rmoo (version 0.3.2)

rmoo_main: R Multi-Objective Optimization Main Function

Description

Main function of rmoo, based on the parameters it will call the different algorithms implemented in the package. Optimization algorithms will minimize a fitness function. For more details of the algorithms see nsga2(), nsga3(), rnsga2().

Usage

rmoo(
  type = c("binary", "real-valued", "permutation", "discrete"),
  algorithm = c("NSGA-II", "NSGA-III", "R-NSGA-II"),
  fitness,
  ...,
  lower,
  upper,
  nBits,
  nvars,
  population = rmooControl(type)$population,
  selection = rmooControl(type)$selection,
  crossover = rmooControl(type)$crossover,
  mutation = rmooControl(type)$mutation,
  pcrossover = 0.8,
  pmutation = 0.1,
  popSize = 50,
  maxiter = 100,
  nObj = NULL,
  names = NULL,
  suggestions = NULL,
  monitor = if (interactive()) rmooMonitor else FALSE,
  parallel = FALSE,
  summary = FALSE,
  seed = NULL,
  reference_dirs = NULL,
  epsilon = 0.001,
  normalization = NULL,
  extreme_points_as_ref_dirs = FALSE,
  weights = NULL
)

Value

Returns an object of class nsga2-class, rnsga2-class or nsga3-class. See nsga2, rnsga2, nsga3 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.

'discrete'

for discrete representations of decision variables.

algorithm

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

'NSGA-II'

for .

'NSGA-III'

for .

'R-NSGA-II'

for .

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'.

...

argument in which all the values necessary for the configuration will be passed as parameters. The user is encouraged to see the documentations.

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.

nvars

a value .

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.

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.

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.

popSize

the population size.

maxiter

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

nObj

number of objective in the fitness function.

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 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.

parallel

An optional argument which allows to specify if the NSGA-II should be run sequentially or in parallel.

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.

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. of nsga2(), rnsga2(), nsga3() in which the necessary parameters for each algorithm are cited, in addition, the chosen strategy to execute must be passed as an argument. This can be seen more clearly in the examples.

Author

Francisco Benitez

Details

Multi- and Many-Optimization of a fitness function using Non-dominated Sorting Genetic Algorithms. The algorithms currently implemented by rmoo are: NSGA-II, NSGA-III and R-NSGA-II

The Non-dominated genetic algorithms II (NSGA-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).

The Non-dominated genetic algorithms III (NSGA-III) is a meta-heuristic proposed by K. Deb and H. Jain in 2013. The purpose of the algorithms is to find an efficient way to optimize multi-objectives functions (more than three).

The Reference point-based Non-dominated genetic algorithms II (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.

References

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

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

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.

K. Deb and H. Jain, "An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints," in IEEE Transactions on Evolutionary Computation, vol. 18, no. 4, pp. 577-601, Aug. 2014, doi: 10.1109/TEVC.2013.2281535.

See Also

nsga2(), rnsga2(), nsga3()

Examples

#Example 1
#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 <- rmoo(type = "real-valued",
               fitness = zdt1,
               algorithm = "NSGA-II",
               lower = c(0,0),
               upper = c(1,1),
               popSize = 100,
               nObj = 2,
               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)
}

#Define uniformly distributed reference points.
ref_points <- generate_reference_points(3,12)

#Not Run
if (FALSE) {
result <- rmoo(type = "real-valued",
                fitness = dtlz1,
                algorithm = "NSGA-III",
                lower = c(0,0,0),
                upper = c(1,1,1),
                popSize = 92,
                nObj = 3,
                reference_dirs = ref_points,
                monitor = FALSE,
                maxiter = 500)
}

#Example 3
#Two Objectives - Real Valued with Preference-guided
zdt2 <- 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 - (x[, 1]/g)^2)))
}

#Define uniformly distributed reference points.
ref_points <- rbind(c(1.0, 0.0), c(0.0, 1.0), c(0.5, 0.5))

#Not run
if (FALSE) {
result <- rmoo(type = "real-valued",
               fitness = zdt2,
               algorithm = "R-NSGA-II",
               lower = c(0,0),
               upper = c(1,1),
               reference_dirs = ref_points,
               popSize = 92,
               nObj = 2,
               monitor = FALSE,
               maxiter = 500)

}