Comparative study of GEK (gradient-enhanced kriging) and Kriging when applied to design optimization

In many engineering optimization design problems, the objective function (s) as well as the constraint function (s) are really computationally expensive. To reduce the computational time and shorten the design process, surrogate models are often used. In recent years, to further improve the design efficiency, a variety of new surrogate models are developed as extensions from the traditional models and verified to have higher efficiency for prediction, such as the variable-fidelity models and gradient-enhanced models. To investigate the design optimization efficiency when these new surrogate models are used, a universal surrogate-based optimization framework, which combines the surrogate models, multi sample point infill criteria, and multi-type traditional optimization algorithms, is developed first. Then, several typical analytical optimization problems are employed to compare the optimization efficiency when the widely used Kriging and a newly developed GEK are used respectively. The results and their analysis show preliminarily that, for most cases, GEK get better optimal solution with the same computational expense. Finally, an engineering problem, the airfoil inverse design is introduced for comparison; the gradients of the objective functions used to construct the GEK are obtained by the efficient adjoint method. The results and their analysis also show preliminarily that, when using the GEK, not only the efficiency, but also the optimal solution can be improved as compared with the Kriging model.