Gradient-enhanced response surface building

Response surfaces are frequently used as approximations in sequential optimization techniques, multidisciplinary optimization and reliability oriented analysis. In this paper several techniques will be exploited to construct response surfaces using both function values and corresponding derivatives, i.e. gradient-enhanced response surfaces (GERS). The way response surfaces are constructed on both function values and derivatives is not well crystallized. In particular how information on function values and derivatives must be weighted against each other is a point of discussion. To a certain extent, the best method seems to depend on the purpose of the response surface. The technique that is studied in this paper treats the response surface building as a multi-objective optimization problem. This enables a well-controlled balance between accuracy of the approximate gradients as well as the approximate function values. The method is studied for a series of test problems and compared to other techniques. This paper addresses in particularly the effect of the plan of experiment on accuracy.