Author: Fabrice Zaoui

# Three ways to call the user functions

#### Fabrice Zaoui

#### October 01 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)

There are three possible choices on how caRamel can call the R user functions. Each choice is parameterized by the carallel value.

# Sequential or parallel mode

The computation of the user functions can be done sequentially or in parallel for each individual of the genetic population according to the choice of carallel when calling caRamel.

The evaluation of the population is done in a sequential mode if carallel is 0, or in parallel if carallel is 1 (this last one is the default option).

For these two options, the R user function takes a single input parameter i giving the number of the individual of the population x. For instance:

    kursawe <- function(i) {
      k1 <- -10 * exp(-0.2 * sqrt(x[i,1] ^ 2 + x[i,2] ^ 2)) - 10 * exp(-0.2 * sqrt(x[i,2] ^2 + x[i,3] ^ 2))
      k2 <- abs(x[i,1]) ^ 0.8 + 5 * sin(x[i,1] ^ 3) + abs(x[i,2]) ^ 0.8 + 5 * sin(x[i,2] ^3) + abs(x[i,3]) ^ 0.8 + 5 * sin(x[i,3] ^ 3)
      return(c(k1, k2))
    }

Two objectives are evaluated here and a vector of the corresponding values is returned for the individual x[i,].

# User-defined mode

If the value of carallel is 2 then the entire population is given to the R user function and one has to decide how to evaluate it. For instance hereafter with a simple for-loop:

    kursawe <- function(x) { # receipt of the entire population
      popsize <- dim(x)[1] # size of the population to evaluate
      nobj <- 2 # number of objectives
      results <- matrix(0, nrow = popsize, ncol = nobj) # matrix of results
      for(i in 1:popsize){
          k1 <- -10 * exp(-0.2 * sqrt(x[i,1] ^ 2 + x[i,2] ^ 2)) - 10 * exp(-0.2 * sqrt(x[i,2] ^2 + x[i,3] ^ 2))
          k2 <- abs(x[i,1]) ^ 0.8 + 5 * sin(x[i,1] ^ 3) + abs(x[i,2]) ^ 0.8 + 5 * sin(x[i,2] ^3) + abs(x[i,3]) ^ 0.8 + 5 * sin(x[i,3] ^ 3)
          results[i,] <- c(k1, k2)
      }
      return(results)
    }