This paper addresses the difficulty of the previously developed Adaptive Response Surface Method (ARSM) for high-dimensional design problems. ARSM was developed to search for the global design optimum for computation-intensive design problems. This method utilizes Central Composite Design (CCD), which results in an exponentially increasing number of required design experiments. In addition, ARSM generates a complete new set of CCD points in a gradually reduced design space. These two factors greatly undermine the efficiency of ARSM. In this work, Latin Hypercube Design (LHD) is utilized to generate saturated design experiments. Because of the use of LHD, historical design experiments can be inherited in later iterations. As a result, ARSM only requires a limited number of design experiments even for high-dimensional design problems. The improved ARSM is tested using a group of standard test problems and then applied to an engineering design problem. In both testing and design application, significant improvement in the efficiency of ARSM is realized. The improved ARSM demonstrates strong potential to be a practical global optimization tool for computation-intensive design problems. Inheriting LHD points, as a general sampling strategy, can be integrated into other approximation-based design optimization methodologies.
Centered $L_2$-discrepancy of random sampling and Latin hypercube
design, and construction of uniform designs
