Progressive Sampling for Response Surface Fitting Using Method of Dividing Rectangles (DIRECT)
Wesley K. Roberts, Satchi Venkataraman · 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference · 2007
This paper demonstrates the use of a space exploring global optimization algorithm, the method of DIviding RECTangles (DIRECT), for progressive sampling in response surface fitting using moving least squares (MLS). The DIRECT algorithm for global optimization searches for the global optimization by subdividing the design space; thus, selecting boxes to subdivide if they have a good objective function value (potential optimum) or if the current size of the box is large (the area of the design space is relatively unexplored). A modification of this method for progressive sampling uses the estimated value of prediction error, and the box size to identify sampling points for response surface fitting using a MLS regression. The method is demonstrated for approximating a two-dimensional analytical multimodal function. The accuracy and convergence is compared with other sampling schemes and design of experiments.