Comparison of Gradient and Response Surface Based Optimization Frameworks Using Adjoint Method

This paper deals with aerodynamic shape optimization using an high fidelity solver. Due to the computational cost and restitution time needed to solve the RANS equations, this type of optimization framework must improve the solution using very few objective function evaluations despite the high number of design variables. The choice of the optimizer is thus largely based on its speed of convergence. The quickest optimization algorithms use gradient information to converge along a descent path departing from the baseline shape to a local optimum. Within the past few decades, numerous design problems were successfully solved using this method. In our framework, the reference algorithm uses a quasi-Newton gradient method and an adjoint method to inexpensively compute the sensitivities of the functions with respect to shape variables. As usual aerodynamic functions show numerous local optima when varying shape, a more global optimizer can be beneficial at the cost of more function evaluations. More recently, the use of expensive global optimizers became possible by implementing response surfaces between optimizer and CFD code. In this way, a Kriging based optimizer is described. This optimizer proceeds in iteratively refining at up to three points per iteration by using a balancing between function minimization and error minimization. It is compared to the reference algorithm on two drag minimization problems. The test cases are 2D and 3D lifting bodies parameterized with six to more than forty design variables driving deformation of meshes with Hicks-Henne bumps. The new optimizer effectively proves to converge to lower function values without prohibitively increasing the cost. However, response surfaces are known to become inefficient when dimension increases. In order to efficiently apply this response surface based optimizer on such problems, a Cokriging method is used to interpolate gradient information at sample locations.