maximinLHD: Generate a maximin Latin-hypercube design (LHD)

In SFDesign: Space-Filling Designs

Generate a maximin Latin-hypercube design (LHD)

Description

This function generates a LHD with large maximin distance.

Usage

maximinLHD(
  n,
  p,
  design = NULL,
  power = 2 * p,
  max.sa.iter = 1e+06,
  temp = 0,
  decay = 0.95,
  no.update.iter.max = 100,
  num.passes = 10,
  max.det.iter = 1e+06,
  method = "full",
  scaled = TRUE
)

Arguments

n	design size.
p	design dimension.
design	an initial LHD. If design=NULL, a random LHD is generated.
power	the power used in the maximin objective function.
max.sa.iter	maximum number of swapping involved in the simulated annealing (SA) algorithm.
temp	initial temperature of the simulated annealing algorithm. If temp=0, it will be automatically determined.
decay	the temperature decay rate of simulated annealing.
no.update.iter.max	the maximum number of iterations where there is no update to the global optimum before SA stops.
num.passes	the maximum number of passes of the whole design matrix if deterministic swapping is used.
max.det.iter	maximum number of swapping involved in the deterministic swapping algorithm.
method	choice of "deterministic", "sa", or "full". If the method="full", the design is first optimized by SA and then deterministic swapping.
scaled	whether the design is scaled to unit hypercube. If scaled=FALSE, the design is represented by integer numbers from 1 to design size. Leave it as TRUE when no initial design is provided.

Details

maximinLHD generates a LHD or optimize an existing LHD to achieve large maximin distance by optimizing the reciprocal distance (see maximin.crit). The optimization details can be found in customLHD.

Value

design	final design points.
total.iter	total number of swaps in the optimization.
criterion	final optimized criterion.
crit.hist	criterion history during the optimization process.

Examples

# We show three different ways to use this function.
n = 20
p = 3
D.random = randomLHD(n, p)
# optimize over a random LHD by SA
D = maximinLHD(n, p, D.random, method='sa')
# optimize over a random LHD by deterministic swapping
D = maximinLHD(n, p, D.random, method='deterministic')
# Directly generate an optimized LHD for maximin criterion which goes
# through the above two optimization stages.
D = maximinLHD(n, p)

SFDesign documentation built on June 22, 2025, 1:06 a.m.