An optimization code called Optima has been developed at the International Centre for Numerical Methods in Engineering (CIMNE). This report validates two reputably robust Evolutionary Algorithms available in Optima and employs them on aerodynamic shape optimization problems. The two schemes, Differential Evolution Scheme 1 (DE1) and Evolution Strategy coupled with Covariance Matrix Adaptation (ES-CMA), were tested and verified on three standard parametric optimization objective functions through comparison against existing results. Analysis of the test data allowed trends to be established and from this, settings to enhance the performance of the algorithms were proposed and substantiated. The algorithms and their suggested settings were applied on an inverse and a direct constrained shape optimization problem involving NACA four digit airfoils. The inverse task involves the recovery of an airfoil profile through its pressure distribution combination of lift and drag coefficients. Simulation of the airfoil in turbulent flow was done using a Computational Fluid Dynamics (CFD) setup. Finally, the results are presented and the ES-CMA method, using the setting CMA-B proposed in this paper, was found to be most robust. Suggestions for improvements and further work in the optimization configuration and the problem simulation are also proposed.