Identifying parameters of photovoltaic (PV) models based on measured current–voltage (IV) characteristic curves is critical for simulating, evaluating, and controlling PV systems. IV characteristics of the latest-generation solar cells (SCs) often display an S-shaped deformation. In this paper, we explore the potential of meta-heuristic algorithms to address the parameter estimation problems associated with PV cells that exhibit S-shaped IV characteristics. This estimation is performed within the framework of the opposed two-diode model. We implemented a total of 14 algorithms from various classes to extract the SC parameters from synthetic IV curves, which were generated using a range of parameter values. The results were compared by using nonparametric statistical methods. These methods include the Wilcoxon signed-rank test for pairwise comparisons, and the Friedman, Friedman Aligned, and Quade tests for multiple comparisons. Comprehensive results and analyses show that the STLBO (Simplified teaching–learning based optimization algorithm) and ADELI (Adaptive differential evolution with the Lagrange interpolation argument) algorithms demonstrate highly competitive performance in terms of accuracy and reliability. This paper underscores the efficacy of advanced meta-heuristic algorithms in solving complex non-linear optimization problems in the domain of photovoltaic research, particularly concerning the unique challenges posed by S-shaped IV characteristics of new-generation solar cells.