In this paper, two hybrid estimation approaches, hybrid genetic algorithm (TR-GA) and hybrid particle swarm optimization (TR-PSO), are used to estimate single-diode model InGaN/GaN solar cell parameters from J?V experimental data under AM0 illumination. These parameters are photocurrent density ($J_{ph}$), reverse saturation current density ($J_{s}$), ideality factor ($A$), series resistance ($R_{s}$), and shunt resistance ($R_{sh}$). The trust region (TR) method used in both approaches provides the initial conditions and helps to avoid the problem of premature convergence (due to local minimum). Simulation results based on the minimization of the mean square error between experimental and theoretical J-V characteristics show that both applied methods have a similar degree of efficiency in terms of precision, whereas the TR-PSO method is more efficient in terms of convergence speed. The effect of different extracted parameters on the characteristics J-V and P-V is evaluated in a simulation study of an identified model.