Automatic Calibration by Evolutionary Multi Objective Algorithm

The caRamel optimizer has been developed to meet the requirement for an automatic calibration procedure that delivers a family of parameter sets that are optimal with regard to a multi-objective target (Monteil et al. ).

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 test function

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.