## 1 Introduction
Nevertheless, precisely and dependably establishing the values of these factors continues to be a substantial difficulty. The \"No-Free-Lunch\" principle hypothesis [7; 40; 41] states that no algorithm can solve optimization problems optimally. This hypothesis provides a possible explanation for the question at hand. This phenomenon occurs because even while an approach may show remarkable effectiveness in solving a specific problem, there is no guarantee that it will achieve comparable levels of success in addressing other challenges. Hence, it is crucial to persist in carrying out studies in order to ascertain a potent meta-heuristic strategy. Many artistic works are influenced by the concept of \"No-Free-Lunch,\" which also allows for the modification of current algorithms to solve new issues. Inspired by the principles behind crystal structure development from adding the basis to the lattice points, [PERSON] et al. [42] proposed a novel metaheuristic optimization approach named CrSA. The algorithm's unique quality lies in its parameter-free design, enabling the adjustment of exploration and exploitation stages within the primary loop. Moreover, its position updating process for candidate solutions is segmented into four distinct phases, achieving exceptional results by effectively catering to both local and global search requirements across the entirety of the search space. In this work, we use the CrSA to accurately model Mono PERC solar PV modules. The proposed algorithm is a succinct and parameter-free method that does not require the determination of any inherent parameters during the optimization phase. It operates by merging the basis and lattice point to generate a crystal structure. The proposed algorithm is adopted to minimize the sum of the squares of the errors at the maximum power point, as well as at the short circuit and open circuit points. Several runs are carried out to examine the \(V\)-\(I\) characteristics of the PV panels under consideration and the nature of the derived parameters. The parameters generated by the proposed technique offer the lowest error over several executions, indicating that it should be implemented in the present scenario. The main aims of this study are:  
1. This study aims to introduce a new nature-inspired intelligence OA named CrSA, which will be used to estimate the parameters of Mono PERC solar PV modules. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **Metaheuristic Approach** & **Analytical Approach** & **Models** \\ \hline
[28; 29] & JAYA method & \(\cdot\cdot\cdot\cdot\) & SDiM, DDiM \\ \hline
[30] & Orthogonal learning strategy-based grey wolf method & \(\cdot\cdot\cdot\cdot\) & SDiM, DDiM, PV module \\ \hline
[32] & Hybrid grey wolf—sine cosine algorithm & \(\cdot\cdot\cdot\) & SDiM, DDiM \\ \hline
[33] & Hybrid sparrow search—exponential distribution based DE & \(\cdot\cdot\cdot\) & SDiM, DDiM \\ \hline
[34] & Hybrid chimp—sine cosine algorithm & \(\cdot\cdot\cdot\) & SDiM, DDiM \\ \hline
[35] & Chaotic war strategy & \(\cdot\cdot\cdot\) & TDiM \\ \hline
[36] & Hybrid marine predators—success history based DE & \(\cdot\cdot\cdot\) & SDiM, DDiM \\ \hline
[37] & Moth search & \(\cdot\cdot\cdot\) & TDiM \\ \hline
[38] & Water cycle & \(\cdot\cdot\cdot\) & TDiM \\ \hline
[39] & Heap optimizer & \(\cdot\cdot\cdot\) & TDiM \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._2. The mathematical modeling of the SDiM and DDiM of the Mono PERC solar PV modules has been analyzed. 3. The error between practical values and simulation results has been examined for high accuracy at short circuit, open circuit, and maximum power points for the PV modules under consideration. 4. The proposed method has been compared with the recent OAs in the literature by using convergence analysis. The structure of the paper is as follows: Section 2 provides an overview of the suggested CrSA. Section 3 presents the mathematical modeling of the SDiM and DDiM.