Inversion of the size distribution of fire smoke particles is an ill-conditioning problem, and it tends to lose global optimal solutions on account of being trapped into local minimum. Under spherical model, the inversion of monodisperse systems and lognormal distribution systems have been performed by simulated annealing algorithm which has a powerful ability in global searching. Before that, the interference of random noise on the angular distribution of Mueller matrixs in the light scattering of fire smoke particles has been analyzed in detail. Errors of inversional results are less than 0.3% when signal mixed with 3% stochastic noise. Then, the optical equivalent radius of smoke particle clusters with different fractal dimensions could be calculated when the program is used to fit the scattering light of the clusters. Furthermore, it has an approximatively linear relationship with radius of gyration of the clusters.