Author: Fabrice Zaoui

# Using a Python function with caRamel

#### Fabrice Zaoui

#### September 29 2020

## Short Description

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 min

Set 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")