optimCEGO: Combinatorial Efficient Global Optimization

Description

Model-based optimization for combinatorial or mixed problems. Based on measures of distance or dissimilarity.

Usage

optimCEGO(x = NULL, fun, control = list())

Value

a list:

xbest: best solution found
ybest: fitness of the best solution
x: history of all evaluated solutions
y: corresponding target function values f(x)
fit: model-fit created in the last iteration
fpred: prediction function created in the last iteration
count: number of performed target function evaluations
message: message string, giving information on termination reason
convergence: error/status code: -1 for termination due to failed model building, 0 for termination due to depleted budget, 1 if attained objective value is equal to or below target (control$targetY)

Arguments

x

Optional initial design as a list. If NULL (default), creationFunction (in control list) is used to create initial design. If x has less individuals than specified by control$evalInit, creationFunction will fill up the design.

fun

target function to be minimized

control

(list), with the options of optimization and model building approaches employed:

evalInit: Number of initial evaluations (i.e., size of the initial design), integer, default is 2

vectorized

Boolean. Defines whether target function is vectorized (takes a list of solutions as argument) or not (takes single solution as argument). Default: FALSE

verbosity

Level of text output during run. Defaults to 0, no output.

plotting

Plot optimization progress during run (TRUE) or not (FALSE). Default is FALSE.

targetY

optimal value to be found, stopping criterion, default is -Inf

budget

maximum number of target function evaluations, default is 100

creationRetries

When a model does not predict an actually improving solution, a random exploration step is performed. creationRetries solutions are created randomly. For each, distance to all known solutions is calculated. The minimum distance is recorded for each random solution. The random solution with maximal minimum distance is chosen doe be evaluated in the next iteration.

model

Model to be used as a surrogate of the target function. Default is "K" (Kriging). Also available are: "LM" (linear, distance-based model), "RBFN" Radial Basis Function Network.

modelSettings

List of settings for model building, passed on as the control argument to the model training functions modelKriging, modelLinear, modelRBFN.

infill

This parameter specifies a function to be used for the infill criterion (e.g., the default is expected improvement infillExpectedImprovement). To use no specific infill criterion this has to be set to NA, in which case the prediction of the surrogate model is used. Infill criteria are only used with models that may provide some error estimate with predictions.

optimizer

Optimizer that finds the minimum of the surrogate model. Default is optimEA, an Evolutionary Algorithm.

optimizerSettings

List of settings (control) for the optimizer function.

initialDesign

Design function that generates the initial design. Default is designMaxMinDist, which creates a design that maximizes the minimum distance between points.

initialDesignSettings

List of settings (control) for the initialDesign function.

creationFunction

Function to create individuals/solutions in search space. Default is a function that creates random permutations of length 6

distanceFunction

distanceFunction a suitable distance function of type f(x1,x2), returning a scalar distance value, preferably between 0 and 1. Maximum distances larger 1 are not a problem, but may yield scaling bias when different measures are compared. Should be non-negative and symmetric. With the setting control$model="K" this can also be a list of different fitness functions. Default is Hamming distance for permutations: distancePermutationHamming.

References

Zaefferer, Martin; Stork, Joerg; Friese, Martina; Fischbach, Andreas; Naujoks, Boris; Bartz-Beielstein, Thomas. (2014). Efficient global optimization for combinatorial problems. In Proceedings of the 2014 conference on Genetic and evolutionary computation (GECCO '14). ACM, New York, NY, USA, 871-878. DOI=10.1145/2576768.2598282

Zaefferer, Martin; Stork, Joerg; Bartz-Beielstein, Thomas. (2014). Distance Measures for Permutations in Combinatorial Efficient Global Optimization. In Parallel Problem Solving from Nature - PPSN XIII (p. 373-383). Springer International Publishing.

Examples

Run this code

seed <- 0
#distance
dF <- distancePermutationHamming
#mutation
mF <- mutationPermutationSwap
#recombination
rF <-  recombinationPermutationCycleCrossover 
#creation
cF <- function()sample(5)
#objective function
lF <- landscapeGeneratorUNI(1:5,dF)
#start optimization
set.seed(seed)
res1 <- optimCEGO(,lF,list(
			creationFunction=cF,
			distanceFunction=dF,
			optimizerSettings=list(budget=100,popsize=10,
			mutationFunction=mF,recombinationFunction=rF),
	evalInit=5,budget=15,targetY=0,verbosity=1,model=modelKriging,
	vectorized=TRUE)) ##target function is "vectorized", expects list as input
set.seed(seed)
res2 <- optimCEGO(,lF,list(
			creationFunction=cF,
			distanceFunction=dF,
			optimizerSettings=list(budget=100,popsize=10,
			mutationFunction=mF,recombinationFunction=rF),
			evalInit=5,budget=15,targetY=0,verbosity=1,model=modelRBFN,
	vectorized=TRUE)) ##target function is "vectorized", expects list as input
res1$xbest 
res2$xbest