createSimulatedTestFunction: 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
)

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.

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.

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.

Examples

Run this code

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()