cmaOptimDP {rCMA}

Perform a CMA-ES optimization with constraints (DP).

Description

The optimization uses DP (death penalty) for handling constraint violations: Each time an infeasible individual is encountered, it is thrown away and a new individual is resampled from the CMA distribution.

Usage

cmaOptimDP(cma, fitFunc, isFeasible = function(x) {     TRUE },
  maxDimPrint = 5, iterPrint = 10, verbose = 2)

Arguments

cma

CMA-ES Java object, already initialized with cmaInit

fitFunc

a function to be minimized. Signature: accepts a vector x, returns a double.

isFeasible

[function(x){TRUE}] a Boolean function checking the feasibility of the vector x. The default is to return always TRUE.

maxDimPrint

[5] how many dimensions of vector x to print in diagnostic output

iterPrint

[10] after how many iterations should diagnostic output be printed?

verbose

[2] possible values are 0 (no output), 1, 2 (much output)

Details

This functions loops through iterations (generations) until a stop condition is met: In each iteration, a population is sampled (infeasible individuals are replaced via Java function resampleSingle), its fitness vector is evaluated and the CMA distribution is updated according to this fitness vector.

Every iterPrint generations a one-line diagnostic output of the form

     iter  fitness | x1 x2 ... xp

is printed where fitness is the current best value of the fitness function to be minimized and x1 x2 ... xp are the first maxDimPrint dimensions of the corresponding best point in input space.

Value

res, a list with diagnostic output from the optimization run:

sMsg

a string vector with all console output from the optimization run. To print it, use: cat(sMsg) or for (x in sMsg) cat(x)

bestX

vector of length dimension with the best-ever solution X

bestFitness

the corresponding best-ever fitness

bestEvalNum

the fitness function evaluation number which gave this best-ever result

nIter

number of iterations

fitnessVec

vector of length nIter: the best fitness after each iteration

xMat

(nIter x dimension)-matrix: xMat[i,] is the best solution X after iteration i

cfe

number of constraint function evaluations (isFeasible)

ffe

number of fitness function evaluations (fitFunc)

Note

If your fitness function depends on other parameters besides x, then encapsulate it in a new function fitFunc at a place where the other parameters are accessible and rely on R's mechanism to locate the other parameters in the environment surrounding fitFunc:

     par1 <- someObject;
   

     fitFunc <- function(x) {  myFuncWithOtherPars(x,par1); }
   

Author(s)

Wolfgang Konen, FHK, 2013-2015

See Also

cmaNew, cmaInit

Examples

## demo/demoCMA2.R: demo usage of package rCMA.
##
## After doing the unconstrained sphere (as in demoCMA1.r, for later reference in plot), 
## the constrained sphere problem TR2 is solved. 
## The problem TR2 has in addition to the fitness function 'sphere' the constraint function
## 'above the hyperplane sum_i(x_i) = n', where n is the input space dimension.
## The constrained optimum is at (1,...,1) and it has the value fTarget2=n.
##
## Note that in this second case, the optimimum lies exactly at the boundary 
## of the feasible region: res2$bestX=c(1,...,1).
##
## This script does exactly the same as class CMAExampleConstr in cma_jAll.jar,
## but it allows to define the functions fitFunc and isFeasible on the R side. 
## They can be replaced by arbitrary other R functions, which may depend on other 
## R variables as well. 
##
## The constraint handling approach is a very simple one: death penalty, i.e. if we get an 
## infeasible individual, it is immediately discarded and a new one is drawn from the distribution. 
## (This approach will run into trouble if the current distribution does not allow to reach any  
## feasible solutions.)
## 
library(rCMA)
fitFunc <- function(x) {  sum(x*x); }
isFeasible <- function(x) {  (sum(x) - length(x)) >= 0;  }
n = 2;

cma <- cmaNew(propFile="CMAEvolutionStrategy.properties");
cmaInit(cma,seed=42,dimension=n,initialX=1.5, initialStandardDeviations=0.2);
res1 = cmaOptimDP(cma,fitFunc,iterPrint=30);

cma <- cmaNew(propFile="CMAEvolutionStrategy.properties");
cmaInit(cma,seed=42,dimension=n,initialX=1.5, initialStandardDeviations=0.2);
res2 = cmaOptimDP(cma,fitFunc,isFeasible,iterPrint=30);

fTarget =c(0,n); 
plot(res1$fitnessVec-fTarget[1],type="l",log="y",xlim=c(1,max(res1$nIter,res2$nIter))
    ,xlab="Iteration",ylab="Distance to target fitness");
lines(res2$fitnessVec-fTarget[2],col="red");
legend("topright",legend=c("TR2","sphere"),lwd=rep(1,2),col=c("red","black"))
str(res2);

bestSolution=rCMA::cmaEvalMeanX(cma,fitFunc,isFeasible);
str(bestSolution);