gena.hybrid {gena}

Hybridization

Description

Hybridization method (algorithm) to be used in the genetic algorithm.

Usage

gena.hybrid(
  population,
  fitness,
  hybrid.n = 1,
  method,
  par,
  opt.par,
  info = FALSE,
  iter = NULL,
  ...
)

Arguments

population

numeric matrix which rows are chromosomes i.e. vectors of parameters values.

fitness

numeric vector which i-th element is the value of fn at point population[i, ].

hybrid.n

positive integer representing the number of hybrids.

method

hybridization method to improve chromosomes via local search.

par

additional parameters to be passed depending on the method.

opt.par

parameters of the local optimization function to be used for hybridization algorithm (including fn and gr).

info

logical; if TRUE then some optimization related information will be printed each iteration.

iter

iteration number of the genetic algorithm.

...

additional parameters to be passed to fn and gr functions.

Details

This function uses gena.mating function to select hybrids. Therefore method and par arguments will be passed to this function. If some chromosomes selected to become hybrids are duplicated then these duplicates will not be subject to local optimization i.e. the number of hybrids will be decreased by the number of duplicates (actual number of hybrids during some iterations may be lower than hybrid.n).

Currently optim is the only available local optimizer. Therefore opt.par is a list containing parameters that should be passed to optim.

For more information on hybridization please see El-mihoub et. al. (2006).

Value

The function returns a list with the following elements:

• population - matrix which rows are chromosomes including hybrids.

• fitness - vector which i-th element is the fitness of the i-th chromosome.

• hybrids.ind - vector of indexes of chromosomes selected for hybridization.

• counts a two-element integer vector giving the number of calls to fn and gr respectively.

References

T. El-mihoub, A. Hopgood, L. Nolle, B. Alan (2006). Hybrid Genetic Algorithms: A Review. Engineering Letters, 13 (3), 124-137.

Examples

# Consider the following fitness function
fn <- function(x)
{
  val <- x[1] * x[2] - x[1] ^ 2 - x[2] ^ 2
}

# Also let's provide it's gradient (optional)
gr <- function(x)
{
  val <- c(x[2] - 2 * x[1],
           x[1] - 2 * x[2])
}

# Randomly initialize the population
set.seed(123)
n_population <- 10
population <- gena.population(pop.n = n_population,
                              lower = c(-5, -5), 
                              upper = c(5, 5))

# Calculate fitness of each chromosome
fitness <- rep(NA, n_population)
for(i in 1:n_population)
{
  fitness[i] <- fn(population[i, ])
}

# Perform hybridization
hybrids <- gena.hybrid(population = population,
                       fitness = fitness,
                       opt.par = list(fn = fn,
                                      gr = gr,
                                      method = "BFGS",
                                      control = list(fnscale = -1,
                                                     abstol = 1e-10,
                                                     reltol = 1e-10,
                                                     maxit = 1000)),
                       hybrid.n = 2,
                       method = "rank",
                       par = 0.8)
print(hybrids)