Abstract
Sliced Latin hypercube designs (SLHDs) are widely used in computer experiments with both quantitative and qualitative factors and in batches. Optimal SLHDs achieve better space-filling property on the whole experimental region. However, most existing methods for constructing optimal SLHDs have restriction on the run sizes. In this paper, we propose a new method for constructing SLHDs with arbitrary run sizes, and a new combined space-filling measurement describing the space-filling property for both the whole design and its slices. Furthermore, we develop general algorithms to search for the optimal SLHD with arbitrary run sizes under the proposed measurement. Examples are presented to illustrate that effectiveness of the proposed methods.
Highlights
Computer experiments are becoming increasingly significant in many fields, such as finite element analysis and computational fluid dynamics
Sliced Latin hypercube designs (SLHDs) are LHDs that can be partitioned into some LHD slices [2], which means that the SLHDs have the optimal univariate uniformity for both the whole design and their slices
In the optimization process of an flexible sliced Latin hypercube designs (FSLHDs), we present three exchange procedures to generate a neighbour of the design which do not change the sliced structure of the design
Summary
Computer experiments are becoming increasingly significant in many fields, such as finite element analysis and computational fluid dynamics. Latin hypercube designs (LHDs) [1] are widely used in computer experiments because of their optimal univariate uniformity. A design with n runs and q factors is called an LHD; if the design is projected onto any one dimension, there is precisely one point lying within one of the n intervals (0, 1/n], (1/n, 2/n], · · · , ((n − 1)/n, 1]. Such an LHD is said to have optimal univariate uniformity. The original SLHDs and almost all existing methods for constructing variants of SLHDs require that the run sizes of each slice are equal; see [7,8,9,10]
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