The Construction And Optimization For Generalized Sliced Latin Hypercube Designs

Sliced Latin hypercube design(SLHD)is a variant of Latin hypercube design,which is widely used in computer experiments with both quantitative and qualitative factors and in batches.This paper takes sliced Latin hypercube designs as the research object.The main work and innovations are as follows:(1)We construct a generalized SLHD.An SLHD requires the run sizes of each slice to be same.In this paper,we propose a random sampling procedure to construct a generalized SLHD.This method can construct an SLHD with multiple slices and different slices have different run sizes.The whole design and each slice of the design can achieve optimal projective uniformity in one dimension.The simulation examples indicate that,compared with some other sampling methods,the constructed design performs well.(2)We propose an optimal generalized SLHD.The optimal SLHD can achieve better space-filling property on the whole experimental region.However,most existing methods for constructing the optimal SLHD have restriction on the run sizes of each slice.In this paper,we propose an improved method to construct SLHD with slices of arbitrary run sizes.The construction method can be easily adapted to generate the optimal generalized SLHD.Furthermore,we provide a new combined space-filling measurement(CSM)to describe the space-filling properties for both the whole design and its slices.Based on an optimization algorithm called the enhanced stochastic evolutionary algorithm(ESE),we propose a sliced ESE algorithm to find the optimal generalized SLHD.We further develop an efficient two-stage algorithm to improve the efficiency in generating optimal generalized SLHD with large runs and factors.Examples are presented to illustrate that effectiveness of the proposed methods.Finally,the simplified calculation of combined space-filling measurement is discussed.