# Source code for deap.tools.crossover

import random
import warnings

try:
from collections.abc import Sequence
except ImportError:
from collections import Sequence

from itertools import repeat

######################################
# GA Crossovers                      #
######################################

[docs]def cxOnePoint(ind1, ind2):
"""Executes a one point crossover on the input :term:sequence individuals.
The two individuals are modified in place. The resulting individuals will
respectively have the length of the other.

:param ind1: The first individual participating in the crossover.
:param ind2: The second individual participating in the crossover.
:returns: A tuple of two individuals.

This function uses the :func:~random.randint function from the
python base :mod:random module.
"""
size = min(len(ind1), len(ind2))
cxpoint = random.randint(1, size - 1)
ind1[cxpoint:], ind2[cxpoint:] = ind2[cxpoint:], ind1[cxpoint:]

return ind1, ind2

[docs]def cxTwoPoint(ind1, ind2):
"""Executes a two-point crossover on the input :term:sequence
individuals. The two individuals are modified in place and both keep
their original length.

:param ind1: The first individual participating in the crossover.
:param ind2: The second individual participating in the crossover.
:returns: A tuple of two individuals.

This function uses the :func:~random.randint function from the Python
base :mod:random module.
"""
size = min(len(ind1), len(ind2))
cxpoint1 = random.randint(1, size)
cxpoint2 = random.randint(1, size - 1)
if cxpoint2 >= cxpoint1:
cxpoint2 += 1
else:  # Swap the two cx points
cxpoint1, cxpoint2 = cxpoint2, cxpoint1

ind1[cxpoint1:cxpoint2], ind2[cxpoint1:cxpoint2] \
= ind2[cxpoint1:cxpoint2], ind1[cxpoint1:cxpoint2]

return ind1, ind2

[docs]def cxTwoPoints(ind1, ind2):
"""
.. deprecated:: 1.0
The function has been renamed.  Use :func:~deap.tools.cxTwoPoint instead.
"""
warnings.warn("tools.cxTwoPoints has been renamed. Use cxTwoPoint instead.",
FutureWarning)
return cxTwoPoint(ind1, ind2)

[docs]def cxUniform(ind1, ind2, indpb):
"""Executes a uniform crossover that modify in place the two
:term:sequence individuals. The attributes are swapped according to the
*indpb* probability.

:param ind1: The first individual participating in the crossover.
:param ind2: The second individual participating in the crossover.
:param indpb: Independent probability for each attribute to be exchanged.
:returns: A tuple of two individuals.

This function uses the :func:~random.random function from the python base
:mod:random module.
"""
size = min(len(ind1), len(ind2))
for i in range(size):
if random.random() < indpb:
ind1[i], ind2[i] = ind2[i], ind1[i]

return ind1, ind2

[docs]def cxPartialyMatched(ind1, ind2):
"""Executes a partially matched crossover (PMX) on the input individuals.
The two individuals are modified in place. This crossover expects
:term:sequence individuals of indices, the result for any other type of
individuals is unpredictable.

:param ind1: The first individual participating in the crossover.
:param ind2: The second individual participating in the crossover.
:returns: A tuple of two individuals.

Moreover, this crossover generates two children by matching
pairs of values in a certain range of the two parents and swapping the values
of those indexes. For more details see [Goldberg1985]_.

This function uses the :func:~random.randint function from the python base
:mod:random module.

.. [Goldberg1985] Goldberg and Lingel, "Alleles, loci, and the traveling
salesman problem", 1985.
"""
size = min(len(ind1), len(ind2))
p1, p2 = [0] * size, [0] * size

# Initialize the position of each indices in the individuals
for i in range(size):
p1[ind1[i]] = i
p2[ind2[i]] = i
# Choose crossover points
cxpoint1 = random.randint(0, size)
cxpoint2 = random.randint(0, size - 1)
if cxpoint2 >= cxpoint1:
cxpoint2 += 1
else:  # Swap the two cx points
cxpoint1, cxpoint2 = cxpoint2, cxpoint1

# Apply crossover between cx points
for i in range(cxpoint1, cxpoint2):
# Keep track of the selected values
temp1 = ind1[i]
temp2 = ind2[i]
# Swap the matched value
ind1[i], ind1[p1[temp2]] = temp2, temp1
ind2[i], ind2[p2[temp1]] = temp1, temp2
# Position bookkeeping
p1[temp1], p1[temp2] = p1[temp2], p1[temp1]
p2[temp1], p2[temp2] = p2[temp2], p2[temp1]

return ind1, ind2

[docs]def cxUniformPartialyMatched(ind1, ind2, indpb):
"""Executes a uniform partially matched crossover (UPMX) on the input
individuals. The two individuals are modified in place. This crossover
expects :term:sequence individuals of indices, the result for any other
type of individuals is unpredictable.

:param ind1: The first individual participating in the crossover.
:param ind2: The second individual participating in the crossover.
:returns: A tuple of two individuals.

Moreover, this crossover generates two children by matching
pairs of values chosen at random with a probability of *indpb* in the two
parents and swapping the values of those indexes. For more details see
[Cicirello2000]_.

This function uses the :func:~random.random and :func:~random.randint
functions from the python base :mod:random module.

.. [Cicirello2000] Cicirello and Smith, "Modeling GA performance for
control parameter optimization", 2000.
"""
size = min(len(ind1), len(ind2))
p1, p2 = [0] * size, [0] * size

# Initialize the position of each indices in the individuals
for i in range(size):
p1[ind1[i]] = i
p2[ind2[i]] = i

for i in range(size):
if random.random() < indpb:
# Keep track of the selected values
temp1 = ind1[i]
temp2 = ind2[i]
# Swap the matched value
ind1[i], ind1[p1[temp2]] = temp2, temp1
ind2[i], ind2[p2[temp1]] = temp1, temp2
# Position bookkeeping
p1[temp1], p1[temp2] = p1[temp2], p1[temp1]
p2[temp1], p2[temp2] = p2[temp2], p2[temp1]

return ind1, ind2

[docs]def cxOrdered(ind1, ind2):
"""Executes an ordered crossover (OX) on the input
individuals. The two individuals are modified in place. This crossover
expects :term:sequence individuals of indices, the result for any other
type of individuals is unpredictable.

:param ind1: The first individual participating in the crossover.
:param ind2: The second individual participating in the crossover.
:returns: A tuple of two individuals.

Moreover, this crossover generates holes in the input
individuals. A hole is created when an attribute of an individual is
between the two crossover points of the other individual. Then it rotates
the element so that all holes are between the crossover points and fills
them with the removed elements in order. For more details see
[Goldberg1989]_.

This function uses the :func:~random.sample function from the python base
:mod:random module.

.. [Goldberg1989] Goldberg. Genetic algorithms in search,
optimization and machine learning. Addison Wesley, 1989
"""
size = min(len(ind1), len(ind2))
a, b = random.sample(range(size), 2)
if a > b:
a, b = b, a

holes1, holes2 = [True] * size, [True] * size
for i in range(size):
if i < a or i > b:
holes1[ind2[i]] = False
holes2[ind1[i]] = False

# We must keep the original values somewhere before scrambling everything
temp1, temp2 = ind1, ind2
k1, k2 = b + 1, b + 1
for i in range(size):
if not holes1[temp1[(i + b + 1) % size]]:
ind1[k1 % size] = temp1[(i + b + 1) % size]
k1 += 1

if not holes2[temp2[(i + b + 1) % size]]:
ind2[k2 % size] = temp2[(i + b + 1) % size]
k2 += 1

# Swap the content between a and b (included)
for i in range(a, b + 1):
ind1[i], ind2[i] = ind2[i], ind1[i]

return ind1, ind2

[docs]def cxBlend(ind1, ind2, alpha):
"""Executes a blend crossover that modify in-place the input individuals.
The blend crossover expects :term:sequence individuals of floating point
numbers.

:param ind1: The first individual participating in the crossover.
:param ind2: The second individual participating in the crossover.
:param alpha: Extent of the interval in which the new values can be drawn
for each attribute on both side of the parents' attributes.
:returns: A tuple of two individuals.

This function uses the :func:~random.random function from the python base
:mod:random module.
"""
for i, (x1, x2) in enumerate(zip(ind1, ind2)):
gamma = (1. + 2. * alpha) * random.random() - alpha
ind1[i] = (1. - gamma) * x1 + gamma * x2
ind2[i] = gamma * x1 + (1. - gamma) * x2

return ind1, ind2

[docs]def cxSimulatedBinary(ind1, ind2, eta):
"""Executes a simulated binary crossover that modify in-place the input
individuals. The simulated binary crossover expects :term:sequence
individuals of floating point numbers.

:param ind1: The first individual participating in the crossover.
:param ind2: The second individual participating in the crossover.
:param eta: Crowding degree of the crossover. A high eta will produce
children resembling to their parents, while a small eta will
produce solutions much more different.
:returns: A tuple of two individuals.

This function uses the :func:~random.random function from the python base
:mod:random module.
"""
for i, (x1, x2) in enumerate(zip(ind1, ind2)):
rand = random.random()
if rand <= 0.5:
beta = 2. * rand
else:
beta = 1. / (2. * (1. - rand))
beta **= 1. / (eta + 1.)
ind1[i] = 0.5 * (((1 + beta) * x1) + ((1 - beta) * x2))
ind2[i] = 0.5 * (((1 - beta) * x1) + ((1 + beta) * x2))

return ind1, ind2

[docs]def cxSimulatedBinaryBounded(ind1, ind2, eta, low, up):
"""Executes a simulated binary crossover that modify in-place the input
individuals. The simulated binary crossover expects :term:sequence
individuals of floating point numbers.

:param ind1: The first individual participating in the crossover.
:param ind2: The second individual participating in the crossover.
:param eta: Crowding degree of the crossover. A high eta will produce
children resembling to their parents, while a small eta will
produce solutions much more different.
:param low: A value or a :term:python:sequence of values that is the lower
bound of the search space.
:param up: A value or a :term:python:sequence of values that is the upper
bound of the search space.
:returns: A tuple of two individuals.

This function uses the :func:~random.random function from the python base
:mod:random module.

.. note::
This implementation is similar to the one implemented in the
original NSGA-II C code presented by Deb.
"""
size = min(len(ind1), len(ind2))
if not isinstance(low, Sequence):
low = repeat(low, size)
elif len(low) < size:
raise IndexError("low must be at least the size of the shorter individual: %d < %d" % (len(low), size))
if not isinstance(up, Sequence):
up = repeat(up, size)
elif len(up) < size:
raise IndexError("up must be at least the size of the shorter individual: %d < %d" % (len(up), size))

for i, xl, xu in zip(range(size), low, up):
if random.random() <= 0.5:
# This epsilon should probably be changed for 0 since
# floating point arithmetic in Python is safer
if abs(ind1[i] - ind2[i]) > 1e-14:
x1 = min(ind1[i], ind2[i])
x2 = max(ind1[i], ind2[i])
rand = random.random()

beta = 1.0 + (2.0 * (x1 - xl) / (x2 - x1))
alpha = 2.0 - beta ** -(eta + 1)
if rand <= 1.0 / alpha:
beta_q = (rand * alpha) ** (1.0 / (eta + 1))
else:
beta_q = (1.0 / (2.0 - rand * alpha)) ** (1.0 / (eta + 1))

c1 = 0.5 * (x1 + x2 - beta_q * (x2 - x1))

beta = 1.0 + (2.0 * (xu - x2) / (x2 - x1))
alpha = 2.0 - beta ** -(eta + 1)
if rand <= 1.0 / alpha:
beta_q = (rand * alpha) ** (1.0 / (eta + 1))
else:
beta_q = (1.0 / (2.0 - rand * alpha)) ** (1.0 / (eta + 1))
c2 = 0.5 * (x1 + x2 + beta_q * (x2 - x1))

c1 = min(max(c1, xl), xu)
c2 = min(max(c2, xl), xu)

if random.random() <= 0.5:
ind1[i] = c2
ind2[i] = c1
else:
ind1[i] = c1
ind2[i] = c2

return ind1, ind2

######################################
# Messy Crossovers                   #
######################################

[docs]def cxMessyOnePoint(ind1, ind2):
"""Executes a one point crossover on :term:sequence individual.
The crossover will in most cases change the individuals size. The two
individuals are modified in place.

:param ind1: The first individual participating in the crossover.
:param ind2: The second individual participating in the crossover.
:returns: A tuple of two individuals.

This function uses the :func:~random.randint function from the python base
:mod:random module.
"""
cxpoint1 = random.randint(0, len(ind1))
cxpoint2 = random.randint(0, len(ind2))
ind1[cxpoint1:], ind2[cxpoint2:] = ind2[cxpoint2:], ind1[cxpoint1:]

return ind1, ind2

######################################
# ES Crossovers                      #
######################################

[docs]def cxESBlend(ind1, ind2, alpha):
"""Executes a blend crossover on both, the individual and the strategy. The
individuals shall be a :term:sequence and must have a :term:sequence
:attr:strategy attribute. Adjustment of the minimal strategy shall be done
after the call to this function, consider using a decorator.

:param ind1: The first evolution strategy participating in the crossover.
:param ind2: The second evolution strategy participating in the crossover.
:param alpha: Extent of the interval in which the new values can be drawn
for each attribute on both side of the parents' attributes.
:returns: A tuple of two evolution strategies.

This function uses the :func:~random.random function from the python base
:mod:random module.
"""
for i, (x1, s1, x2, s2) in enumerate(zip(ind1, ind1.strategy,
ind2, ind2.strategy)):
# Blend the values
gamma = (1. + 2. * alpha) * random.random() - alpha
ind1[i] = (1. - gamma) * x1 + gamma * x2
ind2[i] = gamma * x1 + (1. - gamma) * x2
# Blend the strategies
gamma = (1. + 2. * alpha) * random.random() - alpha
ind1.strategy[i] = (1. - gamma) * s1 + gamma * s2
ind2.strategy[i] = gamma * s1 + (1. - gamma) * s2

return ind1, ind2

[docs]def cxESTwoPoint(ind1, ind2):
"""Executes a classical two points crossover on both the individuals and their
strategy. The individuals shall be a :term:sequence and must have a
:term:sequence :attr:strategy attribute. The crossover points for the
individual and the strategy are the same.

:param ind1: The first evolution strategy participating in the crossover.
:param ind2: The second evolution strategy participating in the crossover.
:returns: A tuple of two evolution strategies.

This function uses the :func:~random.randint function from the python base
:mod:random module.
"""
size = min(len(ind1), len(ind2))

pt1 = random.randint(1, size)
pt2 = random.randint(1, size - 1)
if pt2 >= pt1:
pt2 += 1
else:  # Swap the two cx points
pt1, pt2 = pt2, pt1

ind1[pt1:pt2], ind2[pt1:pt2] = ind2[pt1:pt2], ind1[pt1:pt2]
ind1.strategy[pt1:pt2], ind2.strategy[pt1:pt2] = \
ind2.strategy[pt1:pt2], ind1.strategy[pt1:pt2]

return ind1, ind2

[docs]def cxESTwoPoints(ind1, ind2):
"""
.. deprecated:: 1.0
The function has been renamed. Use :func:cxESTwoPoint instead.
"""
return cxESTwoPoint(ind1, ind2)

# List of exported function names.
__all__ = ['cxOnePoint', 'cxTwoPoint', 'cxUniform', 'cxPartialyMatched',
'cxUniformPartialyMatched', 'cxOrdered', 'cxBlend',
'cxSimulatedBinary', 'cxSimulatedBinaryBounded', 'cxMessyOnePoint',
'cxESBlend', 'cxESTwoPoint']

# Deprecated functions
__all__.extend(['cxTwoPoints', 'cxESTwoPoints'])