multiCOBRA: Perform multiple COBRA runs
In SACOBRA: Self-Adjusting COBRA

Description Usage Arguments Details Value Author(s) See Also Examples

Perform multiple COBRA runs. Each run starts with a different seed so that a different start point, a different initial design and different random restarts are choosen.

multiCOBRA(
  fn,
  lower,
  upper,
  nrun = 10,
  feval = 200,
  funcName = "GXX",
  fName = paste0("mult-", funcName, ".Rdata"),
  path = NULL,
  cobra = NULL,
  optim = NULL,
  target = 0.05,
  saveRdata = FALSE,
  ylim = c(1e-05, 10000),
  plotPDF = FALSE,
  startSeed = 41
)

`fn`	objective function that is to be minimized, should return a vector of the objective function value and the constraint values
`lower`	lower bound of search space
`upper`	upper bound of search space
`nrun`	[10] number of runs
`feval`	[200] function evaluations per run
`funcName`	["GXX"] name of the problem
`fName`	the results (`dfAll` and others) are saved to `<fname>.Rdata` (only if saveRdata==TRUE)
`path`	[NULL] optional path
`cobra`	[NULL] list with COBRA settings. If NULL, initialize `cobra` with a suitable call to `cobraInit`.
`optim`	[NULL] the true optimum (or best known value) of the problem (only for diagnostics)
`target`	[0.05] a single run meets the target, if the final error is smaller than `target`
`saveRdata`	[FALSE] if TRUE, save results (dfAll,optim,target,fName,funcName) on `<fName>.Rdata`
`ylim`	the y limits
`plotPDF`	[FALSE] if TRUE, plot not only to current graphics device but to `<fName>.pdf` as well
`startSeed`	[41] after each run the seed is incremented by 1, starting with `startSeed`

Side effect: An error plot showing each run and the mean and median of all runs (see multiRunPlot). The results (dfAll and others) are saved to <fName>.Rdata.

mres, a list containing

`cobra`	the settings and results from last run
`dfAll`	a data frame with a result summary for all runs (see below)
`z`	a vector containing for each run the ever-best feasible objective value
`z2`	a data frame containing for each run the minimum error (if `optim` is available)

The data frame dfAll contains one row per iteration with columns (among others)

ffc: fitness function calls (i.e. the iterations cobra$iter)
fitVal: true fitness function value
fitSur: surrogate fitness function value
feas: is current iterate feasible on the true constraints?
feval: number of evaluations of the internal optimizer on the surrogate functions (NA if it is a repairInfeasible-step)
XI: the DRC element used in the current iteration
everBestFeas: the ever-best feasible fitness function value
run: the number of the current run
X1,X2,...: the solution in (original) input space

Wolfgang Konen, Samineh Bagheri, Cologne University of Applied Sciences

multiRunPlot, cobraPhaseII

## solve G11 problem nrun times  and plot the results of all nrun runs
nrun=4
feval=25

## Defining the constrained problem (G11)
fn <- function(x) {
  y<-x[1]*x[1]+((x[2]-1)^2)
  y<-as.numeric(y)
  
  g1 <- as.numeric(+(x[2] - x[1]^2))
  
  return(c(objective=y, g1=g1))
}
funcName="G11"
lower<-c(-1,-1) 
upper<-c(+1,+1) 

## Initializing and running cobra
cobra <- cobraInit(xStart=c(0,0), fn=fn, fName=funcName, lower=lower, upper=upper,
                   feval=feval, initDesPoints=3*2, DOSAC=1, cobraSeed=1)

mres <- multiCOBRA(fn,lower,upper,nrun=nrun,feval=feval,optim=0.75
                  ,cobra=cobra,funcName=funcName
                  ,ylim=c(1e-12,1e-0),plotPDF=FALSE,startSeed=42)

## There are two true solutions at 
## solu1 = c(-sqrt(0.5),0.5) and solu2 = c(+sqrt(0.5),0.5)
## where the true optimum is f(solu1) = f(solu2) = -0.75
## The solution from SACOBRA is close to one of the true solutions:
print(getXbest(mres$cobra))
print(getFbest(mres$cobra))
print(mres$z2)