caRamel is a multiobjective evolutionary algorithm combining the MEAS algorithm and the NGSA-II algorithm.
Download the package from CRAN or GitHub and then install and load it.
library(caRamel)This example will use the reticulate package in order to call a Python function from R. Download the package from CRAN and then install and load it
library(reticulate)Kursawe test function has two objectives of three variables. This function will be written in a Python script named kursawe.py with the following content:
import numpy as np
def kursawe(x):
    k1 = -10 * np.exp(-0.2 * np.sqrt(x[0]**2 + x[1]**2)) - \
        10 * np.exp(-0.2 * np.sqrt(x[1]**2 + x[2]**2))
    k2 = np.abs(x[0])**0.8 + 5 * np.sin(x[0]**3) + np.abs(x[1])**0.8 +\
        5 * np.sin(x[1]**3) + np.abs(x[2])**0.8 + 5 * np.sin(x[2]**3)
    return np.array([k1, k2])The Python function has to be loaded in R:
use_python("/usr/local/bin/python3")
source_python("kursawe.py")This function is not directly called from caRamel but with a new wrapper function and finally all can be gathered in it (recommended):
wrapperFunction <- function(i) {
  # load the package
  library(reticulate)
  # python path
  use_python("/usr/local/bin/python3")
  # source the Python function
  source_python("kursawe.py")
  # call the Python function and return the results
  return(kursawe(x[i,]))
}The variables lie in the range [-5, 5]:
nvar <- 3 # number of variables
bounds <- matrix(data = 1, nrow = nvar, ncol = 2) # upper and lower bounds
bounds[, 1] <- -5 * bounds[, 1]
bounds[, 2] <- 5 * bounds[, 2]Both functions are to be minimized:
nobj <- 2 # number of objectives
minmax <- c(FALSE, FALSE) # min and minSet algorithmic parameters and launch caRamel:
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
results <- 
  caRamel(nobj,
          nvar,
          minmax,
          bounds,
          wrapperFunction, # It's the wrapper function that will be called
          popsize,
          archsize,
          maxrun,
          prec)Test if the convergence is successful and plot the optimal front:
print(results$success==TRUE)
plot(results$objectives[,1], results$objectives[,2], main="Kursawe Pareto front", xlab="Objective #1", ylab="Objective #2")Finally plot the convergences of the objective functions:
matplot(results$save_crit[,1],cbind(results$save_crit[,2],results$save_crit[,3]),type="l",col=c("blue","red"), main="Convergence", xlab="Number of calls", ylab="Objectives values")