A0358
Title: Construction of maximin distance Latin hypercube designs via good lattice point sets
Authors: Xueru Zhang - Purdue University (United States) [presenting]
Abstract: Space-filling Latin hypercube designs have found widespread applications in computer experiments, yet their design construction poses significant challenges. The design constructed through algebraic methods is limited to very restricted numbers of runs and factors, whereas those designs generated by algorithmic searches are limited to small numbers of runs and factors. To address these limitations, an approach is proposed for producing space-filling Latin hypercube designs that can accommodate flexible numbers of runs and factors. The proposed approach is hybrid in nature, incorporating an algebraic method and its corresponding algorithm. The algebraic method, built on good lattice point sets and level permutation techniques, applies to any run size and flexible numbers of factors. The proposed algorithmic search can further handle any number of factors, especially those not covered by the algebraic method. A theoretical analysis of optimality is provided for the algebraic component. Numerical studies demonstrate the superior $L_p$-distance properties of the proposed designs. Furthermore, it is demonstrated that the proposed designs exhibit good column-orthogonality and projection uniformity as well.
