Comparison of Gradient-Based and Gradient-Enhanced Response-Surface-Based Optimizers

摘要

This paper deals with aerodynamic shape optimization using a high-fidelity solver. Because of the computationalncost needed to solve the Reynolds-averaged Navier–Stokes equations, the performance of the shape must benimproved using very few objective function evaluations, despite the high number of design variables. In ournframework, the reference algorithm is a quasi-Newton gradient optimizer. An adjoint method inexpensivelyncomputes the sensitivities of the functions, with respect to design variables, to build the gradient of the objectivenfunction. As usual, aerodynamic functions show numerous local optima when the shape varies, and a more globalnoptimizer is expected to be beneficial. Consequently, a kriging-based optimizer is set up and described. It uses annoriginal sampling refinement process that adds up to three points per iteration by using a balancing between functionnminimization and error minimization. To efficiently apply this algorithm to high-dimensional problems, the samensampling process is reused to form a cokriging (gradient-enhanced model) based optimizer. A comparative study isnthen described on two drag-minimization problems depending on 6 and 45 design variables. This study wasnconducted using an original set of performance criteria, characterizing the strength and weakness of each optimizernin terms of improvement, cost, exploration, and exploitation.