Single/two-objective aerodynamic shape optimization by a Stackelberg/adjoint method

In this article, the Stackelberg game strategy is coupled with the adjoint method and applied in single-objective and two-objective aerodynamic shape optimizations. In the proposed method, two types of player (leader and follower) are involved, and each of these players is responsible for the optimization of one objective function by adjusting a subset of design variables. A Stackelberg equilibrium is reached when the leader cannot improve his/her objective function further. Note that the success of the proposed method is highly dependent on the choice of a few influential factors, including the maximal number of iterations for each player, the splitting and mapping schemes of design variables, and the allocation strategies of objective functions to different players. Therefore, the impacts of these factors are firstly assessed by a two-objective optimization case of the NACA0012 airfoil, and some useful inferences are produced for the choice of these factors. After that, single-objective and two-objective aerodynamic optimizations of the RAE2822 airfoil and the ONERA M6 wing are conducted to verify the usefulness of these inferences, and to validate the efficiency and effectiveness of the proposed method in optimization problems with a complex numerical model or a large number of design variables.