## 1 Introduction
In [21], a DE was combined with a Teaching-Learning-Based Optimizer (TLBO) while accounting for the learners' ranking likelihood. For the SDiM and DDiM, a similar DE with a reversible learning process, multi-population tactics, and mutation method has been shown in [22]. An enhanced TLBO was developed in [23] using several instructional strategies and executed in a comparative manner on both the SDiM and DDiM. Both the RTC France solar cell and the Photowatt-PWM201 PV cell had their parameters estimated through two straightforward, direct methods: Rao-2 and Rao-3 [24]. The backtracking search technique was used as part of an elite strategy in [25] and was applied to both the SDiM and DDiM. The Nelder-Mead simplex (horizontal and vertical) crossovers were combined with Harris Hawks optimization in [26] and used on KC200 GT, SM55, and ST40, encompassing the DDiM and SDiM. The Imperialist competitive algorithm was used in [27]to estimate the ideal PV parameters. Considering different electrical models based on the number of diode branches, the JAYA method for PV parameter extraction has been modified by incorporating a chaotic map, as detailed in [28]. This revised method is coupled with a learning approach grounded in an elite opponent process [29]. An orthogonal learning strategy-based grey Wolf method has been demonstrated in [30] to identify the unknowns in various solar PV models. A novel two-step method for deriving the SDiM parameters of PV modules from experimental data on power-voltage characteristics was presented in [31]. In the literature [32; 33; 34; 35; 36], we can observe more hybrid solar parameter extraction algorithms. The characteristics of the InGaP/InGaAs/Ge TJS PV panel were extracted using the moth search [37], water cycle [38], and heap optimizer [39] approaches, taking into account the Triple-Junction (TJS) PV panel. The performances of a TJSC-based PV module under various temperature and irradiation conditions were evaluated and verified in [37; 38; 39] and compared to several alternative optimizing techniques. Various metaheuristic and analytical approaches used for solar parameter extraction are listed in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline
**Reference** & **Metaheuristic Approach** & **Analytical Approach** & **Models** \\ \hline
[4] & Improved Math-Flame & — & SDiM, DDiM, PV module \\ \hline
[6] & Subtraction average-based & — & SDiM, DDiM \\  & algorithm (SABA) & — & SDiM, DDiM \\ \hline
[7] & Enhanced generalized normal & & \\  & distribution optimization with & — & SDiM, DDiM, PV module \\  & neighborhood search & & \\ \hline
[8] & Improved gaining sharing & — & SDiM, DDiM, PV module \\  & knowledge algorithm & — & SDiM, DDiM, PV module \\ \hline
[9] & Modified simplified swarm & — & SDiM, DDiM \\  & optimization & — & SDiM, DDiM \\ \hline
[10] & & Lagrange multiplier method & SDiM, DDiM \\ \hline
[12] & & Analytical and quasi-explicit & SDiM \\  & method & & \\ \hline
[13] & Drone squadron & & SDiM, DDiM \\ \hline
[14] & & Lambert W-functions & SDiM, DDiM \\ \hline
[15] & GTO & — & SDiM, DDiM \\ \hline
[16] & DOA & — & SDiM, DDiM \\ \hline
[17] & AHBO & — & SDiM, DDiM \\ \hline
[18] & Gradient-based optimization & — & SDiM, DDiM, PV module \\ \hline
[19; 20] & Enhanced DE & — & SDiM, DDiM, PV module \\ \hline
[21] & DE combined with TLBO & — & SDiM, DDiM, PV module \\ \hline
[22] & DE with a reversible learning & — & SDiM, DDiM, PV module \\  & process & — & SDiM, DDiM, PV module \\ \hline
[23] & Enhanced prairie dog & — & SDiM, DDiM, PV module \\ \hline
[24] & Rao-2 and Rao-3 & — & SDiM, DDiM, Three diode model (TDiM) \\ \hline
[25] & Backtracking search technique & — & SDiM, DDiM, PV module \\ \hline
[26] & Nelder mead salp swarm & — & SDiM, DDiM, TDiM \\ \hline
[27] & Imperialist competitive & — & SDiM, DDiM \\ \hline \end{tabular}
\end{table} 
Table 1: An overview of the metaheuristic and analytical approaches used in the literature. Several strategies have been suggested to address the problem of acquiring the parameters of the PV model.