Sequential latin hypercube design with both space-filling and projective properties

Space-filling and projective properties are probably the two most important features in computer experiment. The existing research works have tried to develop different kinds of sequential Latin hypercube design (LHD) to meet these two properties. However, most if not all of them cannot simultaneously ensure these two properties in their versions of sequential LHD. In this paper, we propose a novel sequential LHD that can simultaneously meet the space-filling and the projective properties at each stage. A search algorithm is employed to find how many design points should be added in each stage to ensure the projective property; and the “Maximin" criterion is used to meet the space-filling property. Two kinds of examples for low dimension and higher dimension are presented to illustrate how these sequential sampling processes are realized. The proposed method can be applied to the areas where computationally expensive simulations are involved.