## 1 Introduction
Since the photovoltaic cell has triple non-linearity in current-voltage, power-voltage and in intrinsic parameters, deterministic methods cannot extract parameters accurately based on current, voltage and current derivatives with respect to the voltage at short circuit current, maximum power and open circuit voltage. The derivation imposes several model \begin{table}
\begin{tabular}{c c} \hline \hline
**Optimization Method** & **Reference** \\ \hline Least squares and Newton-Raphson method & [29] \\ Iterative curve fitting & [30] \\ Lambert W-functions & [20; 31; 32; 33; 34; 35] \\ Integral-based linear least square identification method & [36; 37] \\ Linear interpolation/extrapolation & [38] \\ Chebyshev polynomials & [39] \\ Taylor’s series expansion & [40] \\ Padé approximants & [41] \\ Symbolic function & [42] \\ Analytical mathematical method & [43; 44; 45] \\ Simple methods based on measured points & [46] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A list of analytical and numerical methods employed in the literature. restrictions such as convexity, continuity and differentiability conditions; moreover, the approximations also reduce accuracy. Due to their great potential in modern global optimization resolution for nonlinear and complex systems, the use of metaheuristic bioinspired optimization algorithms to carry out minimizing procedures has received considerable attention. Metaheuristic methods are stochastic methods inspired by various natural phenomenon, as listed in Table 2. They have been proven to be a promising alternative to deterministic methods applied to the parameter identification of solar/photovoltaic models. However, the cited algorithms are usually trapped at local optima and they have large error values [62]. In fact, the performance of these algorithms highly depends on the settings of specific parameters, such as, for instance, the mutation probability, crossover probability, and the selection operator in the genetic algorithm, as well as the inertia weight, and social and cognitive parameters in particle swarm optimization. Therefore, researchers are still searching for powerful algorithms capable of predicting the optimal parameters of different technology under various conditions with less errors. Metaheuristic bioinspired algorithms have been suggested for parameter extraction and have become an important part of modern optimization. Most metaheuristic algorithms are based on natural or artificial swarm intelligence. Particle swarm optimization is a good example, it mimics the swarming behavior of bees and birds [62]. Recently, a new metaheuristic search algorithm called the firefly algorithm (FA) has been proposed and developed by [PERSON] [63]. The FA is a nature-inspired stochastic optimization algorithm based on the flashing patterns and behavior of swarming fireflies [64]. The FA has become an increasingly valuable tool of swarm intelligence that has been applied in almost all areas of optimization, as well as in engineering practice [65]. It uses a kind of randomization by searching for set solutions, inspired by the flashing lights of fireflies in nature. This algorithm differs from many swarm intelligence techniques [65] for these two features:  
* the first is the so-called local attraction, since the light intensity decreases with distance (the attractions of fireflies can be local or global and depend on the absorbing coefficient);
* the second is related to the subdivision of fireflies and their regrouping into subgroups because a neighboring attraction is stronger than a long-distance attraction, and each subgroup will swarm around a local mode, making the firefly algorithm suitable for multimodal global optimization problems [66]. In [67] the authors provide a detailed background and analysis of the firefly algorithm and test it in a wide range of problems to solve multi-objective dispatch problems. In this paper, the authors propose a comparison among bioinspired algorithms for the prediction of solar cell and photovoltaic module parameters.