Genetic Algorithm (GA)¶

Implementar el Algoritmo Genético simple con las siguientes características:

1. Codificación binaria
2. Selección: ruleta
3. Cruza en un punto
4. Mutación aleatoria
5. La probabilidad de cruza, probabilidad de mutación, tamaño de la población y número de generación quedan a su elección.
6. Precisión de 3 dígitos decimales.

Se deben usar las siguientes funciones de optimización de un solo objetivo para minimización:

1. Esfera (n=2 y n=5) ; -10≤x≤10

2. Bukin (x, y) ; -15≤x≤-5 ; -3≤y≤-3

3. Himmenblau (x, y); -5≤x,y≤5

4. Eggholder (x, y); -512≤x,y≤512

5. [Opcional] Easom (x, y); -100≤x,y≤100

In [1]:

from metazoo.bio.evolutionary import GeneticAlgorithm
from metazoo.bio.evolutionary.operators import selection, mutation, crossover
from metazoo.gym.mono import Function

from metazoo.bio.utils import encoding

# Set offline plotly
import plotly.io as pio
pio.renderers.default = "svg"

from metazoo.bio.evolutionary import GeneticAlgorithm from metazoo.bio.evolutionary.operators import selection, mutation, crossover from metazoo.gym.mono import Function from metazoo.bio.utils import encoding # Set offline plotly import plotly.io as pio pio.renderers.default = "svg"

In [2]:

targets = ['Sphere', 'Bukin', 'Himmelblau', 'EggHolder', 'Easom']

targets = ['Sphere', 'Bukin', 'Himmelblau', 'EggHolder', 'Easom']

In [3]:

mutation_function = mutation.flip_bit

mutation_function = mutation.flip_bit

In [4]:

fitness_function = Function(targets[0], reverse=False)
encoder = encoding.Binary(precision=3, bounds=fitness_function.bounds)

ga = GeneticAlgorithm(
    fitness_function=fitness_function,
    crossover_function=crossover.onepoint,
    mutation_function=mutation_function,
    selection_function=selection.roulette,
    population_size=100,
    mutation_rate=0.01,
    crossover_rate=0.7,
    encoder=encoder,
    elitism=False,
    minimize=True,
)

ga.run(generations=100)

print(f'Best Individual: {ga.best_individual}')
print(f'Best Fitness: {ga.best_fitness}')

best = ga.best_individual.reshape(1, -1)

fig1 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='surface', population=best)
fig2 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='contour', population=best)

fig1.show()
fig2.show()

fitness_function = Function(targets[0], reverse=False) encoder = encoding.Binary(precision=3, bounds=fitness_function.bounds) ga = GeneticAlgorithm( fitness_function=fitness_function, crossover_function=crossover.onepoint, mutation_function=mutation_function, selection_function=selection.roulette, population_size=100, mutation_rate=0.01, crossover_rate=0.7, encoder=encoder, elitism=False, minimize=True, ) ga.run(generations=100) print(f'Best Individual: {ga.best_individual}') print(f'Best Fitness: {ga.best_fitness}') best = ga.best_individual.reshape(1, -1) fig1 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='surface', population=best) fig2 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='contour', population=best) fig1.show() fig2.show()

Output()

Best Individual: [-0.00531282  0.01906366]
Best Fitness: 0.00039164936980193234

In [5]:

fitness_function = Function(targets[0], reverse=True)
encoder = encoding.Binary(precision=3, bounds=[(-5.12, 5.12), (-5.12, 5.12), (-5.12, 5.12), (-5.12, 5.12), (-5.12, 5.12)])

ga = GeneticAlgorithm(
    fitness_function=fitness_function,
    crossover_function=crossover.onepoint,
    mutation_function=mutation_function,
    selection_function=selection.roulette,
    population_size=100,
    mutation_rate=0.01,
    crossover_rate=0.7,
    encoder=encoder,
    elitism=False,
    minimize=True,
)

ga.run(generations=100)

print(f"Shape: {ga.best_individual.shape}")
print(f'Best Individual: {ga.best_individual}')
print(f'Best Fitness: {ga.best_fitness}')

best = ga.best_individual.reshape(1, -1)

fitness_function = Function(targets[0], reverse=True) encoder = encoding.Binary(precision=3, bounds=[(-5.12, 5.12), (-5.12, 5.12), (-5.12, 5.12), (-5.12, 5.12), (-5.12, 5.12)]) ga = GeneticAlgorithm( fitness_function=fitness_function, crossover_function=crossover.onepoint, mutation_function=mutation_function, selection_function=selection.roulette, population_size=100, mutation_rate=0.01, crossover_rate=0.7, encoder=encoder, elitism=False, minimize=True, ) ga.run(generations=100) print(f"Shape: {ga.best_individual.shape}") print(f'Best Individual: {ga.best_individual}') print(f'Best Fitness: {ga.best_fitness}') best = ga.best_individual.reshape(1, -1)

Output()

Shape: (5,)
Best Individual: [ 5.11812489  5.10312397 -4.98749191  5.10874931 -5.10437405]
Best Fitness: -129.2661061231976

In [6]:

fitness_function = Function(targets[1], reverse=False)
encoder = encoding.Binary(precision=3, bounds=fitness_function.bounds)

ga = GeneticAlgorithm(
    fitness_function=fitness_function,
    crossover_function=crossover.onepoint,
    mutation_function=mutation_function,
    selection_function=selection.roulette,
    population_size=100,
    mutation_rate=0.01,
    crossover_rate=0.7,
    encoder=encoder,
    elitism=False,
    minimize=True,
)

ga.run(generations=100)

print(f'Best Individual: {ga.best_individual}')
print(f'Best Fitness: {ga.best_fitness}')

best = ga.best_individual.reshape(1, -1)

fig1 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='surface', population=best)
fig2 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='contour', population=best)

fig1.show()
fig2.show()

fitness_function = Function(targets[1], reverse=False) encoder = encoding.Binary(precision=3, bounds=fitness_function.bounds) ga = GeneticAlgorithm( fitness_function=fitness_function, crossover_function=crossover.onepoint, mutation_function=mutation_function, selection_function=selection.roulette, population_size=100, mutation_rate=0.01, crossover_rate=0.7, encoder=encoder, elitism=False, minimize=True, ) ga.run(generations=100) print(f'Best Individual: {ga.best_individual}') print(f'Best Fitness: {ga.best_fitness}') best = ga.best_individual.reshape(1, -1) fig1 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='surface', population=best) fig2 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='contour', population=best) fig1.show() fig2.show()

Output()

Best Individual: [-13.95013123   1.94598059]
Best Fitness: 0.9396385788307542

In [7]:

fitness_function = Function(targets[2], reverse=False)
encoder = encoding.Binary(precision=3, bounds=fitness_function.bounds)

ga = GeneticAlgorithm(
    fitness_function=fitness_function,
    crossover_function=crossover.onepoint,
    mutation_function=mutation_function,
    selection_function=selection.roulette,
    population_size=100,
    mutation_rate=0.01,
    crossover_rate=0.7,
    encoder=encoder,
    elitism=False,
    minimize=True,
)

ga.run(generations=100)

print(f'Best Individual: {ga.best_individual}')
print(f'Best Fitness: {ga.best_fitness}')

best = ga.best_individual.reshape(1, -1)

fig1 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='surface', population=best)
fig2 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='contour', population=best)

fig1.show()
fig2.show()

fitness_function = Function(targets[2], reverse=False) encoder = encoding.Binary(precision=3, bounds=fitness_function.bounds) ga = GeneticAlgorithm( fitness_function=fitness_function, crossover_function=crossover.onepoint, mutation_function=mutation_function, selection_function=selection.roulette, population_size=100, mutation_rate=0.01, crossover_rate=0.7, encoder=encoder, elitism=False, minimize=True, ) ga.run(generations=100) print(f'Best Individual: {ga.best_individual}') print(f'Best Fitness: {ga.best_fitness}') best = ga.best_individual.reshape(1, -1) fig1 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='surface', population=best) fig2 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='contour', population=best) fig1.show() fig2.show()

Output()

Best Individual: [-2.81297687  3.13037905]
Best Fitness: 0.0020555828097402243

In [8]:

fitness_function = Function(targets[3], reverse=False)
encoder = encoding.Binary(precision=3, bounds=fitness_function.bounds)

ga = GeneticAlgorithm(
    fitness_function=fitness_function,
    crossover_function=crossover.onepoint,
    mutation_function=mutation_function,
    selection_function=selection.roulette,
    population_size=100,
    mutation_rate=0.01,
    crossover_rate=0.7,
    encoder=encoder,
    elitism=False,
    minimize=True,
)

ga.run(generations=100)

print(f'Best Individual: {ga.best_individual}')
print(f'Best Fitness: {ga.best_fitness}')

best = ga.best_individual.reshape(1, -1)

fig1 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='surface', population=best)
fig2 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='contour', population=best)

fig1.show()
fig2.show()

fitness_function = Function(targets[3], reverse=False) encoder = encoding.Binary(precision=3, bounds=fitness_function.bounds) ga = GeneticAlgorithm( fitness_function=fitness_function, crossover_function=crossover.onepoint, mutation_function=mutation_function, selection_function=selection.roulette, population_size=100, mutation_rate=0.01, crossover_rate=0.7, encoder=encoder, elitism=False, minimize=True, ) ga.run(generations=100) print(f'Best Individual: {ga.best_individual}') print(f'Best Fitness: {ga.best_fitness}') best = ga.best_individual.reshape(1, -1) fig1 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='surface', population=best) fig2 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=100, mode='contour', population=best) fig1.show() fig2.show()

Output()

Best Individual: [510.93163961 403.51747467]
Best Fitness: -955.7702119015352

In [9]:

fitness_function = Function(targets[4], reverse=False)
encoder = encoding.Binary(precision=3, bounds=fitness_function.bounds)

ga = GeneticAlgorithm(
    fitness_function=fitness_function,
    crossover_function=crossover.onepoint,
    mutation_function=mutation_function,
    selection_function=selection.roulette,
    population_size=100,
    mutation_rate=0.01,
    crossover_rate=0.7,
    encoder=encoder,
    elitism=False,
    minimize=True,
)

ga.run(generations=200)

print(f'Best Individual: {ga.best_individual}')
print(f'Best Fitness: {ga.best_fitness}')

best = ga.best_individual.reshape(1, -1)

fig1 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=300, mode='surface', population=best)
fig2 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=300, mode='contour', population=best)

fig1.show()
fig2.show()

fitness_function = Function(targets[4], reverse=False) encoder = encoding.Binary(precision=3, bounds=fitness_function.bounds) ga = GeneticAlgorithm( fitness_function=fitness_function, crossover_function=crossover.onepoint, mutation_function=mutation_function, selection_function=selection.roulette, population_size=100, mutation_rate=0.01, crossover_rate=0.7, encoder=encoder, elitism=False, minimize=True, ) ga.run(generations=200) print(f'Best Individual: {ga.best_individual}') print(f'Best Fitness: {ga.best_fitness}') best = ga.best_individual.reshape(1, -1) fig1 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=300, mode='surface', population=best) fig2 = fitness_function.plot(bounds=fitness_function.bounds, dim=2, num_points=300, mode='contour', population=best) fig1.show() fig2.show()

Output()

Best Individual: [ 2.96212373 -3.37029789]
Best Fitness: -3.5594754561549357e-19