nsga2: NSGA II MOEA

In mco: Multi criteria optimization algorithms and related functions

Description

Multicriterion optimization algorithm

Usage

nsga2(fn, idim, odim, ..., constraints = NULL, cdim = 0, lower.bounds = rep(-Inf, idim), upper.bounds = rep(Inf, idim), popsize = 100, generations = 100, cprob = 0.7, cdist = 5, mprob = 0.2, mdist = 10)

Arguments

fn	Function
idim	Input dimension
odim	Output dimension
...	Arguments passed through to 'fn'
constraints	Constraint function
cdim	Constraint dimension
lower.bounds	Lower bound of input
upper.bounds	Upper bound of input
popsize	Size of population
generations	Number of generations to breed. If a vector, then the result will contain the population at each given generation.
cprob	Crossing probability
cdist	Crossing distribution index
mprob	Mutation probability
mdist	Mutation distribution index

Value

If generation is an integer, a list describing the final population with components par, value and pareto.optimal. If generations is a vector, a list is returned. The i-th element of the list contains the population after generations[i] generations.

Author(s)

Heike Trautmann [e-mail], Detlef Steuer [e-mail] and Olaf Mersmann [e-mail]

References

Deb, K., Pratap, A., and Agarwal, S.. A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6 (8) (2002), 182-197.

Examples

## Binh 1 problem:
binh1 <- function(x) {
  y <- numeric(2)
  y[1] <- crossprod(x, x)
  y[2] <- crossprod(x - 5, x - 5)
  return (y)
}
r1 <- nsga2(binh1, 2, 2,
           generations=150, popsize=100,
           cprob=0.7, cdist=20,
           mprob=0.2, mdist=20,
           lower.bounds=rep(-5, 2),
           upper.bounds=rep(10, 2))
plot(r1)

## VNT problem:
vnt <- function(x) {  
  y <- numeric(3)
  xn <- crossprod(x, x)
  y[1] <- xn/2 + sin(xn);
  y[2] <- (crossprod(c(3, -2), x) + 4)^2/8 + (crossprod(c(1, -1), x) + 1)^2/27 + 15
  y[3] <- 1/(xn + 1) - 1.1*exp(-xn)
  return (y)
}

r2 <- nsga2(vnt, 2, 3,
           generations=150, popsize=100,
           lower.bounds=rep(-3, 2),
           upper.bounds=rep(3, 2))
plot(r2)

Example output

Loading required package: scatterplot3d

mco documentation built on May 2, 2019, 5:01 p.m.