A0714
Title: Generalized uniform projection designs
Authors: Yishan Zhou - Qingdao University of Science & Technology (China) [presenting]
Abstract: Uniform projection designs (UPDs) are an important class of computer experiment designs that address design space-filling properties for low-dimensional projections. Especially in most computer experimental designs, only a few factors are active. In this case, UPDs are very suitable. However, the existing UPDs only care about the uniformity of designs corresponding to the main effects model. In more complex practical models that include second-order interaction effects, it is not sufficient to consider linear main effects alone. To reduce the impact of the second-order interaction effect on the main effect, the 3-dimensional uniform projection designs are proposed, which can realize the 3-dimensional projection uniformity in all projection spaces. In addition, some theoretical connections are established between the 3-dimensional uniform projection criterion and the criteria of maximin distance and 3-orthogonality, which help find better space-filling designs under multiple criteria. Moreover, the 2-dimensional and 3-dimensional projection uniformity of a design is also comprehensively considered, and the generalized uniform projection criterion is proposed. The corresponding optimal design is called the minimum uniform projection design and provides the optimization search algorithm. It can simultaneously achieve 2-dimensional and 3-dimensional projection uniformity in all projection spaces. Numerical simulations confirm the rationality of the proposed designs.
