Extraction of the photovoltaic (PV) model parameters is critical for forecasting these systems’ energy output. Numerous research have reviewed and presented approaches for figuring out the PV models parameter optimization problem in the literature. However, few studies have been undertaken to construct the objective function, or no review papers have been published on the applied methodologies for solving the equations of nonlinear, multi-variable, and complicated PV models based on the datasheet information or actual experimental data. Therefore, this study seeks to first explore the acquired approaches to solve the equations of PV models. Then, utilizing actual measured laboratory data collected under a variety of environmental circumstances, a hybrid approach for efficiently determining unknown the parameters of the single, double, and three diodes PV model has been developed. The proposed guaranteed convergence arithmetic optimization algorithm based on efficient modified third order Newton Raphson (GCAOAEmNR) method highlights important contributions to the literature in terms of methodology (explorer-exploiter phases) and objective function design. The experimental findings exhibit that the GCAOAEmNR minimizes the error to zero under diverse statistical criteria and environmental conditions. Moreover, the GCAOAEmNR beats all well-published approaches in the literature in terms of accuracy, stability, and convergence rate while requiring a reasonable amount of processing time.