In modern day Formula One, aerodynamics has become the key performance differentiator. The two tools used for the aerodynamic design are the wind tunnel and Computational Fluid Dynamics (CFD). For a rapid development rate, it is crucial to use these tools as effciently as possible. The goal of this thesis is to improve the optimization methodology at the CFD department of Lotus Renault GP (LRGP). This is a challenge because CFD simulations are expensive; they require a relatively large amount of wall clock time to complete and in addition there is a restriction on the number of runs that can be carried out. This restriction was agreed upon between the Formula One teams to reduce the cost of the sport. The pre-existing optimization methodology makes extensive use of the design of experiments (DOE) approach, in which the design space is filled with a set of points that are run in CFD. The results are then analyzed and the best design is chosen, possibly followed by tweaking it manually to improve the performance. Two approaches are investigated to improve upon this methodology and two CFD test cases are set up to assess them. The idea of the first approach is to make use of local optimization algorithms. Gradient-free and gradient-based algorithms are investigated. SQP (Sequential Quadratic Programming) methods are found to be the most efficient solver.