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from math import factorial
import random
import matplotlib.pyplot as plt
import numpy
import pymop.factory
from deap import algorithms
from deap import base
from deap.benchmarks.tools import igd
from deap import creator
from deap import tools
# Problem definition
PROBLEM = "dtlz2"
NOBJ = 3
K = 10
NDIM = NOBJ + K - 1
P = 12
H = factorial(NOBJ + P - 1) / (factorial(P) * factorial(NOBJ - 1))
BOUND_LOW, BOUND_UP = 0.0, 1.0
problem = pymop.factory.get_problem(PROBLEM, n_var=NDIM, n_obj=NOBJ)
##
# Algorithm parameters
MU = int(H + (4 - H % 4))
NGEN = 400
CXPB = 1.0
MUTPB = 1.0
##
# Create uniform reference point
ref_points = tools.uniform_reference_points(NOBJ, P)
# Create classes
creator.create("FitnessMin", base.Fitness, weights=(-1.0,) * NOBJ)
creator.create("Individual", list, fitness=creator.FitnessMin)
##
# Toolbox initialization
def uniform(low, up, size=None):
try:
return [random.uniform(a, b) for a, b in zip(low, up)]
except TypeError:
return [random.uniform(a, b) for a, b in zip([low] * size, [up] * size)]
toolbox = base.Toolbox()
toolbox.register("attr_float", uniform, BOUND_LOW, BOUND_UP, NDIM)
toolbox.register("individual", tools.initIterate, creator.Individual, toolbox.attr_float)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)
toolbox.register("evaluate", problem.evaluate, return_values_of=["F"])
toolbox.register("mate", tools.cxSimulatedBinaryBounded, low=BOUND_LOW, up=BOUND_UP, eta=30.0)
toolbox.register("mutate", tools.mutPolynomialBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0, indpb=1.0/NDIM)
toolbox.register("select", tools.selNSGA3, ref_points=ref_points)
##
def main(seed=None):
random.seed(seed)
# Initialize statistics object
stats = tools.Statistics(lambda ind: ind.fitness.values)
stats.register("avg", numpy.mean, axis=0)
stats.register("std", numpy.std, axis=0)
stats.register("min", numpy.min, axis=0)
stats.register("max", numpy.max, axis=0)
logbook = tools.Logbook()
logbook.header = "gen", "evals", "std", "min", "avg", "max"
pop = toolbox.population(n=MU)
# Evaluate the individuals with an invalid fitness
invalid_ind = [ind for ind in pop if not ind.fitness.valid]
fitnesses = toolbox.map(toolbox.evaluate, invalid_ind)
for ind, fit in zip(invalid_ind, fitnesses):
ind.fitness.values = fit
# Compile statistics about the population
record = stats.compile(pop)
logbook.record(gen=0, evals=len(invalid_ind), **record)
print(logbook.stream)
# Begin the generational process
for gen in range(1, NGEN):
offspring = algorithms.varAnd(pop, toolbox, CXPB, MUTPB)
# Evaluate the individuals with an invalid fitness
invalid_ind = [ind for ind in offspring if not ind.fitness.valid]
fitnesses = toolbox.map(toolbox.evaluate, invalid_ind)
for ind, fit in zip(invalid_ind, fitnesses):
ind.fitness.values = fit
# Select the next generation population from parents and offspring
pop = toolbox.select(pop + offspring, MU)
# Compile statistics about the new population
record = stats.compile(pop)
logbook.record(gen=gen, evals=len(invalid_ind), **record)
print(logbook.stream)
return pop, logbook
if __name__ == "__main__":
pop, stats = main()
pop_fit = numpy.array([ind.fitness.values for ind in pop])
pf = problem.pareto_front(ref_points)
print(igd(pop_fit, pf))
import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d as Axes3d
fig = plt.figure(figsize=(7, 7))
ax = fig.add_subplot(111, projection="3d")
p = numpy.array([ind.fitness.values for ind in pop])
ax.scatter(p[:, 0], p[:, 1], p[:, 2], marker="o", s=24, label="Final Population")
ax.scatter(pf[:, 0], pf[:, 1], pf[:, 2], marker="x", c="k", s=32, label="Ideal Pareto Front")
ref_points = tools.uniform_reference_points(NOBJ, P)
ax.scatter(ref_points[:, 0], ref_points[:, 1], ref_points[:, 2], marker="o", s=24, label="Reference Points")
ax.view_init(elev=11, azim=-25)
ax.autoscale(tight=True)
plt.legend()
plt.tight_layout()
plt.savefig("nsga3.png")
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