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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) |