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The involvement of heterogeneous solid/liquid reactions in growing colloidal nanoparticles makes it challenging to quantitatively understand the fundamental steps that determine nanoparticles' growth kinetics. A global optimization protocol relying on simulated annealing fitting and the LSW growth model is developed to analyze the evolution data of colloidal silver nanoparticles synthesized from a microwave-assisted polyol reduction reaction. Fitting all data points of the entire growth process determines with high fidelity the diffusion coefficient of precursor species and the heterogeneous reduction reaction rate parameters on growing silver nanoparticles, which represent the principal functions to determine the growth kinetics of colloidal nanoparticles. The availability of quantitative results is critical to understanding the fundamentals of heterogeneous solid/liquid reactions, such as identifying reactive species and reaction activation energy barriers.