Solving Stackelberg equilibrium for multi objective aerodynamic shape optimization

Affiliation of Author(s):航空学院

Journal:Appl. Math. Model.

Abstract:Numerical methods coupling evolutionary algorithms and/or adjoint methods with a two level hierarchical game between leader and follower, called the Stackelberg game, are presented for solving multi objective aerodynamic shape optimization problems in this paper, in which both leader and follower can be a Nash sub-game with multiple players. The decision making process of leader and follower is hierarchically and non-cooperatively in numerical implementation, more accurately they are alternate. The leader enounces a decision (a Nash sub-game solution), and the follower takes into account this decision and solves the other Nash sub-game optimization problem. The elitist information that follower passes to leader is the response function of follower to leader's decision, instead of its response only. Then, the leader optimizes his objective based on elitist information accepted from follower depending on his behavior. The approximate response function is obtained by recalculating the follower's Nash sub-game with a small perturbation on leader's decision. Finally, a multi-objective shape optimization problem of hypersonic air-breathing vehicle is solved by using the optimization algorithm presented in this paper, and the converged result of the algorithm is proved to be a Stackelberg equilibrium. © 2019 Elsevier Inc.

ISSN No.:0307-904X

Translation or Not:no

Date of Publication:2019-08-01

Correspondence Author:Tang Zhili

Date of Publication:2019-08-01