Description Usage Arguments Details Value References Examples
Setup a GAReal
object that can be used to perform
a real-based optimization.
1 2 3 4 5 |
FUN |
The fitness function, which should take a vector as argument and return a numeric value (See details). |
lb |
A numeric vector specifying the lower bounds for the search domain. |
ub |
A numeric vector specifying the upper bounds for the search domain. |
popSize |
The population size. |
mutRate |
The mutation rate, a numeric value between 0 and 1. When implementing a custom mutation function, this value should be one of the parameters (see details and examples). |
cxRate |
The crossover rate, a numeric value between 0 and 1. This parameter specifies the probability of two individuals effectively exchange DNA during crossover. In case the individuals didn't crossover, the offspring is a exact copy of the parents. When implementing a custom crossover function, this value should be one of the arguments (see details and examples). |
eliteRate |
A numeric value between 0 and 1. The
|
selection |
The selection operator to be used. You can also implement a custom selection function (see details and examples). |
crossover |
The crossover operator to be used. You can also implement a custom crossover function (see details and examples). |
mutation |
The mutation operator to be used. You can also implement a custom mutation function (see details and examples). |
This is the function used to configure and fine-tune a
real-based optimization. The basic usage requires only
the FUN
parameter (function to be maximized),
together with the lb
and ub
parameters
(lower and upper search domain), all the other parameters
have sensible defaults.
The parameters selection
, crossover
and
mutation
can also take a custom function as
argument, which needs to be in the appropriate format
(see the examples). The text below explains the default
behaviour for these parameters, which will be usefull if
you want to override one or more genetic operators.
selection
: The fitness
option performs a fitness-proportionate selection,
so that the fittest individuals will have greater chances
of being selected. If you choose this option, the value
returned by FUN
(the fitness value) should be
non-negative. The uniform
option will
randomly sample the individuals to mate, regardless of
their fitness value. See the examples if you want to
implement a custom selection function.
crossover
: The blend
option
will perform a linear combination of the individuals DNA,
effectively introducing new information into the
resulting offspring. For details, see Practical
genetic algorithms in the references. The
two.points
option will perform the classic 2-point
crossover. See the examples if you need to implement a
custom crossover function.
mutation
: The default
implementation will uniformly sample n
mutation
points along the population matrix, where n
is
given by mutRate * popSize * nvars
and
nvars
is the number of variables in your problem.
Each sampled locus will be replaced by a
random-uniform number between 0 and 1. See the examples
to learn how to use a custom mutation function.
An object of class GAReal
, which you can pass as
an argument to plot
or summary
. This object
is a list with the following accessor functions:
bestFit : | Returns a vector with the best fitness achieved in each generation. |
meanFit : | Returns a vector with the mean fitness achieved in each generation. |
bestIndividual : | Returns a vector with the best solution found. |
evolve(h) : | This is the function you call to evolve your population. |
You also need to specify the number of generations to evolve. | |
population : | Returns the current population matrix. |
Randy L. Haupt, Sue Ellen Haupt (2004). Practical genetic algorithms - 2nd ed.
Michalewicz, Zbigniew. Genetic Algorithms + Data Structures = Evolution Programs - 3rd ed.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 | # Maximize a trivial 5 variable function
# The function and search-space below will be used for all examples
fitness.FUN = function(x) sum(x)
lb = c(0, 0, 0, 0, 0)
ub = c(10, 10, 10, 10, 10)
ga1 = GAReal(fitness.FUN, lb, ub)
ga1$evolve(200)
plot(ga1)
# A custom selection example
selec.FUN = function(population, fitnessVec, nleft)
{
# population - The population matrix
# fitnessVec - The corresponding fitness vector for the population matrix
# nleft - The number of individuals you should select
half = as.integer(nleft/2)
remain = nleft - half
idxs = 1:nrow(population)
# pick half using fitness-proportionate
rowIdxs = sample(idxs, half, replace = TRUE, prob = fitnessVec)
# pick the other half randomly
rowIdxs = c(rowIdxs, sample(idxs, remain, replace = TRUE))
# Just return the nLeft selected row indexes
return(rowIdxs)
}
ga2 = GAReal(fitness.FUN, lb, ub, selection = selec.FUN)
ga2$evolve(200)
summary(ga2)
# A custom crossover example
crossover.FUN = function(parent1, parent2, prob)
{
# parent1, parent2 - The individuals to crossover
# prob - The probability of a crossover happen (cxRate parameter)
# Respect the cxRate parameter: if DNA is not exchanged, just return the parents
if (runif(1) > prob)
return(matrix(c(parent1, parent2), nrow = 2, byrow = TRUE))
# A simple uniform crossover - just swap the 'genes' with a probability of 0.5
for (i in 1:length(parent1))
{
if (runif(1) > 0.5)
{
tempval = parent1[i]
parent1[i] = parent2[i]
parent2[i] = tempval
}
}
# You should return a matrix in this format
return(matrix(c(parent1, parent2), nrow = 2, byrow = TRUE))
}
ga3 = GAReal(fitness.FUN, lb, ub, crossover = crossover.FUN)
ga3$evolve(200)
plot(ga3)
# A custom mutation example
mutation.FUN = function(population, nMut)
{
# population - The population matrix to apply mutation
# nMut - The number of mutations you supposed to apply, according to mutRate
rows = sample(1:nrow(population), nMut, replace = TRUE)
cols = sample(1:ncol(population), nMut, replace = TRUE)
noise = (runif(nMut))^2
# extract the matrix indexes
ext = matrix(c(rows, cols), nMut, 2)
population[ext] = noise
return(population)
}
ga4 = GAReal(fitness.FUN, lb, ub, mutation = mutation.FUN)
ga4$evolve(200)
summary(ga4)
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