This paper presents the discussion and comparison of the different optimization strategies and their associated evolutionary tools for the multi-point design optimization of a multi-element airfoil system during landing and taking off operations of an aircraft. New optimization algorithms based on binary coded genetic algorithms (GAs) coupling with Game Theory, such as Nash GAs (N-GAs) and Stackelberg GAs (S-GAs), are introduced and implemented to optimize the position of slat and flap of a high lift system operating simultaneous at taking off and landing conditions. A cheap nondifferentiable CFD solver coupling an inviscid panel approach with laminar or turbulent boundary layers and wake is used to solve the flow field around this system. Numerical results are compared with different strategies which demonstrates the flexible capability and robustness of such algorithms for multi-objective and multidisciplinary optimization problems in aerodynamics.