landscapeGeneratorGaussian {CEGO}

Create Gaussian Landscape

Description

This function is loosely based on the Gaussian Landscape Generator by Bo Yuan and Marcus Gallagher. It creates a Gaussian Landscape every time it is called. This Landscape can be evaluated like a function. To adapt to combinatorial spaces, the Gaussians are here based on a user-specified distance measure. Due to the expected nature of combinatorial spaces and their lack of direction, the resulting Gaussians are much simplified in comparison to the continuous, vector-valued case (e.g., no rotation). Since the CEGO package is tailored to minimization, the landscape is inverted.

Usage

landscapeGeneratorGaussian(
  nGaussian = 10,
  theta = 1,
  ratio = 0.2,
  seed = 1,
  distanceFunction,
  creationFunction
)

Arguments

nGaussian

number of Gaussian components in the landscape. Default is 10.

theta

controls width of Gaussian components as a multiplier. Default is 1.

ratio

minimal function value of the local minima. Default is 0.2. (Note: Global minimum will be at zero, local minima will be in range [ratio;1])

seed

seed for the random number generator used before creation of the landscape. Generator status will be saved and reset afterwards.

distanceFunction

A function of type f(x,y), to evaluate distance between to samples in their given representation.

creationFunction

function to randomly generate the centers of the Gaussians, in form of their given representation.

Value

returns a function.The function requires a list of candidate solutions as its input, where each solution is suitable for use with the distance function.

References

B. Yuan and M. Gallagher (2003) "On Building a Principled Framework for Evaluating and Testing Evolutionary Algorithms: A Continuous Landscape Generator". In Proceedings of the 2003 Congress on Evolutionary Computation, IEEE, pp. 451-458, Canberra, Australia.

Examples

#rng seed
seed=101
# distance function
dF <- function(x,y)(sum((x-y)^2)) #sum of squares 
#dF <- function(x,y)sqrt(sum((x-y)^2)) #euclidean distance
# creation function
cF <- function()runif(1)
# plot pars
par(mfrow=c(3,1),mar=c(3.5,3.5,0.2,0.2),mgp=c(2,1,0))
## uni modal distance landscape
# set seed
set.seed(seed)
#landscape
lF <- landscapeGeneratorUNI(cF(),dF)
x <- as.list(seq(from=0,by=0.001,to=1))
plot(x,lF(x),type="l")
## multi-modal distance landscape
# set seed
set.seed(seed)
#landscape
lF <- landscapeGeneratorMUL(replicate(5,cF(),FALSE),dF)
plot(x,lF(x),type="l")
## glg landscape
#landscape
lF <- landscapeGeneratorGaussian(nGaussian=20,theta=1,
ratio=0.3,seed=seed,dF,cF)
plot(x,lF(x),type="l")