## 4 Simulation Results
### IMGO for the PV Parameter Estimation Problem
The proposed IMGO is applied, considering their upper (_UIP_) and lower (_LOW_) boundaries and the acquired parameters which are shown in Table 17. Also, the results are compared with MGO, a Dwarf Mongoose Optimizer (DMO), and a prime algorithm (RIME) [59] under the similar conditions of 1000 iterations and 200 solutions. From this table, the proposed IMGO displays a similar performance, with MGO achieving the lowest RMSE value of 9.824848 \(\times\) 10\({}^{-4}\) and both acquiring lower RMSE compared to DMO and RIME, which attain values equal to 1.028696 \(\times\) 10\({}^{-3}\) and 9.9382 \(\times\) 10\({}^{-4}\), respectively. Additionally, the observed and predicted I-V and P-V characteristics for the DD-PV model are shown in Figure 19a,b. The data produced by the IMGO approach can be shown to closely match the data obtained through experimentation, indicating that the MGA technique was effective in generating power and current over a variety of voltages. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{2}{c}{**RTC France**} & \multirow{2}{*}{**Proposed IMGO**} & \multirow{2}{*}{**MGO [59]**} & \multirow{2}{*}{**DMO [59]**} & \multirow{2}{*}{**RIME [59]**} \\ \cline{2-2} \cline{5-6}  & \(LOW\) & \(UP\) & & & & \\ \hline \(l_{\text{P}h}\) (A) & 0 & 1 & 0.760781079 & 0.760781079 & 0.761086003 & 0.760864277 \\ \hline \(\text{R}_{ss}\) (\(\Omega\)) & 0 & 0.5 & 0.03674043 & 0.03674043 & 0.036452844 & 0.036173672 \\ \hline \(\text{R}_{Sh}\) (\(\Omega\)) & 0 & 100 & 55.48544961 & 55.48544096 & 56.0407128 & 53.58354831 \\ \hline \(l_{S1}\) (A) & 0 & 1 & \(2.25974\times 10^{-7}\) & \(7.49347\times 10^{-7}\) & \(3.81141\times 10^{-7}\) & \(4.3113\times 10^{-8}\) \\ \hline \(\eta_{1}\) & 1 & 2 & 1.451016761 & 2 & 1.83357911 & 1.827202939 \\ \hline \(l_{S2}\) (A) & 0 & 1 & \(7.49348\times 10^{-7}\) & \(2.25974\times 10^{-7}\) & \(2.38858\times 10^{-7}\) & \(3.25421\times 10^{-7}\) \\ \hline \(\eta_{2}\) & 1 & 2 & 2 & 1.45101678 & 1.458364626 & 1.482783518 \\ \hline \(RMSE\) & & & \(9.824848\times 10^{-4}\) & \(9.82485\times 10^{-4}\) & \(1.028696\times 10^{-3}\) & \(9.9382\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Limits of the PV cell parameters and acquired parameters regarding IMGO, MGO, DMO, and RIME for the RTC France cell. Figure 19: IMGO extracted versus experimental (**a**) I-V and (**b**) P-V characteristics for the R.T.C. France cell. Also, the sensitivity analysis for MGO and IMGO are presented in Figure 20, which provides key insights into the performance differences between the two algorithms for RTC cell parameter estimation. The results reveal how the algorithms perform under varying configurations of solutions and iterations. In terms of the best RMSE (Figure 20a), both algorithms show similar performance across most configurations. For instance, at the configuration of 50 solutions and 500 iterations, IMGO slightly outperforms MGO with an RMSE of 0.000983 compared to 0.000984. As the number of iterations increases, the differences diminish, with both algorithms converging to comparable values. The mean RMSE values (Figure 20b) highlight IMGO's significant advantage in stability and robustness. For lower configurations such as 50 solutions and 500 iterations, IMGO achieves a mean RMSE of 0.001053, noticeably better than MGO's 0.001195. This trend continues across various configurations, with IMGO maintaining a consistent edge, particularly when the number of iterations is low. IMGO's ability to handle extreme cases is evidenced in the worst RMSE results (Figure 20c). At a configuration of 50 solutions and 500 iterations, IMGO records an RMSE of 0.001399, significantly lower than MGO's 0.002029. This pattern holds across different configurations, showcasing IMGO's robustness in mitigating outliers and delivering more reliable solutions across iterations. The standard deviation of the RMSE values (Figure 20d) further underscores IMGO's enhanced precision.