Given observational data from systems of interacting galaxies, we seek to determine the values of various dynamical parameters through the optimization of numerical models via genetic algorithms. However, fitting these models can be quite difficult. The core challenges include 1) developing an objective fitness function for quantifying the similarity between model and target images and 2) understanding the inherent symmetries of the dynamical system which promote morphological degeneracies and impede optimization. In this presentation, we show how naive implementations of fitness functions can yield unintuitive results. We then propose a novel fitness function which was developed by utilizing data from the Galaxy Zoo: Mergers project. These human-scored models were used to validate our fitness functions and led to the adoption of a tidal distortion term which dramatically improved results. We also give a characterization of various geometric and dynamical symmetries inherent within the system and show how the knowledge of these symmetries can be used to reduce the volume of the parameter search space when performing optimization.