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ORTHOGONAL-MAXIMIN LATIN HYPERCUBE DESIGNS

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Optimal Experimental Design Methods Advanced Multi-Objective Optimization Algorithms Mathematical Approximation and Integration

Abstract

A randomly generated Latin hypercube design (LHD) can be quite structured: the variables may be highly correlated or the design may not have good space-filling properties. There are procedures to find good LHDs by minimizing the pairwise correlations or maximizing the inter-site distances. In this article we have shown that these two criteria need not agree with each other. In fact, maximization of inter-site distances can result in LHDs where the variables are highly correlated and vice versa. Therefore, we propose a multi-objective optimization approach to find good LHDs by combining correlation and distance performance measures. We also propose a new exchange algorithm for efficiently generating such designs. Several examples are presented to show that the new algorithm is fast and that the optimal designs are good in terms of both the correlation and distance criteria.

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References

2000A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code 1989Design and Analysis of Computer Experiments 1982A distribution-free approach to inducing rank correlation among input variables 1990Minimax and maximin distance designs 2005Design and Modeling for Computer Experiments 1993Orthogonal Array-Based Latin Hypercubes 2005Use of Kriging Models to Approximate Deterministic Computer Models 2004An efficient algorithm for constructing optimal design of computer experiments

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2011Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling 2016Space-filling designs for computer experiments: A review 2011Latin hypercube sampling with multidimensional uniformity 2014Optimal Sliced Latin Hypercube Designs 2008Finding maximin latin hypercube designs by Iterated Local Search heuristics 2015Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification

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