LHD (version 1.1.0)

SA2008: Simulated Annealing for LHD with Multi-objective Optimization Approach

Description

SA2008 returns an LHD matrix generated by simulated annealing algorithm with multi-objective optimization approach.

Usage

SA2008(
  n,
  k,
  N = 10,
  T0 = 10,
  rate = 0.1,
  Tmin = 1,
  Imax = 5,
  OC = "phi_p",
  p = 15,
  q = 1
)

Arguments

n

A positive integer.

k

A positive integer.

N

A positive integer.

T0

A positive number.

rate

A positive percentage.

Tmin

A positive number.

Imax

A positive integer.

OC

An optimality criterion.

p

A positive integer.

q

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

Value

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

Details

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

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

• N stands for the number of iterations. The default is set to be 10.

• T0 stands for the user-defined initial temperature. The default is set to be 10.

• 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. The default is set to be 10%.

• Tmin stands for the minimium temperature allowed. When current temperature becomes smaller or equal to Tmin, the stopping criterion for current loop is met. The default is set to be 1.

• 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, which is the default setting.

• OC stands for the optimality criterion, the default setting is "phi_p", and it could be one of the following: "phi_p", "AvgAbsCor", "MaxAbsCor", "MaxProCriterion".

• p is the parameter in the phi_p formula, and p is prefered to be large. The default is set to be 15.

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

References

Joseph, V.R., and Hung, Y. (2008) Orthogonal-maximin Latin hypercube designs. Statistica Sinica, 18, 171-186.

Examples

# NOT RUN {
#generate a 5 by 3 maximin distance LHD with the default setting
try=SA2008(n=5,k=3)
try
phi_p(try)   #calculate the phi_p of "try".

#Another example
#generate a 8 by 4 nearly orthogonal LHD
try2=SA2008(n=8,k=4,OC="AvgAbsCor")
try2
AvgAbsCor(try2)  #calculate the average absolute correlation.
# }