Gradient-free trust-region-based adaptive response surface method for expensive aircraft optimization

This paper presents a novel gradient-free trust region assisted adaptive response surface method for aircraft optimization problems with expensive functions. A gradient-free trust region sampling space approach is developed for design space reduction and sequential sampling, and response surface metamodel refitting enables the trust region assisted adaptive response surface method to possess higher optimization efficiency and better global convergence capability. Besides, an election sequential Latin hypercube sampling method is developed to improve the space-filling property and feasibility of the sequential samples. Moreover, the augmented Lagrangian method is employed to handle expensive constraints. The trust region assisted adaptive response surface method outperforms several adaptive response surface metamodel variants in the comparative study on a number of benchmark problems. Additionally, compared with several other well-known metamodel-based global optimization algorithms, the proposed algorithm also shows favorable performance in global convergence, efficiency, and robustness. Next, the trust region assisted adaptive response surface method is successfully applied to solve an airfoil aerodynamic optimization problem based on computational fluid dynamics simulation to demonstrate its effectiveness for realworld engineering problems. Finally, limitations of the proposed method and future work are discussed.