The design of accurate in silico cancer models capable of quantitatively predicting tumor growth is an important goal in cancer research today. Mesoscopic models have shown great promise in this scenario; however, their use is often inhibited by the difficulty in correctly assigning parameter values. In this paper, enabled by an extremely computationally efficient mesoscopic model, we propose a generic algorithms' (GAs) approach to the exploration of parameter space. Analysis of the results suggest that this novel application of GAs to tumor growth models both facilitates the attribution of parameter values to the fitting of experimental data and, more importantly, lends insight to the role played by the different parameters in regulating the tumor model growth.