crossover.py

import random
import warnings

from collections import Sequence
from itertools import repeat

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

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

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

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)

def cxUniform(ind1, ind2, indpb):
    """Executes a uniform crossover that modify in place the two
    :term:`sequence` individuals. The attributes are swapped accordingto the
    *indpb* probability.
    
    :param ind1: The first individual participating in the crossover.
    :param ind2: The second individual participating in the crossover.
    :param indpb: Independent probabily 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
    
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

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

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

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

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


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                   #
######################################

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                      #
######################################

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. Adjustement 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

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

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