Over the past two decades, helioseismology has revolutionized our understanding of the interior structure and dynamics of the Sun. Asteroseismology will soon place this knowledge into a broader context by providing structural data for hundreds of Sun-like stars. Solar-like oscillations have already been detected from the ground in several stars, and NASA's Kepler mission is poised to unleash a flood of stellar pulsation data. Deriving reliable asteroseismic information from these observations demands a significant improvement in our analysis methods. In this paper, we report the initial results of our efforts to develop an objective stellar model-fitting pipeline for asteroseismic data. The cornerstone of our automated approach is an optimization method using a parallel genetic algorithm. We describe the details of the pipeline and we present the initial application to Sun-as-a-star data, yielding an optimal model that accurately reproduces the known solar properties.