The purpose of this work is to develop and evaluate an inverse optimization algorithm which designs two-dimensional fan blade shapes. Given a prescribed pressure distribution and inlet and outlet flow angles, this design optimization technique finds the optimal fan blade shape, stagger angle, and pitch/chord ratio. The algorithm is coded into a completely self-contained C++ program. Its three main components are: a surface vorticity panel method flow solver, a Bezier curve surface definition routine, and an optimization method. Three different optimizers are tested and compared. A relatively new genetic algorithm, Differential Evolution, is determined to be the most effective. To demonstrate the abilities of the aerodynamic shape optimization algorithm, several fan blades are designed to exhibit a Liebeck pressure distribution. For each design, the optimal fan blade spacing is also found, verifying theoretically a claim that until now has been supported experimentally and with simple modelling.