## 5 Results and Discussion
### Parameter Estimation Results
Table 10 represents the statistical result based on the Wilcoxon rank sum test. [PERSON]'s rank test is represented in Table 11. Based on the results of this test, it is clear that the newly generated hybrid algorithm is more reliable and superior to other similar algorithms. Based on the results of both tests, it is clear that PSOGSA is superior to other compared algorithms. Figure 7: The P-V curve at standard temperature conditions. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameter/Algorithm** & **MVO** & **PSO** & **SCA** & **HBO** & **PO** & **GSA** & **PSOGSA** \\ \hline \(\mathbf{I_{pv}}\) & 9.1834 & 9.4699 & 9.1982 & 9.2130 & 9.2808 & 4.5140 & 9.1905 \\ \(\mathbf{Alpha_{1}}\) & 1.6664 & 1.0193 & 1.2959 & 1.4758 & 1.5994 & 1.0457 & 1.5969 \\ \(\mathbf{Alpha_{2}}\) & 1.4637 & 0.8275 & 1.4142 & 1.4570 & 1.6487 & 1.2933 & 1.5713 \\ \(\mathbf{R_{ee}}\) & 0.0275 & 0.0023 & 0.0349 & 0.0901 & 0.0010 & 0.3198 & 0.0233 \\ \(\mathbf{R_{sh}}\) & 330.334 & 99.411 & 251.018 & 294.329 & 275.913 & 272.241 & 306.862 \\ \(\mathbf{I_{a1}}\) & \(8.00\times 10^{-7}\) & \(3.49\times 10^{-7}\) & \(1.73\times 10^{-7}\) & \(3.01\times 10^{-7}\) & \(2.66\times 10^{-7}\) & \(5.61\times 10^{-7}\) & 0 \\ \(\mathbf{I_{a2}}\) & 0 & \(1.81\times 10^{-7}\) & \(4.73\times 10^{-7}\) & \(4.18\times 10^{-7}\) & \(7.47\times 10^{-7}\) & \(5.80\times 10^{-7}\) & \(7.00\times 10^{-7}\) \\ \(\mathbf{R_{s}}\) & 0.0155 & 0.0048 & 0.0585 & 0.0658 & 0.0032 & 0.2589 & 0.0325 \\ \multicolumn{2}{c}{**Computation time per run (s)**} & 2.015 & 3.248 & 3.142 & 2.723 & 2.001 & 1.358 & 1.421 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The monocrystalline MDDM parameter estimation results. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter/Algorithm** & **MVO** & **PSO** & **SCA** & **HBO** & **PO** & **GSA** & **PSOGSA** \\ \hline \(\mathbf{I_{pv}}\) & 9.1834 & 9.4699 & 9.1982 & 9.2130 & 9.2808 & 4.5140 & 9.1905 \\ \(\mathbf{Alpha_{1}}\) & 1.6664 & 1.0193 & 1.2959 & 1.4758 & 1.5994 & 1.0457 & 1.5969 \\ \(\mathbf{Alpha_{2}}\) & 1.4637 & 0.8275 & 1.4142 & 1.4570 & 1.6487 & 1.2933 & 1.5713 \\ \(\mathbf{R_{ee}}\) & 0.0275 & 0.0023 & 0.0349 & 0.0901 & 0.0010 & 0.3198 & 0.0233 \\ \(\mathbf{R_{sh}}\) & 330.334 & 99.411 & 251.018 & 294.329 & 275.913 & 272.241 & 306.862 \\ \(\mathbf{I_{a1}}\) & \(8.00\times 10^{-7}\) & \(3.49\times 10^{-7}\) & \(1.73\times 10^{-7}\) & \(3.01\times 10^{-7}\) & \(2.66\times 10^{-7}\) & \(5.61\times 10^{-7}\) & 0 \\ \(\mathbf{I_{a2}}\) & 0 & \(1.81\times 10^{-7}\) & \(4.73\times 10^{-7}\) & \(4.18\times 10^{-7}\) & \(7.47\times 10^{-7}\) & \(5.80\times 10^{-7}\) & \(7.00\times 10^{-7}\) \\ \(\mathbf{R_{s}}\) & 0.0155 & 0.0048 & 0.0585 & 0.0658 & 0.0032 & 0.2589 & 0.0325 \\ \multicolumn{2}{c}{**Computation time per run (s)**} & 2.015 & 3.248 & 3.142 & 2.723 & 2.001 & 1.358 & 1.421 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The monocrystalline MSDM parameter estimation results. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** & **MSE** & **AE** & **MAE** & **MSE** & **RMSE** \\ \hline \multirow{4}{*}{**GSA**} & **Minimum** & \(1.31\times 10^{-7}\) & \(3.60\times 10^{-4}\) & \(1.81\times 10^{-5}\) & \(6.55\times 10^{-9}\) & \(8.09\times 10^{-5}\) \\  & **Maximum** & \(7.87\times 10^{-7}\) & \(8.84\times 10^{-4}\) & \(4.43\times 10^{-5}\) & \(3.93\times 10^{-8}\) & \(1.96\times 10^{-4}\) \\  & **Mean** & \(4.32\times 10^{-7}\) & \(6.57\  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** & \multicolumn{1}{c}{**SSE**} & **AE** & **MAE** & **MSE** & **RMSE** \\ \hline \multirow{4}{*}{**GSA**} & **Minimum** & \(1.30\times 10^{-5}\) & \(3.61\times 10^{-3}\) & \(1.84\times 10^{-4}\) & \(6.50\times