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358 lines (302 loc) · 16.3 KB
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"""
The pygad.utils.crossover module has all the built-in crossover operators.
"""
import numpy
class Crossover:
def __init__():
pass
def single_point_crossover(self, parents, offspring_size):
"""
Apply single-point crossover between pairs of parents. One
random split point is picked per offspring; the genes before
the point come from the first parent and the genes from the
point onward come from the second parent.
Parameters
----------
parents : numpy.ndarray
A 2D array of parent solutions, one row per parent.
offspring_size : tuple
``(num_offspring, num_genes)``. Shape of the offspring
array to return.
Returns
-------
offspring : numpy.ndarray
A 2D array of the produced offspring with shape
``offspring_size``.
"""
offspring = self.initialize_parents_array(offspring_size)
# Randomly generate all the K points at which crossover takes place between each two parents. The point does not have to be always at the center of the solutions.
# This saves time by calling the self.numpy_random_generator.randint() function only once.
crossover_points = self.numpy_random_generator.randint(low=0,
high=parents.shape[1],
size=offspring_size[0])
for k in range(offspring_size[0]):
# Check if the crossover_probability parameter is used.
if not (self.crossover_probability is None):
probs = self.numpy_random_generator.random(size=parents.shape[0])
indices = list(set(numpy.where(probs < self.crossover_probability)[0]))
# If no parent satisfied the probability, no crossover is applied and a parent is selected as is.
if len(indices) == 0:
offspring[k, :] = parents[k % parents.shape[0], :]
continue
elif len(indices) == 1:
parent1_idx = indices[0]
parent2_idx = parent1_idx
else:
indices = self.python_random_generator.sample(indices, 2)
parent1_idx = indices[0]
parent2_idx = indices[1]
else:
# Index of the first parent to mate.
parent1_idx = k % parents.shape[0]
# Index of the second parent to mate.
parent2_idx = (k+1) % parents.shape[0]
# The first half of the offspring's genes comes from the first parent.
offspring[k, 0:crossover_points[k]] = parents[parent1_idx, 0:crossover_points[k]]
# The second half of the offspring's genes comes from the second parent.
offspring[k, crossover_points[k]:] = parents[parent2_idx, crossover_points[k]:]
if self.allow_duplicate_genes == False:
offspring[k], _, _ = self.solve_duplicate_genes(solution=offspring[k])
return offspring
def two_points_crossover(self, parents, offspring_size):
"""
Apply two-points crossover. Two split points are picked per
offspring; the genes outside ``[point1, point2)`` come from the
first parent and the genes inside come from the second parent.
Parameters
----------
parents : numpy.ndarray
A 2D array of parent solutions, one row per parent.
offspring_size : tuple
``(num_offspring, num_genes)``. Shape of the offspring
array to return.
Returns
-------
offspring : numpy.ndarray
A 2D array of the produced offspring with shape
``offspring_size``.
"""
offspring = self.initialize_parents_array(offspring_size)
# Randomly generate all the K pairs of points at which crossover takes place between each two parents.
# This saves time by calling the self.numpy_random_generator.randint() function only twice.
# The 2 points of a pair are different values in [0, num_genes], and every such pair is equally likely.
# If the chromosome has only a single gene, the points are 0 and 1: the gene is copied from the second parent.
points_a = self.numpy_random_generator.randint(low=0,
high=parents.shape[1] + 1,
size=offspring_size[0])
points_b = self.numpy_random_generator.randint(low=0,
high=parents.shape[1],
size=offspring_size[0])
# Skip the value of the first point so that the 2 points differ.
points_b[points_b >= points_a] += 1
# The second point must always be greater than the first point.
crossover_points_1 = numpy.minimum(points_a, points_b)
crossover_points_2 = numpy.maximum(points_a, points_b)
for k in range(offspring_size[0]):
if not (self.crossover_probability is None):
probs = self.numpy_random_generator.random(size=parents.shape[0])
indices = list(set(numpy.where(probs < self.crossover_probability)[0]))
# If no parent satisfied the probability, no crossover is applied and a parent is selected.
if len(indices) == 0:
offspring[k, :] = parents[k % parents.shape[0], :]
continue
elif len(indices) == 1:
parent1_idx = indices[0]
parent2_idx = parent1_idx
else:
indices = self.python_random_generator.sample(indices, 2)
parent1_idx = indices[0]
parent2_idx = indices[1]
else:
# Index of the first parent to mate.
parent1_idx = k % parents.shape[0]
# Index of the second parent to mate.
parent2_idx = (k+1) % parents.shape[0]
# The genes from the beginning of the chromosome up to the first point are copied from the first parent.
offspring[k, 0:crossover_points_1[k]] = parents[parent1_idx, 0:crossover_points_1[k]]
# The genes from the second point up to the end of the chromosome are copied from the first parent.
offspring[k, crossover_points_2[k]:] = parents[parent1_idx, crossover_points_2[k]:]
# The genes between the 2 points are copied from the second parent.
offspring[k, crossover_points_1[k]:crossover_points_2[k]] = parents[parent2_idx, crossover_points_1[k]:crossover_points_2[k]]
if self.allow_duplicate_genes == False:
offspring[k], _, _ = self.solve_duplicate_genes(solution=offspring[k])
return offspring
def uniform_crossover(self, parents, offspring_size):
"""
Apply uniform crossover. For each gene independently, the value
is copied from one of the two mating parents picked at random.
Parameters
----------
parents : numpy.ndarray
A 2D array of parent solutions, one row per parent.
offspring_size : tuple
``(num_offspring, num_genes)``. Shape of the offspring
array to return.
Returns
-------
offspring : numpy.ndarray
A 2D array of the produced offspring with shape
``offspring_size``.
"""
offspring = self.initialize_parents_array(offspring_size)
# Randomly generate all the genes sources at which crossover takes place between each two parents.
# This saves time by calling the self.numpy_random_generator.randint() function only once.
# There is a list of 0 and 1 for each offspring.
# [0, 1, 0, 0, 1, 1]: If the value is 0, then take the gene from the first parent. If 1, take it from the second parent.
genes_sources = self.numpy_random_generator.randint(low=0,
high=2,
size=offspring_size)
for k in range(offspring_size[0]):
if not (self.crossover_probability is None):
probs = self.numpy_random_generator.random(size=parents.shape[0])
indices = list(set(numpy.where(probs < self.crossover_probability)[0]))
# If no parent satisfied the probability, no crossover is applied and a parent is selected.
if len(indices) == 0:
offspring[k, :] = parents[k % parents.shape[0], :]
continue
elif len(indices) == 1:
parent1_idx = indices[0]
parent2_idx = parent1_idx
else:
indices = self.python_random_generator.sample(indices, 2)
parent1_idx = indices[0]
parent2_idx = indices[1]
else:
# Index of the first parent to mate.
parent1_idx = k % parents.shape[0]
# Index of the second parent to mate.
parent2_idx = (k+1) % parents.shape[0]
# The gene will be copied from the first parent if the current gene index is 0.
# The gene will be copied from the second parent if the current gene index is 1.
offspring[k, :] = numpy.where(genes_sources[k] == 0,
parents[parent1_idx, :],
parents[parent2_idx, :])
if self.allow_duplicate_genes == False:
offspring[k], _, _ = self.solve_duplicate_genes(solution=offspring[k])
return offspring
def sbx_crossover(self, parents, offspring_size):
"""
Apply Simulated Binary Crossover (SBX). For each gene, the
offspring value is drawn from a distribution centered on the
parents. The spread of this distribution is set by
``self.sbx_crossover_eta`` (a higher value means the child
stays closer to the parents).
The bounded form is used. The per-gene bounds come from
``get_initial_population_range``.
Parameters
----------
parents : numpy.ndarray
A 2D array of parent solutions, one row per parent.
offspring_size : tuple
(num_offspring, num_genes). Shape of the offspring array
to return.
Returns
-------
offspring : numpy.ndarray
A 2D array of offspring with shape offspring_size.
"""
offspring = self.initialize_parents_array(offspring_size)
eta = float(self.sbx_crossover_eta)
near_zero = 1e-14
for k in range(offspring_size[0]):
if not (self.crossover_probability is None):
probs = self.numpy_random_generator.random(size=parents.shape[0])
indices = list(set(numpy.where(probs < self.crossover_probability)[0]))
if len(indices) == 0:
offspring[k, :] = parents[k % parents.shape[0], :]
continue
elif len(indices) == 1:
parent1_idx = indices[0]
parent2_idx = parent1_idx
else:
indices = self.python_random_generator.sample(indices, 2)
parent1_idx = indices[0]
parent2_idx = indices[1]
else:
parent1_idx = k % parents.shape[0]
parent2_idx = (k + 1) % parents.shape[0]
for gene_idx in range(offspring_size[1]):
range_min, range_max = self.get_bounded_operator_gene_range(gene_idx)
lower, upper = float(range_min), float(range_max)
p1 = float(numpy.clip(parents[parent1_idx, gene_idx], lower, upper))
p2 = float(numpy.clip(parents[parent2_idx, gene_idx], lower, upper))
y1 = min(p1, p2)
y2 = max(p1, p2)
if y2 - y1 < near_zero:
# The two parents have the same value on this gene.
offspring[k, gene_idx] = self.convert_bounded_operator_gene_value(gene_idx, p1)
continue
# Beta is the spread factor that controls how far the
# child can move away from the parents.
beta = 1.0 + 2.0 * min(y1 - lower, upper - y2) / (y2 - y1)
alpha = 2.0 - pow(beta, -(eta + 1.0))
rand_u = self.numpy_random_generator.random()
if rand_u <= 1.0 / alpha:
beta_q = pow(rand_u * alpha, 1.0 / (eta + 1.0))
else:
beta_q = pow(1.0 / (2.0 - rand_u * alpha), 1.0 / (eta + 1.0))
# SBX makes 2 children, symmetric around the parents' mean.
# Pick one of them at random so that the child is not always below the mean.
if self.numpy_random_generator.random() < 0.5:
child = 0.5 * ((y1 + y2) - beta_q * (y2 - y1))
else:
child = 0.5 * ((y1 + y2) + beta_q * (y2 - y1))
child = numpy.clip(child, lower, upper)
offspring[k, gene_idx] = self.convert_bounded_operator_gene_value(gene_idx, child)
offspring[k] = self.prepare_bounded_operator_solution(parents[parent1_idx], offspring[k])
return offspring
def scattered_crossover(self, parents, offspring_size):
"""
Apply scattered crossover. For each gene independently, the
value is copied from one of the two mating parents picked at
random. (Same mechanic as ``uniform_crossover`` but kept as a
separate operator for backwards compatibility.)
Parameters
----------
parents : numpy.ndarray
A 2D array of parent solutions, one row per parent.
offspring_size : tuple
``(num_offspring, num_genes)``. Shape of the offspring
array to return.
Returns
-------
offspring : numpy.ndarray
A 2D array of the produced offspring with shape
``offspring_size``.
"""
offspring = self.initialize_parents_array(offspring_size)
# Randomly generate all the genes sources at which crossover takes place between each two parents.
# This saves time by calling the self.numpy_random_generator.randint() function only once.
# There is a list of 0 and 1 for each offspring.
# [0, 1, 0, 0, 1, 1]: If the value is 0, then take the gene from the first parent. If 1, take it from the second parent.
genes_sources = self.numpy_random_generator.randint(low=0,
high=2,
size=offspring_size)
for k in range(offspring_size[0]):
if not (self.crossover_probability is None):
probs = self.numpy_random_generator.random(size=parents.shape[0])
indices = list(set(numpy.where(probs < self.crossover_probability)[0]))
# If no parent satisfied the probability, no crossover is applied and a parent is selected.
if len(indices) == 0:
offspring[k, :] = parents[k % parents.shape[0], :]
continue
elif len(indices) == 1:
parent1_idx = indices[0]
parent2_idx = parent1_idx
else:
indices = self.python_random_generator.sample(indices, 2)
parent1_idx = indices[0]
parent2_idx = indices[1]
else:
# Index of the first parent to mate.
parent1_idx = k % parents.shape[0]
# Index of the second parent to mate.
parent2_idx = (k+1) % parents.shape[0]
# The gene will be copied from the first parent if the current gene index is 0.
# The gene will be copied from the second parent if the current gene index is 1.
offspring[k, :] = numpy.where(genes_sources[k] == 0,
parents[parent1_idx, :],
parents[parent2_idx, :])
if self.allow_duplicate_genes == False:
offspring[k], _, _ = self.solve_duplicate_genes(solution=offspring[k])
return offspring