Frequently in the physical sciences experimental data are analyzed to determine model parameters using techniques known as parameter estimation. Eliminating the effects of noise from experimental data often involves Tikhonov or Maximum-Entropy regularization. These methods introduce a bias which smoothes the solution. In the problems considered here, the exact answer is sharp, containing a sparse set of parameters. Therefore, it is desirable to find the simplest set of model parameters for the data with an equivalent goodness-of-fit. This paper explains how to bias the solution towards a parsimonious model with a careful application of Genetic Algorithms. A method of representation, initialization and mutation is introduced to efficiently find this model. The results are compared with results from two other methods on simulated data with known content. Our method is shown to be the only one to achieve the desired results. Analysis of Analytical Ultracentrifugation sedimentation velocity experimental data is the primary example application.