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

Description

SA2008 returns a maximin distance LHD constructed by simulated annealing algorithm with multi-objective optimization approach.

Usage

SA2008(n, k, N, T0, rate, Tmin, Imax, p = 50, q = 1)

Arguments

A positive integer.

A positive number.

rate

A positive percentage.

Tmin

A positive number.

Imax

A positive integer.

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.
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.

References

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

Examples

Run this code

# NOT RUN {
#create a 5 by 3 maximin distance LHD, with # of iterations =10, initial
#temperature is set to be 10, decrease rate is 10%, minimium temperature is 1,
#maximum perturbations the algorithm will try without improvements is 5, and p=50
try=SA2008(n=5,k=3,N=10,T0=10,rate=0.1,Tmin=1,Imax=5,p=50,q=1)
try
phi_p(try,p=50)   #calculate the phi_p of "try".

#Another example with different input
try2=SA2008(n=9,k=2,N=5,T0=8,rate=0.1,Tmin=1,Imax=3,p=50,q=1)
try2
# }

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