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using StatsBase
using PyPlot
#=
Parents <— {randomly generated population}
While not (termination criterion)
Calculate the fitness of each parent in the population
Children <- 0
While | Children | < | Parents |
Use fitnesses to probabilistically select a pair of parents for mating
Mate the parents to create children c\ and c<i
Children <— Children U {ci,C2}
Loop
Randomly mutate some of the children
Parents <— Children
Next generation
Use continuous GA, not binary
include array of independent variables along with associated range
=#
function initialize_population(populationSize::Int, chromosomeSize::Int, bounds::Array{Tuple{Float64, Float64},1})
"""
Initializes the population based on the given population size and chromosome size
Values will be from lb to ub (lower to upper bound)
"""
# Check to see if we dont have enough bounds or have too many
if length(bounds) != chromosomeSize
println("Length of bounds ($(length(bounds))) not equal to specified chromosome size ($chromosomeSize)")
exit()
end
# Init population
population = Array{Array{Float64}}(0)
# Foreach member in population
for i = 1:populationSize
# Init the member
row = []
# Create member elements based on bounds
for bound in bounds
push!(row, rand(bound[1]:0.01:bound[2]))
end
# Add another element to the end to keep score
push!(row, 1.0)
# hcat row, append to 2D population matrix
population = push!(population, row)
end
return population
end
function score_sort_population(population::Array{Array{Float64}}, fitness_function::Function)
"""
Args
population: The population to score. Must be 2D array of Float64 elements
fitness_function: Function to score the population
Must be able to take array as argument
For example f(x,y) should be f(A) where A[1]=x, A[2]=y
Returns scored population. Score is the last element of each chromosome (row)
in population
"""
# Enumerate through population, set last element of each chromosome to score
for (index,member) in enumerate(population)
population[index][end] = fitness_function(member)
end
sort!(population, by = x -> x[end])
return population
end
function create_next_generation(population::Array{Array{Float64}}, recombRate::Float64)
"""
Creates children given a population and recombination rate
Uses an elite selection of 0.10 (rounded up)
Creates random chance
TODO: Implement ranking
"""
popSize = length(population)
memberSize = length(population[1])
# Init children array
children = Array{Array{Float64}}(0)
# Elite selection
for i in 1:Int(ceil(popSize*0.10))
push!(children, population[i])
end
# Generate rest of population
while length(children) < popSize
# Two random children
choices = sample(1:popSize, 2, replace=false)
# Check for crossover
if rand() < recombRate
# Choose xover point
# Use -2 since last one is score, and last actual element cant be crossedover since that means there is none
xover = rand(1:memberSize-2)
child1 = cat(1,population[choices[1]][1:xover],population[choices[2]][xover+1:end])
child2 = cat(1,population[choices[2]][1:xover],population[choices[1]][xover+1:end])
else
# Else no crossover, just copy
child1 = population[choices[1]]
child2 = population[choices[2]]
end
# Push child 1 and 2 to children array
push!(children, child1, child2)
end
# We might have one extra due to rounding in the elite selection, let's check
if length(children) != popSize
pop!(children)
end
return children
end
function mutate(population::Array{Array{Float64}}, mutateRate::Float64, bounds::Array{Tuple{Float64, Float64},1})
"""
Iterates through each chromosome and mutates if needed
"""
for member in population
for i = 1:length(member)-1
if rand() < mutateRate
member[i] = rand(bounds[i][1]:0.01:bounds[i][2])
end
end
end
return population
end
function GA(populationSize::Int, chromosomeSize::Int, fitness_function::Function, bounds::Array{Tuple{Float64, Float64},1})
"""
Args
populationSize: Total number of chromosomes
chromosomeSize: How long each chromosome should be (variables in fitness function)
fitness_function: Function to determine fitness of each solution
Should take an array as an arg
Example: f(x,y,z) = x+y+z
should be f(X) = X[1]+X[2]+X[3]
in order to allow GA to take in any function with any
amount of args to the fitness function
bounds: 1D array of tuples, each tuple is the (lower, upper) bounds
for each variable. Both lower and upper need to be Float64 types
Length should match chromosomeSize
e.g: [(1.0,2.0), (3.5,4.5)]
"""
# Set recombination and mutation rate, lower and upper bound
recombRate = 0.7
mutateRate = 0.05
maxIterations = 100
runs = 20
# First initialize the population
# Then loop for the required iterations
# Initialize iteration counter, run counter, and array to hold generations of best population
i = 0
run = 0
bestGenerations = [[[0.0,0.0,Inf]]]
generations = Array{Array{Array{Float64}}}(0)
# For each run
while run < runs
nextPopulation = initialize_population(populationSize, chromosomeSize, bounds)
# Iterate through max amount of generations
while i < maxIterations
# Score and sort the population
population = score_sort_population(nextPopulation, fitness_function)
# Push current population to generations array
push!(generations, deepcopy(population))
# Create children
nextPopulation = create_next_generation(population, recombRate)
# Mutate children
nextPopulation = mutate(nextPopulation, mutateRate, bounds)
i += 1
end
#=
At the end of the run, if the last generations best solution
# is better than that of the best of all runs so far
set new best run so we can graph later
=#
if generations[end][1][end] < bestGenerations[end][1][end]
bestGenerations = deepcopy(generations)
end
clear!(:generations)
clear!(:population)
run += 1
end
# Reporting and plotting
# Report best solution and value
bestVariables = bestGenerations[end][1][1:end-1]
bestScore = bestGenerations[end][1][end]
println("Best solution\nVariables: $bestVariables\nScore: $bestScore")
# Generate best fitness vs. # generation
# Init score array
y = Array{Float64}(0)
# Get scores, push to array
for g in bestGenerations
push!(y,g[1][end])
end
# Plot and label
PyPlot.plot(y)
xlabel("Generation #")
ylabel("Fitness")
# Save and close
PyPlot.savefig("BestFitness.png")
PyPlot.close()
# Contour
# Check to make sure we only have two variables, otherwise exit
if length(bestGenerations[1][1]) > 3
println("Plotting the 4th dimension currently disabled to avoid tearing the space-time continuum")
quit()
end
# Pick X and Y range for contour plot based on bounds
xrange = bounds[1][1]:0.01:bounds[1][2]
yrange = bounds[2][1]:0.01:bounds[2][2]
size = length(xrange)
# Init z array for values of fitness function
z = zeros(size,size)
for i in 1:size
for j in 1:size
# Generate a z value for each x and y value
z[i,j] = fitness_function([xrange[i],yrange[j]])
end
end
# If we are at 1st gen or evry 10th, plot
for (index, gen) in enumerate(bestGenerations)
if (index == 1) || (mod(index,10) == 0)
# Re-init x and y for the generation
x = Array{Float64}(0)
y = Array{Float64}(0)
# Push x and y to separate arrays
for m in gen
push!(x,m[1])
push!(y,m[2])
end
# Plt the contour plot
contour(xrange,yrange,z)
# Then plot the scatter underneath
scatter(x,y)
title("Generation $index")
savefig("contour_gen$index.png")
close()
end
end
end
function fitness_function(X)
return e - 20*exp(-0.2*sqrt((X[1]^2 + X[2]^2)/2)) - exp((cos(2*pi*X[1]) + cos(2*pi*X[2]))/2)
end
bounds = [(-2.0,2.0), (-2.0,2.0)]
GA(25,2,fitness_function,bounds)
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