SLHD

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Sliced Latin Hypercube Design (SLHD)

SLHD returns a maximin distance LHD constructed by "improved two-stage algorithm" from Ba et al. (2015).

Usage
SLHD(n, k, t, N, T0, rate, Tmin, Imax, p = 50, q = 1, stage2 = FALSE)
Arguments
n

A positive integer.

k

A positive integer.

t

A positive integer.

N

A positive integer.

T0

A positive number.

rate

A positive percentage.

Tmin

A positive number.

Imax

A positive integer.

p

A positive integer.

q

The default is set to be 1, and it could be either 1 or 2.

stage2

The default is set to be FALSE, and it could be either FALSE or TRUE.

Details

  • n stands for the number of rows (or run size).

  • k stands for the number of columns (or the number of factors).

  • t stands for the number of slices. n/t must be an integer, that is, n is divisible by t. Since S(X) needs to be 0 for the algorithm to continue, t must not exceed k for n is 9 or larger, and t must be smaller than k for n is smaller than 9. Otherwise, the funtion will never stop.

  • N stands for the number of iterations.

  • T0 stands for the user-defined initial temperature.

  • rate stands for temperature decrease rate, and it should be in (0,1). For example, rate=0.25 means the temperature decreases by 25% each time.

  • Tmin stands for the minimium temperature allowed. When current temperature becomes smaller or equal to Tmin, the stopping criterion for current loop is met.

  • Imax stands for the maximum perturbations the algorithm will try without improvements before temperature is reduced. For the computation complexity consideration, Imax is recommended to be smaller or equal to 5.

  • p is the parameter in the phi_p formula, and p is prefered to be large.

  • If q is 1 (the default setting), dij is the rectangular distance. If q is 2, dij is the Euclidean distance.

  • If stage2 is FALSE (the default setting), SLHD will only implement the first stage of the algorithm. If stage2 is TRUE, SLHD will implement the whole algorithm.

Value

If all inputs are logical, then the output will be a n by k LHD.

Note

As mentioned from the original paper, the first stage plays a much more important role since it optimizes the slice level. More resources should be given to the first stage if computational budgets are limited. Let m=n/t, where m is the number of rows for each slice, if (m)^k >> n, the second stage becomes optional. That is the reason why we add a stage2 parameter to let users decide if the second stage is needed. If stage2 is FALSE, randomly generated \Pi_l's will be used.

References

Ba, S., Myers, W.R., and Brenneman, W.A. (2015) Optimal Sliced Latin Hypercube Designs. Technometrics, 57, 479-487.

Aliases
  • SLHD
Examples
# NOT RUN {
#Try SLHD without stage II: create a 5 by 3 maximin distance LHD, with # of
#slices is 1, # of iterations = 5, initial temperature is set to be 5,
#decrease rate is 20%, minimium temperature is 1, maximum perturbations the
#algorithm will try without improvements is 3, and p=50
trySLHD1=SLHD(n=5,k=3,t=1,N=5,T0=5,rate=0.2,Tmin=1,Imax=3,p=50,q=1)
trySLHD1
phi_p(trySLHD1,p=50)   #calculate the phi_p of "trySLHD1".

#Try SLHD with stage II
trySLHD2=SLHD(n=5,k=3,t=1,N=5,T0=5,rate=0.2,Tmin=1,Imax=3,p=50,q=1,stage2=TRUE)
trySLHD2
phi_p(trySLHD2,p=50)   #calculate the phi_p of "trySLHD2".
# }
Documentation reproduced from package LHD, version 0.1.0, License: MIT + file LICENSE

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