The parameter assessment of solar cells and photovoltaic (PV) modules is a challenging task due to the non-linearity behavior of the current–voltage (I–V) characteristic curve. This paper presents two hybrid nature-inspired algorithms for estimating the unknown parameters of the Single-Diode Model (SDM), and Double-Diode Model (DDM). These algorithms are based on borrowed exploration and exploitation schemes from three well-known optimization algorithms: Whale optimization algorithm (WOA), Marine Predators Algorithm (MPA), and Generalized Normal Distribution Optimization (GNDO) algorithm. The first proposed algorithm is called Marine-Whale-Generalized (MWG) algorithm. In addition, MWG is effectively integrated with novel exploration and exploitation schemes to further its exploration and exploitation operators in a new variant known as (MWGG). A solar cell from RTC France and five commercial PV module models, including Photowatt-PWP201 (PWP), Ultra 85-P (Ultra), and STM6-40/36 (STM), are being used to test the efficacy and efficiency of the proposed algorithms. The experimental findings proved that MWGG is more accurate and faster at convergent results compared to other comparators.