In this paper, optimal airfoil shapes are found through manipulation of the velocity distribution by a genetic algorithm. The airfoil geometries are generated by an inverse method from velocity distribution parameters, and a viscous-flow analysis code is used to determine proper fitness values for candidate airfoils based on preset performance criteria. The method is compared with the more traditional approach of direct geometry manipulation for a simple single-objective aerodynamic optimization problem for a symmetric airfoil. The inverse and direct approaches are compared using a simple genetic algorithm and a hybrid genetic algorithm, where the hybrid method is formed by combining a simple genetic algorithm and a specialized local search method. Finally, the method is used to design a cambered airfoil that outperforms the existing state-of-the-art. Results indicate that using the design variables defining the velocity distribution in the inverse method has great potential for increasing the efficiency of airfoil shape optimization using genetic algorithms.