rmoo (version 0.2.0)

nsga2: Non-Dominated Sorting in Genetic Algorithms II

Description

Minimization of a fitness function using non-dominated sorting genetic algorithms - II (NSGA-IIs). Multiobjective evolutionary algorithms

Usage

nsga2(
  type = c("binary", "real-valued", "permutation"),
  fitness,
  ...,
  lower,
  upper,
  nBits,
  population = nsgaControl(type)$population,
  selection = nsgaControl(type)$selection,
  crossover = nsgaControl(type)$crossover,
  mutation = nsgaControl(type)$mutation,
  popSize = 50,
  nObj = ncol(fitness(matrix(10000, ncol = 100, nrow = 100))),
  pcrossover = 0.8,
  pmutation = 0.1,
  maxiter = 100,
  run = maxiter,
  maxFitness = Inf,
  names = NULL,
  suggestions = NULL,
  monitor = if (interactive()) nsgaMonitor else FALSE,
  summary = FALSE,
  seed = NULL
)

Value

Returns an object of class nsga2-class. See nsga2 for a description of available slots information.

Arguments

type

the type of genetic algorithm to be run depending on the nature of decision variables. Possible values are:

'binary'

for binary representations of decision variables.

'real-valued'

for optimization problems where the decision variables are floating-point representations of real numbers.

'permutation'

for problems that involves reordering of a list of objects.

fitness

the fitness function, any allowable R function which takes as input an individual string representing a potential solution, and returns a numerical value describing its 'fitness'.

...

additional arguments to be passed to the fitness function. This allows to write fitness functions that keep some variables fixed during the search

lower

a vector of length equal to the decision variables providing the lower bounds of the search space in case of real-valued or permutation encoded optimizations.

upper

a vector of length equal to the decision variables providing the upper bounds of the search space in case of real-valued or permutation encoded optimizations.

nBits

a value specifying the number of bits to be used in binary encoded optimizations

population

an R function for randomly generating an initial population. See nsga_Population() for available functions.

selection

an R function performing selection, i.e. a function which generates a new population of individuals from the current population probabilistically according to individual fitness. See nsga_Selection() for available functions.

crossover

an R function performing crossover, i.e. a function which forms offsprings by combining part of the genetic information from their parents. See nsga_Crossover() for available functions.

mutation

an R function performing mutation, i.e. a function which randomly alters the values of some genes in a parent chromosome. See nsga_Mutation() for available functions.

popSize

the population size.

nObj

number of objective in the fitness function.

pcrossover

the probability of crossover between pairs of chromosomes. Typically this is a large value and by default is set to 0.8.

pmutation

the probability of mutation in a parent chromosome. Usually mutation occurs with a small probability, and by default is set to 0.1.

maxiter

the maximum number of iterations to run before the NSGA search is halted.

run

the number of consecutive generations without any improvement in the best fitness value before the NSGA is stopped

maxFitness

the upper bound on the fitness function after that the NSGA search is interrupted.

names

a vector of character strings providing the names of decision variables.

suggestions

a matrix of solutions strings to be included in the initial population. If provided the number of columns must match the number of decision variables.

monitor

a logical or an R function which takes as input the current state of the nsga-class object and show the evolution of the search. By default, for interactive sessions the function nsgaMonitor prints the average and best fitness values at each iteration. If set to plot these information are plotted on a graphical device. Other functions can be written by the user and supplied as argument. In non interactive sessions, by default monitor = FALSE so any output is suppressed.

summary

If there will be a summary generation after generation.

seed

an integer value containing the random number generator state. This argument can be used to replicate the results of a NSGA search. Note that if parallel computing is required, the doRNG package must be installed.

Author

Francisco Benitez

Details

The Non-dominated genetic algorithms II is a meta-heuristic proposed by K. Deb, A. Pratap, S. Agarwal and T. Meyarivan in 2002. The purpose of the algorithms is to find an efficient way to optimize multi-objectives functions (two or more).

References

K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, 'A fast and elitist multiobjective genetic algorithm: NSGA-II,' in IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182-197, April 2002, doi: 10.1109/4235.996017.

Scrucca, L. (2017) On some extensions to 'GA' package: hybrid optimisation, parallelisation and islands evolution. The R Journal, 9/1, 187-206. doi: 10.32614/RJ-2017-008

See Also

nsga(), nsga3()

Examples

#Example
#Two Objectives - Real Valued
zdt1 <- function (x) {
 if (is.null(dim(x))) {
   x <- matrix(x, nrow = 1)
 }
 n <- ncol(x)
 g <- 1 + rowSums(x[, 2:n, drop = FALSE]) * 9/(n - 1)
 return(cbind(x[, 1], g * (1 - sqrt(x[, 1]/g))))
}

#Not run:
if (FALSE) {
result <- nsga2(type = "real-valued",
                fitness = zdt1,
                lower = c(0,0),
                upper = c(1,1),
                popSize = 100,
                monitor = FALSE,
                maxiter = 500)
}

#Example 2
#Three Objectives - Real Valued
dtlz1 <- function (x, nobj = 3){
    if (is.null(dim(x))) {
        x <- matrix(x, 1)
    }
    n <- ncol(x)
    y <- matrix(x[, 1:(nobj - 1)], nrow(x))
    z <- matrix(x[, nobj:n], nrow(x))
    g <- 100 * (n - nobj + 1 + rowSums((z - 0.5)^2 - cos(20 * pi * (z - 0.5))))
    tmp <- t(apply(y, 1, cumprod))
    tmp <- cbind(t(apply(tmp, 1, rev)), 1)
    tmp2 <- cbind(1, t(apply(1 - y, 1, rev)))
    f <- tmp * tmp2 * 0.5 * (1 + g)
    return(f)
}

#Not run:
if (FALSE) {
result <- nsga2(type = "real-valued",
                fitness = dtlz1,
                lower = c(0,0,0), upper = c(1,1,1),
                popSize = 92,
                monitor = FALSE,
                maxiter = 500)
}