## 1 Introduction
The user's text does not contain any information to rewrite. The equations of the suggested PV models, derived by analytical methods, have been identified as the primary cause for the low precision and efficiency observed in the extraction of PV parameters [16]. Several research publications have employed numerical methods to extract PV parameters [17]. By utilizing iterative algorithms, these strategies seek to achieve a closer alignment  
Figure 2: The DDM’s equivalent circuit. between the simulated and experimental I-V characteristic curves, resulting in more precise results. Researchers often utilize the Newton-Raphson approach as a prevalent process for iteratively solving the exponential model [17]. Similarly, the Levenberg-Marquardt method is utilized for solving the I-V curve [8; 17]. Additionally, the Lambert W function can be used to manage the explicit relationship between current and voltage. This argument's fundamental premise asserts that a suboptimal initial condition may result in convergence and inaccuracy. Initial values are assumed for diode's forward current \(I_{s}\), reverse saturation current \(I_{sh}\), and ideality factor \(n\). Upon successful implementation of the iterative method, the photo-generated current, \(I_{ph}\), and the current flowing through the series resistor, \(I_{s}\), are determined. The efficacy of these numerical algorithms is notable in identifying local optima, although their ability to detect global optima presents a significant challenge. However, these strategies necessitate more computational resources and often yield suboptimal parameter values. This phenomenon occurs due to the sensitivity of these methods to the simulated algorithm, as they heavily depend on the original prediction. The phenomenon of the local optimum poses a significant challenge for solution-seeking processes. The utilization of these strategies is limited to the resolution of differential and convex models [5; 18]. Several authors have found that the previously described procedures for deriving PV parameters from equivalent circuit models are not the most effective. The meta-heuristic approaches have demonstrated superior performance in the extraction and evaluation of PV parameters, especially when compared to analytical and numerical approaches that rely on strict requirements, assumptions, or initial estimates. In recent years, a variety of meta-heuristic techniques inspired by natural phenomena have been used to determine PV characteristics. The aforementioned algorithms demonstrated greater precision and efficacy than previous methods. For the preponderance of meta-heuristic procedures, the issue of computational time remains a challenge. In addition, the outcome is uncertain due to the probabilistic nature of these approaches. Various optimization strategies have been employed to extract parameters from PV models, including teaching-earning-based optimization, cuckoo search, artificial bee colonies, and particle swarm optimization [5]. Utilizing meta-heuristic techniques that seek to minimize the difference between the deduced current derived from experimental data and simulation data can effectively determine PV parameters. The aforementioned methodologies show advantages in the acquisition and analysis of PV properties. However, there is room for enhancement in terms of computational time efficiency. Differential Evolution (DE) is a highly regarded evolutionary technique that has been extensively employed to solve numerous optimization problems. The DE technique has been subject to several modifications in order to effectively tackle the challenges associated with parameter extraction in the PV model. In the study conducted in [19], a penalty-based DE technique was introduced. This method aims to identify feasible solutions while simultaneously enhancing the overall quality of the solutions. This strategy has been shown to be effective in terms of both precision and computational efficiency. [PERSON].