Comparison of Gradient Based and Gradient Enhanced Response Surface Based Optimizers

This paper deals with aerodynamic shape optimization using a high fidelity solver. Due to the computational cost needed to solve the Reynolds-averaged Navier-Stokes equations, the performance of the shape must be improved using very few objective function evaluations despite the high number of design variables. In our framework, the reference algorithm is a quasi-Newton gradient optimizer. An adjoint method inexpensively computes the sensitivities of the functions with respect to design variables to build the gradient of the objective function. As usual aerodynamic functions show numerous local optima when the shape varies, a more global optimizer is expected to be beneficial. Consequently, a Kriging based optimizer is set up and described. It uses an original sampling refinement process which adds up to three points per iteration by using a balancing between function minimization and error minimization. In order to efficiently apply this algorithm to high-dimensional problems, the same sampling process is reused to form a Cokriging (gradient-enhanced model) based optimizer. A comparative study is then described on two drag minimization problems depending on six and forty-five design variables. This study was conducted using an original set of performance criteria characterizing the strength and weakness of each optimizer in terms of improvement, cost, exploration and exploitation.