean** & \(3.8\times 10^{-3}\) & \(6.21\times 10^{-2}\) & \(3.1\times 10^{-3}\) & \(1.9\times 10^{-4}\) & \(1.38\times 10^{-2}\) \\  & **Standard deviation** & \(3.1\times 10^{-3}\) & \(5.60\times 10^{-2}\) & \(2.8\times 10^{-3}\) & \(1.5\times 10^{-4}\) & \(1.25\times 10^{-2}\) \\ \hline \multirow{4}{*}{**PSOSA**} & **Minimum** & \(1.09\times 10^{-22}\) & \(1.04\times 10^{-11}\) & \(5.22\times 10^{-13}\) & \(5.46\times 10^{-24}\) & \(2.33\times 10^{-12}\) \\  & **Maximum** & \(9.77\times 10^{-21}\) & \(9.88\times 10^{-11}\) & \(4.94\times 10^{-12}\) & \(4.89\times 10^{-22}\) & \(2.21\times 10^{-11}\) \\ \cline{1-1}  & **Mean** & \(3.97\times 10^{-21}\) & \(6.30\times 10^{-11}\) & \(3.15\times 10^{-12}\) & \(1.99\times 10^{-22}\) & \(1.40\times 10^{-11}\) \\ \cline{1-1}  & **Standard deviation** & \(3.32\times 10^{-21}\) & \(5.76\times 10^{-11}\) & \(2.88\times 10^{-12}\) & \(1.66\times 10^{-22}\) & \(1.28\times 10^{-11}\) \\ \hline \hline \end{tabular}
\end{table}