This paper presents a new methodology to extract the unknown parameters of a single-diode photovoltaic (PV) cell model. The first contribution of this paper is the development and implementation of a new version of the wind driven optimization (WDO) algorithm, called an adaptive wind driven optimization (AWDO) algorithm. The second contribution is the identification of a generalization model to generalize the extracted parameters of a single-diode PV cell model. That provides the ability of the proposed methodology to work with any of I-V characteristic curve of PV cells and at any weather condition. To validate the proposed methodology, it has been tested for 1307 I-V characteristic curves of a PV module at different weather conditions on a 15-minute basis. Additionally, its accuracy and computational efficiency are verified and compared with five well-known existing extraction methods by both simulation and outdoor measurements. The results show that the AWDO algorithm can provide the extracted five parameters with an acceptable range of accuracy and faster than the benchmark's models. As a result, the proposed methodology (AWDO based on Chenlo's model) can be confidently recommended as a reliable, feasible, valuable and fast optimization algorithm for parameter extraction of a single-diode PV cell model.