rnsga2: Reference Point Based Non-Dominated Sorting in Genetic...

In benitezfj/rmoo: Multi-Objective Optimization in R

Reference Point Based Non-Dominated Sorting in Genetic Algorithms II

Description

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

Usage

rnsga2(
  type = c("binary", "real-valued", "permutation"),
  fitness,
  ...,
  lower,
  upper,
  nBits,
  population = rmooControl(type)$population,
  selection = rmooControl(type)$selection,
  crossover = rmooControl(type)$crossover,
  mutation = rmooControl(type)$mutation,
  reference_dirs = NULL,
  epsilon = 0.001,
  normalization = c("ever", "front", "no"),
  extreme_points_as_ref_dirs = FALSE,
  weights = NULL,
  popSize = 50,
  nObj = NULL,
  pcrossover = 0.8,
  pmutation = 0.1,
  maxiter = 100,
  run = maxiter,
  maxFitness = Inf,
  names = NULL,
  suggestions = NULL,
  parallel = FALSE,
  monitor = if (interactive()) rmooMonitor else FALSE,
  summary = FALSE,
  seed = NULL
)

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 rmoo_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 rmoo_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 rmoo_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 rmoo_Mutation() for available functions.
reference_dirs	Function to generate reference points using Das and Dennis approach or matrix with supplied reference points.
epsilon	controls the extent of obtained solutions by grouping all solutions that have a normalized difference sum in objective values of epsilon or less.
normalization	of the ideal points and nadir. They can be: 'ever' . 'front' . 'no' .
extreme_points_as_ref_dirs	flag to use extreme points as reference points.
weights	vector specifies the importance of one objective function over the other, by default all objectives have equal weights.
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.
parallel	An optional argument which allows to specify if the NSGA-II should be run sequentially or in parallel.
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 rmooMonitor 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.

Details

R-NSGA-II is a meta-heuristic proposed by K. Deb and J. Sundar in 2006. It is a modification of NSGA-II based on reference points in which the decision-maker supplies one or more preference points and a weight vector that will guide the solutions towards regions desired by the user.

Value

Returns an object of class rnsga2-class. See rnsga2 for a description of available slots information.

Author(s)

Francisco Benitez [e-mail]

References

Kalyanmoy Deb and J. Sundar. 2006. Reference point based multi-objective optimization using evolutionary algorithms. In Proceedings of the 8th annual conference on Genetic and evolutionary computation (GECCO '06). Association for Computing Machinery, New York, NY, USA, 635–642. doi: 10.1145/1143997.1144112

See Also

nsga(), nsga2(), 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))))
}

#Define the reference points
reference_points = rbind(c(0.2, 0.8), c(0.8, 0.2), c(0.4, 0.5))

#Not run:
## Not run: 
result <- rnsga2(type = "real-valued",
                fitness = zdt1,
                lower = c(0,0),
                upper = c(1,1),
                reference_dirs = reference_points,
                popSize = 100,
                nObj = 2,
                monitor = FALSE,
                maxiter = 500,
                seed = 45)

## End(Not run)

#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)
}

#Define the reference points
reference_points <- rbind(c(1.0, 0.5, 0.0), c(0.0, 0.5, 1.0), c(0.5, 0.5, 0.5))

#Not run:
## Not run: 
result <- rnsga2(type = "real-valued",
                fitness = dtlz1,
                lower = c(0,0,0),
                upper = c(1,1,1),
                reference_dirs = reference_points,
                popSize = 92,
                nObj = 3,
                monitor = FALSE,
                maxiter = 500)

## End(Not run)

benitezfj/rmoo documentation built on Oct. 23, 2024, 9:15 p.m.