Abstract: This paper approaches the question of multi-objective optimization for optimum shape design in aerodynamics via constrained control theory. The employed optimizer is based on control theory. A scalar adjoint variable to implement the constraints is introduced. Furthermore, the above method is combined with a formulation derived from game theory to treat multi-point airfoil optimization. Airfoil shapes are optimized according to various aerodynamics criteria (in conflict). In the symmetric Nash Game, each "player" is responsible for one criterion. Several kinds of equilibrium provide a solution to the multi-point optimization. Several kinds of airfoil splittings and design cases are shown for virtual and real game strategies in aerodynamic design,and successful design results confirm the validity and efficiency of the present design method.

Key words: game theory, multi-objective optimization, distributed optimization, optimum control theory, constrained optimization