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Short Description

caRamel is an R package for optimization implementing a multiobjective evolutionary algorithm combining the MEAS algorithm and the NGSA-II algorithm.

Installation

Download and install the package from CRAN:

{r caRa} install.packages('caRamel')

and then load it: {r caRa} library(caRamel)

Test function

Schaffer

Schaffer test function has two objectives with one variable.

Schaffer test function

{r schaffer} schaffer <- function(i) { if (x[i,1] <= 1) { s1 <- -x[i,1] } else if (x[i,1] <= 3) { s1 <- x[i,1] - 2 } else if (x[i,1] <= 4) { s1 <- 4 - x[i,1] } else { s1 <- x[i,1] - 4 } s2 <- (x[i,1] - 5) * (x[i,1] - 5) return(c(s1, s2)) }

Note that :

• parameter i is mandatory for the management of parallelism.
• the variable must be named x and is a matrix of size [npopulation, nvariables].

The variable lies in the range [-5, 10]:

{r schaffer_variable} nvar <- 1 # number of variables bounds <- matrix(data = 1, nrow = nvar, ncol = 2) # upper and lower bounds bounds[, 1] <- -5 * bounds[, 1] bounds[, 2] <- 10 * bounds[, 2]

Both functions are to be minimized:

{r schaffer_objectives} nobj <- 2 # number of objectives minmax <- c(FALSE, FALSE) # min and min

Before calling caRamel in order to optimize the Schaffer’s problem, some algorithmic parameters need to be set:

{r schaffer_param} popsize <- 100 # size of the genetic population archsize <- 100 # size of the archive for the Pareto front maxrun <- 1000 # maximum number of calls prec <- matrix(1.e-3, nrow = 1, ncol = nobj) # accuracy for the convergence phase

Then the minimization problem can be launched:

{r schaffer_launch, fig.show="hide", results="hide"} results <- caRamel(nobj, nvar, minmax, bounds, schaffer, popsize, archsize, maxrun, prec, carallel=FALSE) # no parallelism

Test if the convergence is successful:

{r schaffer_OK} print(results$success==TRUE)

Plot the Pareto front:

{r schaffer_plot1} plot(results$objectives[,1], results$objectives[,2], main="Schaffer Pareto front", xlab="Objective #1", ylab="Objective #2")

{r schaffer_plot2} plot(results$parameters, main="Corresponding values for X", xlab="Element of the archive", ylab="X Variable")

References

• Efstratiadis, A. and Koutsoyiannis, D., The multiobjective evolutionary annealing-simplex method and its application in calibrating hydrological models, EGU General Assembly 2005, Geophysical Research Abstracts, vol.7, Vienna, European Geophysical Union
• Reed, P. and Devireddy, D., Groundwater monitoring design: a case study combining epsilon-dominance archiving and automatic parameterization for the NGSA-II, Coello-Coello C editor, Applications of multiobjective evolutionary algorithms, Advances in natural computation series, vol. 1, pp. 79-100, Word Scientific, New-York, 2004

License

GPL v3

Contributors

Contributions are always welcome ;-)

When contributing to caRamel please consider discussing the changes you wish to make via issue or e-mail to the maintainer.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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