## 4 Results and Discussions
### Experimental Results and Comparison
#### 4.3.1 Results Comparison on the Single Diode Model
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Min** & **Max** & **Mean** & **Std. Dev.** \\ \hline IADE & \(9.8900\times 10^{-4}\) & NA & NA & NA \\ ABSO & \(9.9124\times 10^{-4}\) & NA & NA & NA \\ BBO-M & \(9.8634\times 10^{-4}\) & NA & NA & NA \\ GGHS & \(9.9078\times 10^{-4}\) & NA & NA & NA \\ GOTLBO & \(9.87442\times 10^{-4}\) & \(1.98244\times 10^{-3}\) & \(1.33488\times 10^{-3}\) & \(2.99407\times 10^{-4}\) \\ CARO & \(9.8665\times 10^{-4}\) & NA & NA & NA \\ DE & \(9.8602\times 10^{-4}\) & NA & NA & NA \\ IJAYA & \(9.8603\times 10^{-4}\) & \(1.0622\times 10^{-3}\) & \(9.9204\times 10^{-4}\) & \(1.4033\times 10^{-5}\) \\ BMO & \(9.8608\times 10^{-4}\) & NA & NA & NA \\ PS & \(2.863\times 10^{-1}\) & NA & NA & NA \\ SA & \(1.70\times 10^{-3}\) & NA & NA & NA \\ ANS & \(9.9689\times 10^{-4}\) & \(1.4385\times 10^{-3}\) & \(1.1051\times 10^{-3}\) & \(1.0141\times 10^{-4}\) \\ BLPSO & \(1.4836\times 10^{-3}\) & \(2.2415\times 10^{-3}\) & \(1.9092\times 10^{-3}\) & \(1.7404\times 10^{-4}\) \\ CSO & \(1.6358\times 10^{-3}\) & \(2.4104\times 10^{-3}\) & \(2.0058\times 10^{-3}\) & \(1.7398\times 10^{-4}\) \\ CTLA & \(1.0991\times 10^{-3}\) & \(1.8027\times 10^{-3}\) & \(1.3772\times 10^{-3}\) & \(1.7132\times 10^{-4}\) \\ LWOA & \(1.0873\times 10^{-3}\) & \(9.1622\times 10^{-3}\) & \(3.1119\times 10^{-3}\) & \(1.8838\times 10^{-3}\) \\ SOS & \(9.8609\times 10^{-4}\) & \(1.1982\times 10^{-3}\) & \(1.0245\times 10^{-3}\) & \(5.2184\times 10^{-5}\) \\ \hline \end{tabular}
\end{table} 
Table 2: RMSE results for the single diode model. Figure 3: Extraction results by SOS for the single diode model. (**a**) Current; (**b**) power. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **\(\mathbf{I_{\text{ph}}}\) (A)** & \(\mathbf{I_{\text{sd}}}\) (**uA**) & \(\mathbf{R_{\text{s}}}\) (**f**) & \(\mathbf{R_{\text{sh}}}\) (**f**) & \(\mathbf{n}\) & **RMSE** \\ \hline IADE & 0.7607 & 0.33613 & 0.03621 & 54.7643 & 1.4852 & \(9.8900\times 10^{-4}\) \\ ABSO & 0.76080 & 0.30623 & 0.03659 & 52.2903 & 1.47583 & \(9.9124\times 10^{-4}\) \\ BBO-M & 0.76078 & 0.31874 & 0.03642 & 53.36277 & 1.47984 & \(9.8634\times 10^{-4}\) \\ GGHS & 0.76092 & 0.32620 & 0.03631 & 53.0647 & 1.48217 & \(9.9079\times 10^{-4}\) \\ GOTLBO & 0.760780 & 0.331552 & 0.036265 & 54.115426 & 1.483820 & \(9.8744\times 10^{-4}\) \\ CARO & 0.76079 & 0.31724 & 0.03644 & 53.0893 & 1.48168 & \(9.8665\times 10^{-4}\) \\ DE & 0.7608 & 0.323 & 0.0364 & 53.719 & 1.4812 & \(9.8602\times 10^{-4}\) \\ IJAYA & 0.7608 & 0.3228 & 0.0364 & 53.7595 & 1.4811 & \(9.8603\times 10^{-4}\) \\ PS & 0.7617 & 0.9980 & 0.0313 & 64.1026 & 1.6000 & \(2.863\times 10^{-1}\) \\ SA & 0.7620 & 0.4798 & 0.0345 & 43.1034 & 1.5172 & \(1.70\times 10^{-3}\) \\ ANS & 0.7607 & 0.3407 & 0.0362 & 54.7917 & 1.4866 & \(9.9689\times 10^{-4}\) \\ BLPSO & 0.7599 & 0.4977 & 0.0347 & 96.5115 & 1.5257 & \(1.4836\times 10^{-3}\) \\ CSO & 1.0205 & 0.3658 & 1.2122 & 1699.0050 & 48.8206 & \(1.6385\times 10^{-3}\) \\ CTLA & 0.7650 & 0.4280 & 0.0357 & 61.1131 & 1.5092 & \(1.0991\times 10^{-3}\) \\ LWOA & 1.0284 & 0.3145 & 1.2218 & 1272.0197 & 48.2413 & \(1.0873\times 10^{-3}\) \\ SOS & 0.7608 & 0.3579 & 0.0359 & 53.7835 & 1.4916 & \(9.8609\times 10^{-4}\) \\ \hline \end{tabular}
\end{table} 
Table 3: xtracted parameters for the single diode model. Besides, the convergence curves are presented in Figure 4. It is obvious that SOS is slightly slower than LWOA in the opening phase, however, the latter stagnates soon and then suffers from premature convergence, indicating that it has been caught in a local optimum. For the other four methods, SOS consistently converges faster than them throughout the whole evolutionary process.