Gravitational n-body models can be used to simulate the dynamical evolution of colliding galaxies. Given observational data in the form of images of the galaxies, we seek to estimate the true values of various dynamical parameters through the careful application of optimization methods. However, optimizing n-body models can be quite difficult for a number of reasons. First, full n-body codes are computationally expensive and the application of any optimization method requires numerous simulations. Second, due to the dimensionality and non-linearity of the system, the parameter space that must be explored is very complex. To address these challenges, we developed multi-factor fitness functions which are able to accurately perform morphological comparisons between model and target images. Using these functions, we apply a novel adaptive kernel mixing strategy which can be applied in both stochastic optimization and Markov chain Monte Carlo contexts. Using simulated models with known parameters as a surrogate for actual observational targets, we test our fitness and optimization techniques for robustness and convergence. In the long-term, we are interested in understanding the uncertainties and degeneracies inherent in this dynamical system. This first poster focuses primarily on the theoretical and mathematical aspects of our research, while part II compares our models with observed interacting systems.