knitr::opts_chunk$set(echo = TRUE)
caRamel is a multiobjective evolutionary algorithm combining the MEAS algorithm and the NGSA-II algorithm.
Download the package from CRAN or GitHub and then install and load it.
Dealing with constraints is possible with caRamel by returning a NaN value for an infeasible solution. See the example below.
library(caRamel)
Constr-Ex test function has two objectives with two variables and two inequality constraints.
constr_ex <- function(i) { # functions f1 and f2 s1 <- x[i,1] s2 <- (1. + x[i,2]) / x[i,1] # now test for the feasibility # constraint g1 if((x[i,2] + 9. * x[i,1] - 6.) < 0. | (-x[i,2] + 9. * x[i,1] -1.) < 0.) { s1 <- NaN s2 <- NaN } return(c(s1, s2)) }
Note that :
The variable lies in the range [0.1, 1] and [0, 5]:
nvar <- 2 # number of variables bounds <- matrix(data = 0., nrow = nvar, ncol = 2) # upper and lower bounds bounds[1, 1] <- 0.1 bounds[1, 2] <- 1. bounds[2, 1] <- 0. bounds[2, 2] <- 5.
Both functions are to be minimized:
nobj <- 2 # number of objectives minmax <- c(FALSE, FALSE) # min and min
Before calling caRamel in order to optimize the Constr_Ex problem, some algorithmic parameters need to be set:
popsize <- 100 # size of the genetic population archsize <- 100 # size of the archive for the Pareto front maxrun <- 1000 # maximum number of calls prec <- matrix(1.e-3, nrow = 1, ncol = nobj) # accuracy for the convergence phase
Then the minimization problem can be launched:
results <- caRamel(nobj, nvar, minmax, bounds, constr_ex, popsize, archsize, maxrun, prec, carallel=FALSE) # no parallelism
Test if the convergence is successful:
print(results$success==TRUE)
Plot the Pareto front:
plot(results$objectives[,1], results$objectives[,2], main="Constr_Ex Pareto front", xlab="Objective #1", ylab="Objective #2")
plot(results$parameters, main="Corresponding values for X", xlab="Element of the archive", ylab="X Variable")
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