maximin.crit {SFDesign} | R Documentation |
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)