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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:

install.packages('caRamel')

and then load it:

library(caRamel)

Test function

Schaffer

Schaffer test function has two objectives with one variable.

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]:

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:

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:

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:

results <-
  caRamel(nobj,
          nvar,
          minmax,
          bounds,
          schaffer,
          popsize,
          archsize,
          maxrun,
          prec,
          carallel=FALSE) # no parallelism

Test if the convergence is successful:

print(results$success==TRUE)

Plot the Pareto front:

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

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Version

Install

install.packages('caRamel')

Version

1.4

License

GPL-3 | file LICENSE

Issues

Pull Requests

Stars

Forks

Maintainer

Last Published

July 29th, 2024

Functions in caRamel (1.4)

downsize

Downsizing of a population to only one individual per box up to a given accuracy
plot_caramel

Plotting of caRamel results
val2rank

Converting the values of a vector into their rank
newXval

Generation of a new population of parameter sets following the five rules of caRamel
vol_splx

Volume of a simplex
decrease_pop

Decreasing of the population of parameters sets
Cinterp

Interpolation in simplexes of the objective space
Dimprove

Determination of directions for improvement
dominate

Successive Pareto fronts of a population
caRamel

MAIN FUNCTION: multi-objective optimizer
Cextrap

Extrapolation along orthogonal directions to the Pareto front in the space of the objectives
Cusecovar

New parameter vectors generation respecting a covariance structure
Crecombination

Recombination of the sets of parameters
boxes

Box numbering for each points individual of the population
caRamel-package

caRamel optimizer
matvcov

Calculation of the variances-covariances matrix on the reference population
plot_population

Plotting of a population of objectives
plot_pareto

Plotting of a population of objectives and Pareto front
rselect

Selection of n points
dominated

Rows domination of a matrix by a vector
pareto

Indicates which rows are Pareto