rmoo_func {rmoo}

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 nsga(), nsga2(), nsga3().

Usage

rmoo(...)

Arguments

...

argument in which all the values necessary for the configuration will be passed as parameters. The user is encouraged to see the documentations of nsga(), nsga2(), 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.

Details

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

The original Non-dominated Sorting Genetic Slgorithms (NSGA-I)is a meta-heuristic proposed by N. Srinivas and K. Deb in 1994. The purpose of the algorithms is to find an efficient way to optimize multi-objectives functions (two or more).

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).

Value

Returns an object of class ga-class, nsga1-class, nsga2-class or nsga3-class. See nsga1, nsga2, nsga3 for a description of available slots information.

Author(s)

Francisco Benitez [e-mail]

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

N. Srinivas and K. Deb, "Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms, in Evolutionary Computation, vol. 2, no. 3, pp. 221-248, Sept. 1994, doi: 10.1162/evco.1994.2.3.221.

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

nsga(), nsga2(), 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:
## Not run: 
result <- rmoo(type = "real-valued",
               fitness = zdt1,
               strategy = "NSGA-I",
               lower = c(0,0),
               upper = c(1,1),
               popSize = 100,
               dshare = 1,
               monitor = FALSE,
               maxiter = 500)


## 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)
}

#Not run:
## Not run: 
result <- rmoo(type = "real-valued",
                fitness = dtlz1,
                strategy = "NSGA-II",
                lower = c(0,0,0),
                upper = c(1,1,1),
                popSize = 92,
                monitor = FALSE,
                maxiter = 500)

## End(Not run)
#Example 3
#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
## Not run: 
result <- rmoo(type = "real-valued",
                fitness = zdt1,
                strategy = "NSGA-III",
                lower = c(0,0),
                upper = c(1,1),
                popSize = 100,
                n_partitions = 100,
                monitor = FALSE,
                maxiter = 500)


## End(Not run)

#Example 4
#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
## Not run: 
result <- rmoo(type = "real-valued",
                fitness = dtlz1,
                strategy = "NSGA-III",
                lower = c(0,0,0),
                upper = c(1,1,1),
                popSize = 92,
                n_partitions = 12,
                monitor = FALSE,
                maxiter = 500)

## End(Not run)

#Example 5
#Single Objective - Real Valued
f <- function(x,  ...)  (x^2+x)*cos(x)

#Not Run
## Not run: 
result <- rmoo(type = "real-valued",
               fitness = f,
               strategy = "GA",
               lower = -20,
               upper = 20,
               maxiter = 100)

## End(Not run)