Efficient Global Optimization of Expensive Black-Box Functions
Journal of Global Optimization
Packing equal circles in a square: a deterministic global optimization approach
Discrete Applied Mathematics
A New Verified Optimization Technique for the "Packing Circles in a Unit Square" Problems
SIAM Journal on Optimization
Design and Analysis of Experiments
Design and Analysis of Experiments
Two-dimensional minimax Latin hypercube designs
Discrete Applied Mathematics
Orthogonal-column Latin hypercube designs with small samples
Computational Statistics & Data Analysis
Bounds for Maximin Latin Hypercube Designs
Operations Research
A hybrid multiagent approach for global trajectory optimization
Journal of Global Optimization
One-dimensional nested maximin designs
Journal of Global Optimization
Generating sequential space-filling designs using genetic algorithms and Monte Carlo methods
SEAL'10 Proceedings of the 8th international conference on Simulated evolution and learning
Maximin design on non hypercube domains and kernel interpolation
Statistics and Computing
Design of computer experiments: space filling and beyond
Statistics and Computing
Blind Kriging: Implementation and performance analysis
Advances in Engineering Software
Efficiently packing unequal disks in a circle
Operations Research Letters
On a Dispersion Problem in Grid Labeling
SIAM Journal on Discrete Mathematics
Competitive comparison of optimal designs of experiments for sampling-based sensitivity analysis
Computers and Structures
Optimizing Latin hypercube designs by particle swarm
Statistics and Computing
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The problem of finding a maximin Latin hypercube design in two dimensions can be described as positioning n nonattacking rooks on an n 脙聴 n chessboard such that the minimal distance between pairs of rooks is maximized. Maximin Latin hypercube designs are important for the approximation and optimization of black-box functions. In this paper, general formulas are derived for maximin Latin hypercube designs for general n, when the distance measure is l∞ or l1. Furthermore, for the distance measure l2, we obtain maximin Latin hypercube designs for n ≤ 70 and approximate maximin Latin hypercube designs for other values of n. All these maximin Latin hypercube designs can be downloaded from the website http://www.spacefillingdesigns.nl. We show that the reduction in the maximin distance caused by imposing the Latin hypercube design structure is small. This justifies the use of maximin Latin hypercube designs instead of unrestricted designs.