Genetic Algorithm setup

Description

Setup a GAReal object that can be used to perform a real-based optimization.

Usage

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  GAReal(FUN, lb, ub, popSize = 100, mutRate = 0.01,
    cxRate = 0.9, eliteRate = 0.4,
    selection = c("fitness", "uniform"),
    crossover = c("blend", "two.points"),
    mutation = c("noise"))

Arguments

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 eliteRate * popSize best-fitted individuals will automatically be selected for the next generation.

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).

Details

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.

Value

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.

References

Randy L. Haupt, Sue Ellen Haupt (2004). Practical genetic algorithms - 2nd ed.

Michalewicz, Zbigniew. Genetic Algorithms + Data Structures = Evolution Programs - 3rd ed.

Examples

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# 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)