Current transport phenomena based welding models are designed to calculate temperature and velocity fields and other weld attributes such as the weld geometry. However, in many instances, the desired attribute such as the geometry is known and the correct set of welding parameters need to be determined. The mismatch between the practical need and the capability of the current models has restricted the use of these powerful models. This paper shows that by combining a numerical thermo-fluid model with an appropriate genetic algorithm based optimization scheme, many possible sets of welding variables that are capable of producing a given weld geometry can be determined. A three-dimensional numerical heat transfer and fluid flow model for the gas metal arc (GMA) welding of fillet joints is combined with a genetic algorithm (GA) based optimization scheme to obtain a window of welding variables. To reduce the computation time, the model is parallelized to run on multiple processors simultaneously. The approach outlined in this paper completely restructures numerical heat transfer and fluid flow calculations and empowers users to determine a window of input variables consisting of several sets of welding variables all of which would lead to a target weld geometry.