createSimulatedTestFunction {CEGO}

Simulation-based Test Function Generator, Object Interface

Description

Generate test functions for assessment of optimization algorithms with non-conditional or conditional simulation, based on real-world data. For a more streamlined interface, see testFunctionGeneratorSim.

Usage

createSimulatedTestFunction(
  xsim,
  fit,
  nsim = 10,
  conditionalSimulation = TRUE,
  seed = NA
)

Arguments

xsim

list of samples in input space, for simulation

fit

an object generated by modelKriging

nsim

the number of simulations, or test functions, to be created

conditionalSimulation

whether (TRUE) or not (FALSE) to use conditional simulation

seed

a random number generator seed. Defaults to NA; which means no seed is set. For sake of reproducibility, set this to some integer value.

Value

a list of functions, where each function is the interpolation of one simulation realization. The length of the list depends on the nsim parameter.

References

N. A. Cressie. Statistics for Spatial Data. JOHN WILEY & SONS INC, 1993.

C. Lantuejoul. Geostatistical Simulation - Models and Algorithms. Springer-Verlag Berlin Heidelberg, 2002.

Zaefferer, M.; Fischbach, A.; Naujoks, B. & Bartz-Beielstein, T. Simulation Based Test Functions for Optimization Algorithms Proceedings of the Genetic and Evolutionary Computation Conference 2017, ACM, 2017, 8.

See Also

modelKriging, simulate.modelKriging, testFunctionGeneratorSim

Examples

nsim <- 10
seed <- 12345
n <- 6
set.seed(seed)
#target function:
fun <- function(x){
  exp(-20* x) + sin(6*x^2) + x
}
# "vectorize" target
f <- function(x){sapply(x,fun)}
# distance function
dF <- function(x,y)(sum((x-y)^2)) #sum of squares 
#start pdf creation
# plot params
par(mfrow=c(4,1),mar=c(2.3,2.5,0.2,0.2),mgp=c(1.4,0.5,0))
#test samples for plots
xtest <- as.list(seq(from=-0,by=0.005,to=1))
plot(xtest,f(xtest),type="l",xlab="x",ylab="Obj. function")
#evaluation samples (training)
xb <- as.list(runif(n)) 
yb <- f(xb)
# support samples for simulation
x <- as.list(sort(c(runif(100),unlist(xb))))
# fit the model	
fit <- modelKriging(xb,yb,dF,control=list(
   algThetaControl=list(method="NLOPT_GN_DIRECT_L",funEvals=100),useLambda=FALSE))
fit
#predicted obj. function values
ypred <- predict(fit,as.list(xtest))$y
plot(unlist(xtest),ypred,type="l",xlab="x",ylab="Estimation")
points(unlist(xb),yb,pch=19)
##############################	
# create test function non conditional
##############################
fun <- createSimulatedTestFunction(x,fit,nsim,FALSE,seed=1)
ynew <- NULL
for(i in 1:nsim)
  ynew <- cbind(ynew,fun[[i]](xtest))
rangeY <- range(ynew)
plot(unlist(xtest),ynew[,1],type="l",ylim=rangeY,xlab="x",ylab="Simulation")
for(i in 2:nsim){
  lines(unlist(xtest),ynew[,i],col=i,type="l")
}
##############################	
# create test function conditional
##############################
fun <- createSimulatedTestFunction(x,fit,nsim,TRUE,seed=1)
ynew <- NULL
for(i in 1:nsim)
  ynew <- cbind(ynew,fun[[i]](xtest))
rangeY <- range(ynew)
plot(unlist(xtest),ynew[,1],type="l",ylim=rangeY,xlab="x",ylab="Conditional sim.")
for(i in 2:nsim){
  lines(unlist(xtest),ynew[,i],col=i,type="l")
}
points(unlist(xb),yb,pch=19)
dev.off()