knitr::opts_chunk$set(echo = TRUE)
caRamel is a multiobjective evolutionary algorithm combining the MEAS algorithm and the NGSA-II algorithm.
Download the package from CRAN or GitHub and then install and load it.
library(caRamel)
The Kursawe test function to optimize has two objectives and three variables.
kursawe <- function(i) { k1 <- -10 * exp(-0.2 * sqrt(x[i,1] ^ 2 + x[i,2] ^ 2)) - 10 * exp(-0.2 * sqrt(x[i,2] ^2 + x[i,3] ^ 2)) k2 <- abs(x[i,1]) ^ 0.8 + 5 * sin(x[i,1] ^ 3) + abs(x[i,2]) ^ 0.8 + 5 * sin(x[i,2] ^3) + abs(x[i,3]) ^ 0.8 + 5 * sin(x[i,3] ^ 3) return(c(k1, k2)) }
For instance, the following caRamel parameters for all the Kursawe optimizations can be:
nvar <- 3 # number of variables bounds <- matrix(data = 1, nrow = nvar, ncol = 2) # upper and lower bounds bounds[, 1] <- -5 * bounds[, 1] bounds[, 2] <- 5 * bounds[, 2] nobj <- 2 # number of objectives minmax <- c(FALSE, FALSE) # minimization for both objectives popsize <- 100 # size of the genetic population archsize <- 100 # size of the archive for the Pareto front maxrun <- 1000 # maximum number of calls prec <- matrix(1.e-3, nrow = 1, ncol = nobj) # convergence criteria
In this part we will run caRamel three times on the Kursawe test function and save all the front results.
nrepeat <- 3 # number of calls to caRamel concat_results_objectives <- NULL # save results for all the calls concat_results_parameters <- NULL for (i in seq(nrepeat)) { optres <- caRamel(nobj, nvar, minmax, bounds, kursawe, popsize, archsize, maxrun, prec, carallel = 0, graph = FALSE, verbose = FALSE) concat_results_objectives <- rbind(concat_results_objectives, optres$objectives) concat_results_parameters <- rbind(concat_results_parameters, optres$parameters) }
Then all the results are reduced using the pareto function in order to get a new global front:
results_objectives <- concat_results_objectives results_objectives[, !minmax] <- -results_objectives[, !minmax] # important ! is_pareto <- pareto(results_objectives) # mask global_results_objectives <- concat_results_objectives[is_pareto, ] # front from the three previous fronts global_results_parameters <- concat_results_parameters[is_pareto, ]
All the results can now be plotted:
plot(concat_results_objectives[, 1], concat_results_objectives[, 2], main = "Kursawe Pareto fronts", xlab = "Objective #1", ylab = "Objective #2") points(global_results_objectives[, 1], global_results_objectives[, 2], col = "red", pch = "*")
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