spot: Sequential Parameter Optimization
In bartzbeielstein/SPOT: Sequential Parameter Optimization Toolbox

Description Usage Arguments Value Examples

This is one of the main interfaces for using the SPOT package. Based on a user-given objective function and configuration, spot finds the parameter setting that yields the lowest objective value (minimization). To that end, it uses methods from the fields of design of experiment, statistical modeling / machine learning and optimization.

1	spot(x = NULL, fun, lower, upper, control = list(), ...)

`x`	is an optional start point (or set of start points), specified as a matrix. One row for each point, and one column for each optimized parameter.
`fun`	is the objective function. It should receive a matrix x and return a matrix y. In case the function uses external code and is noisy, an additional seed parameter may be used, see the `control$seedFun` argument below for details.
`lower`	is a vector that defines the lower boundary of search space. This determines also the dimensionality of the problem.
`upper`	is a vector that defines the upper boundary of search space.
`control`	is a list with control settings for spot. See `spotControl`.
`...`	additional parameters passed to `fun`.

This function returns a list with:

xbest: Parameters of the best found solution (matrix).
ybest: Objective function value of the best found solution (matrix).
x: Archive of all evaluation parameters (matrix).
y: Archive of the respective objective function values (matrix).
count: Number of performed objective function evaluations.
msg: Message specifying the reason of termination.
modelFit: The fit of the last build model, i.e., an object returned by the last call to the function specified by control$model.

## Most simple example: Kriging + LHS + predicted 
## mean optimization (not expected improvement)
res <- spot(,funSphere,c(-2,-3),c(1,2),control=list(funEvals=15))
res$xbest
## With expected improvement
res <- spot(,funSphere,c(-2,-3),c(1,2),
   control=list(funEvals=15,modelControl=list(target="ei"))) 
res$xbest
### With additional start point:
#res <- spot(matrix(c(0.05,0.1),1,2),funSphere,c(-2,-3),c(1,2))
#res$xbest
#res <- spot(,funSphere,c(-2,-3),c(1,2),
#    control=list(funEvals=50)) 
#res$xbest
### Use local optimization instead of LHS
#res <- spot(,funSphere,c(-2,-3),c(1,2),
#    control=list(optimizer=optimLBFGSB)) 
#res$xbest
### Random Forest instead of Kriging
#res <- spot(,funSphere,c(-2,-3),c(1,2),
#    control=list(model=buildRandomForest)) 
#res$xbest    
### LM instead of Kriging
#res <- spot(,funSphere,c(-2,-3),c(1,2),
#    control=list(model=buildLM)) #lm as surrogate
#res$xbest
### LM and local optimizer (which for this simple example is perfect)
#res <- spot(,funSphere,c(-2,-3),c(1,2),
#    control=list(model=buildLM, optimizer=optimLBFGSB)) 
#res$xbest
### Or a different Kriging model:
#res <- spot(,funSphere,c(-2,-3),c(1,2),
#    control=list(model=buildKrigingDACE, optimizer=optimLBFGSB)) 
#res$xbest
## With noise: (this takes some time)
#res1 <- spot(,function(x)funSphere(x)+rnorm(nrow(x)),c(-2,-3),c(1,2),
#		control=list(funEvals=100,noise=TRUE)) #noisy objective
#res2 <- spot(,function(x)funSphere(x)+rnorm(nrow(x)),c(-2,-3),c(1,2),
#		control=list(funEvals=100,noise=TRUE,replicates=2,
#		designControl=list(replicates=2))) #noise with replicated evaluations
#res3 <- spot(,function(x)funSphere(x)+rnorm(nrow(x)),c(-2,-3),c(1,2),
#		control=list(funEvals=100,noise=TRUE,replicates=2,OCBA=T,OCBABudget=1,
#		designControl=list(replicates=2))) #and with OCBA
### Check results with non-noisy function:
#funSphere(res1$xbest)
#funSphere(res2$xbest)
#funSphere(res3$xbest)
## The following is for demonstration only, to be used for random number 
## seed handling in case of external noisy target functions.
#res3 <- spot(,function(x,seed){set.seed(seed);funSphere(x)+rnorm(nrow(x))},
#    c(-2,-3),c(1,2),control=list(funEvals=100,noise=TRUE,seedFun=1))
## 
## Next Example: Handling factor variables
## Note: factors should be coded as integer values, i.e., 1,2,...,n
## create a test function:
braninFunctionFactor <- function (x) {  
  y <- (x[2]  - 5.1/(4 * pi^2) * (x[1] ^2) + 5/pi * x[1]  - 6)^2 + 
    10 * (1 - 1/(8 * pi)) * cos(x[1] ) + 10
  if(x[3]==1)
    y <- y +1
  else if(x[3]==2)
    y <- y -1
  y  
}
## vectorize
objFun <- function(x){apply(x,1,braninFunctionFactor)}
set.seed(1)
res <- spot(fun=objFun,lower=c(-5,0,1),upper=c(10,15,3),     
    control=list(model=buildKriging, 
      types= c("numeric","numeric","factor"), 
      optimizer=optimLHD)) 
res$xbest
res$ybest