maximin.crit: Maximin criterion

In SFDesign: Space-Filling Designs

Maximin criterion

Description

This function calculates the maximin distance or the average reciprocal distance of a design.

Usage

maximin.crit(design, r = 2 * ncol(design), surrogate = FALSE)

Arguments

design	the design matrix.
r	the power used in the reciprocal distance objective function. The default value is set as twice the dimension of the design.
surrogate	whether to return the surrogate average reciprocal distance objective function or the maximin distance. If setting surrogate=TRUE, then the average reciprocal distance is returned.

Details

maximin.crit calculates the maximin distance or the average reciprocal distance of a design. The maximin distance for a design D=[\bm x_1, \dots, \bm x_n]^T is defined as \phi_{Mm} = \min_{i\neq j} \|\bm x_i- \bm x_j\|_2. In optimization, the average reciprocal distance is usually used (Morris and Mitchell, 1995):

\phi_{\text{rec}} = \left(\frac{2}{n(n-1)} \sum_{i\neq j}\frac{1}{\|\bm{x}_i-\bm{x}_j\|_2^r}\right)^{1/r}.

The r is a power parameter and when it is large enough, the reciprocal distance is similar to the exact maximin distance.

Value

the maximin distance or reciprocal distance of the design.

References

Morris, M. D. and Mitchell, T. J. (1995), “Exploratory designs for computational experiments,” Journal of statistical planning and inference, 43, 381–402.

Examples

n = 20
p = 3
D = randomLHD(n, p)
maximin.crit(D)

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