This paper investigates the High Lift System (HLS) application of complex aerodynamic design problem using Genetic Algorithms (GAs) coupled to Game strategies. Two types of optimization methods are used; the first method is a standard GA based on Pareto dominance and the second method hybridises GA with a wellknown Nash Game strategies named Hybrid-GA. These optimization techniques are coupled to a pre/post processor GiD providing unstructured meshes during the optimisation procedure and a transonic analysis software PUMI. The computational efficiency and quality design obtained by GA and Hybrid-GA are compared. The numerical results for the multi-objective HLS design optimisation clearly shows the benefits of hybridising a GA with the Nash game and makes promising the above methodology for solving other more complex multi-physics optimisation problems in Aeronautics