Bounds for Maximin Latin Hypercube Designs

Authors:
Edwin R. van Dam;Gijs Rennen;Bart Husslage
Affiliations:
Department of Econometrics and Operations Research, Tilburg University, Tilburg, The Netherlands;Department of Econometrics and Operations Research, Tilburg University, Tilburg, The Netherlands;Department of Econometrics and Operations Research, Tilburg University, Tilburg, The Netherlands
Venue:
Operations Research
Year:
2009

Citing 3
Cited 9

Efficient Global Optimization of Expensive Black-Box Functions

Journal of Global Optimization
Design and Analysis of Experiments

Design and Analysis of Experiments
Maximin Latin Hypercube Designs in Two Dimensions

Operations Research

Two-dimensional minimax Latin hypercube designs

Discrete Applied Mathematics
Orthogonal-column Latin hypercube designs with small samples

Computational Statistics & Data Analysis
One-dimensional nested maximin designs

Journal of Global Optimization
Design of computer experiments: space filling and beyond

Statistics and Computing
On a Dispersion Problem in Grid Labeling

SIAM Journal on Discrete Mathematics
Metamodeling of simulations consisting of time series inputs and outputs

Proceedings of the Winter Simulation Conference
Competitive comparison of optimal designs of experiments for sampling-based sensitivity analysis

Computers and Structures
Integrated experimental design and nonlinear optimization to handle computationally expensive models under resource constraints

Journal of Global Optimization
Optimizing Latin hypercube designs by particle swarm

Statistics and Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Latin hypercube designs (LHDs) play an important role when approximating computer simulation models. To obtain good space-filling properties, the maximin criterion is frequently used. Unfortunately, constructing maximin LHDs can be quite time consuming when the number of dimensions and design points increase. In these cases, we can use heuristical maximin LHDs. In this paper, we construct bounds for the separation distance of certain classes of maximin LHDs. These bounds are useful for assessing the quality of heuristical maximin LHDs. Until now only upper bounds are known for the separation distance of certain classes of unrestricted maximin designs, i.e., for maximin designs without a Latin hypercube structure. The separation distance of maximin LHDs also satisfies these “unrestricted” bounds. By using some of the special properties of LHDs, we are able to find new and tighter bounds for maximin LHDs. Within the different methods used to determine the upper bounds, a variety of combinatorial optimization techniques are employed. Mixed-integer programming, the traveling salesman problem, and the graph-covering problem are among the formulations used to obtain the bounds. Besides these bounds, also a construction method is described for generating LHDs that meet Baer's bound for the ℓ∞ distance measure for certain values of n.