# Multi-caRamel optimization with MPI

#### Fabrice Zaoui

#### March 02 2021

# 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 pbdMPI package in order to use several processes of caRamel. Download the package from CRAN and then install and load it. Make also sure that you have an MPI distribution installed on your system, see for instance Open MPI if necessary.

    library(pbdMPI)

Kursawe test function has two objectives of three variables.

    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))
    }

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) # minimization for both functions

Set algorithmic parameters for 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

# Combining distributed and shared memory parallelism

The caRamel parameters carallel and numcores help to define the shared memory parallelism used to evaluate by the user’s function each member of the genetic population.

The shared memory parallelism runs on a single computational node (or workstation). For instance 20 cores can be defined with the following call:

    results <-
      caRamel(nobj,
              nvar,
              minmax,
              bounds,
              kursawe,
              popsize,
              archsize,
              maxrun,
              prec,
              carallel = 1,
              numcores = 20,
              graph = FALSE,
              verbose = FALSE)

For calling several times caRamel on a distributed memory cluster of computers (or nodes) MPI is used.

At the end of the script, the different results of optimizations can be gathered with:

    init()  # MPI functions from the pbdMPI package
    size <- comm.size()
    rank <- comm.rank()

    results <- gather(optres, rank.dest = 0)  # gather all results on the main process

    if (rank == 0) saveRDS(results, "Results.Rds")  # save all the results on disk

    finalize()

Finally, the previous script can be launched in parallel on a number of nodes, for instance 4 nodes:

    mpirun -n 4 Rscript --vanilla my_kursawe_optim.R