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#
# DEAP is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as
# published by the Free Software Foundation, either version 3 of
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#
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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"""The :mod:`algorithms` module is intended to contain some specific algorithms
in order to execute very common evolutionary algorithms. The method used here
are more for convenience than reference as the implementation of every
evolutionary algorithm may vary infinitely. Most of the algorithms in this
module use operators registered in the toolbox. Generally, the keyword used are
:meth:`mate` for crossover, :meth:`mutate` for mutation, :meth:`~deap.select`
for selection and :meth:`evaluate` for evaluation.
You are encouraged to write your own algorithms in order to make them do what
you really want them to do.
"""
import random
from . import tools
[docs]def varAnd(population, toolbox, cxpb, mutpb):
r"""Part of an evolutionary algorithm applying only the variation part
(crossover **and** mutation). The modified individuals have their
fitness invalidated. The individuals are cloned so returned population is
independent of the input population.
:param population: A list of individuals to vary.
:param toolbox: A :class:`~deap.base.Toolbox` that contains the evolution
operators.
:param cxpb: The probability of mating two individuals.
:param mutpb: The probability of mutating an individual.
:returns: A list of varied individuals that are independent of their
parents.
The variation goes as follow. First, the parental population
:math:`P_\mathrm{p}` is duplicated using the :meth:`toolbox.clone` method
and the result is put into the offspring population :math:`P_\mathrm{o}`. A
first loop over :math:`P_\mathrm{o}` is executed to mate pairs of
consecutive individuals. According to the crossover probability *cxpb*, the
individuals :math:`\mathbf{x}_i` and :math:`\mathbf{x}_{i+1}` are mated
using the :meth:`toolbox.mate` method. The resulting children
:math:`\mathbf{y}_i` and :math:`\mathbf{y}_{i+1}` replace their respective
parents in :math:`P_\mathrm{o}`. A second loop over the resulting
:math:`P_\mathrm{o}` is executed to mutate every individual with a
probability *mutpb*. When an individual is mutated it replaces its not
mutated version in :math:`P_\mathrm{o}`. The resulting :math:`P_\mathrm{o}`
is returned.
This variation is named *And* because of its propensity to apply both
crossover and mutation on the individuals. Note that both operators are
not applied systematically, the resulting individuals can be generated from
crossover only, mutation only, crossover and mutation, and reproduction
according to the given probabilities. Both probabilities should be in
:math:`[0, 1]`.
"""
offspring = [toolbox.clone(ind) for ind in population]
# Apply crossover and mutation on the offspring
for i in range(1, len(offspring), 2):
if random.random() < cxpb:
offspring[i - 1], offspring[i] = toolbox.mate(offspring[i - 1],
offspring[i])
del offspring[i - 1].fitness.values, offspring[i].fitness.values
for i in range(len(offspring)):
if random.random() < mutpb:
offspring[i], = toolbox.mutate(offspring[i])
del offspring[i].fitness.values
return offspring
[docs]def eaSimple(population, toolbox, cxpb, mutpb, ngen, stats=None,
halloffame=None, verbose=__debug__):
"""This algorithm reproduce the simplest evolutionary algorithm as
presented in chapter 7 of [Back2000]_.
:param population: A list of individuals.
:param toolbox: A :class:`~deap.base.Toolbox` that contains the evolution
operators.
:param cxpb: The probability of mating two individuals.
:param mutpb: The probability of mutating an individual.
:param ngen: The number of generation.
:param stats: A :class:`~deap.tools.Statistics` object that is updated
inplace, optional.
:param halloffame: A :class:`~deap.tools.HallOfFame` object that will
contain the best individuals, optional.
:param verbose: Whether or not to log the statistics.
:returns: The final population
:returns: A class:`~deap.tools.Logbook` with the statistics of the
evolution
The algorithm takes in a population and evolves it in place using the
:meth:`varAnd` method. It returns the optimized population and a
:class:`~deap.tools.Logbook` with the statistics of the evolution. The
logbook will contain the generation number, the number of evaluations for
each generation and the statistics if a :class:`~deap.tools.Statistics` is
given as argument. The *cxpb* and *mutpb* arguments are passed to the
:func:`varAnd` function. The pseudocode goes as follow ::
evaluate(population)
for g in range(ngen):
population = select(population, len(population))
offspring = varAnd(population, toolbox, cxpb, mutpb)
evaluate(offspring)
population = offspring
As stated in the pseudocode above, the algorithm goes as follow. First, it
evaluates the individuals with an invalid fitness. Second, it enters the
generational loop where the selection procedure is applied to entirely
replace the parental population. The 1:1 replacement ratio of this
algorithm **requires** the selection procedure to be stochastic and to
select multiple times the same individual, for example,
:func:`~deap.tools.selTournament` and :func:`~deap.tools.selRoulette`.
Third, it applies the :func:`varAnd` function to produce the next
generation population. Fourth, it evaluates the new individuals and
compute the statistics on this population. Finally, when *ngen*
generations are done, the algorithm returns a tuple with the final
population and a :class:`~deap.tools.Logbook` of the evolution.
.. note::
Using a non-stochastic selection method will result in no selection as
the operator selects *n* individuals from a pool of *n*.
This function expects the :meth:`toolbox.mate`, :meth:`toolbox.mutate`,
:meth:`toolbox.select` and :meth:`toolbox.evaluate` aliases to be
registered in the toolbox.
.. [Back2000] Back, Fogel and Michalewicz, "Evolutionary Computation 1 :
Basic Algorithms and Operators", 2000.
"""
logbook = tools.Logbook()
logbook.header = ['gen', 'nevals'] + (stats.fields if stats else [])
# Evaluate the individuals with an invalid fitness
invalid_ind = [ind for ind in population if not ind.fitness.valid]
fitnesses = toolbox.map(toolbox.evaluate, invalid_ind)
for ind, fit in zip(invalid_ind, fitnesses):
ind.fitness.values = fit
if halloffame is not None:
halloffame.update(population)
record = stats.compile(population) if stats else {}
logbook.record(gen=0, nevals=len(invalid_ind), **record)
if verbose:
print(logbook.stream)
# Begin the generational process
for gen in range(1, ngen + 1):
# Select the next generation individuals
offspring = toolbox.select(population, len(population))
# Vary the pool of individuals
offspring = varAnd(offspring, 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
# Update the hall of fame with the generated individuals
if halloffame is not None:
halloffame.update(offspring)
# Replace the current population by the offspring
population[:] = offspring
# Append the current generation statistics to the logbook
record = stats.compile(population) if stats else {}
logbook.record(gen=gen, nevals=len(invalid_ind), **record)
if verbose:
print(logbook.stream)
return population, logbook
[docs]def varOr(population, toolbox, lambda_, cxpb, mutpb):
r"""Part of an evolutionary algorithm applying only the variation part
(crossover, mutation **or** reproduction). The modified individuals have
their fitness invalidated. The individuals are cloned so returned
population is independent of the input population.
:param population: A list of individuals to vary.
:param toolbox: A :class:`~deap.base.Toolbox` that contains the evolution
operators.
:param lambda\_: The number of children to produce
:param cxpb: The probability of mating two individuals.
:param mutpb: The probability of mutating an individual.
:returns: The final population.
The variation goes as follow. On each of the *lambda_* iteration, it
selects one of the three operations; crossover, mutation or reproduction.
In the case of a crossover, two individuals are selected at random from
the parental population :math:`P_\mathrm{p}`, those individuals are cloned
using the :meth:`toolbox.clone` method and then mated using the
:meth:`toolbox.mate` method. Only the first child is appended to the
offspring population :math:`P_\mathrm{o}`, the second child is discarded.
In the case of a mutation, one individual is selected at random from
:math:`P_\mathrm{p}`, it is cloned and then mutated using using the
:meth:`toolbox.mutate` method. The resulting mutant is appended to
:math:`P_\mathrm{o}`. In the case of a reproduction, one individual is
selected at random from :math:`P_\mathrm{p}`, cloned and appended to
:math:`P_\mathrm{o}`.
This variation is named *Or* because an offspring will never result from
both operations crossover and mutation. The sum of both probabilities
shall be in :math:`[0, 1]`, the reproduction probability is
1 - *cxpb* - *mutpb*.
"""
assert (cxpb + mutpb) <= 1.0, (
"The sum of the crossover and mutation probabilities must be smaller "
"or equal to 1.0.")
offspring = []
for _ in range(lambda_):
op_choice = random.random()
if op_choice < cxpb: # Apply crossover
ind1, ind2 = [toolbox.clone(i) for i in random.sample(population, 2)]
ind1, ind2 = toolbox.mate(ind1, ind2)
del ind1.fitness.values
offspring.append(ind1)
elif op_choice < cxpb + mutpb: # Apply mutation
ind = toolbox.clone(random.choice(population))
ind, = toolbox.mutate(ind)
del ind.fitness.values
offspring.append(ind)
else: # Apply reproduction
offspring.append(random.choice(population))
return offspring
[docs]def eaMuPlusLambda(population, toolbox, mu, lambda_, cxpb, mutpb, ngen,
stats=None, halloffame=None, verbose=__debug__):
r"""This is the :math:`(\mu + \lambda)` evolutionary algorithm.
:param population: A list of individuals.
:param toolbox: A :class:`~deap.base.Toolbox` that contains the evolution
operators.
:param mu: The number of individuals to select for the next generation.
:param lambda\_: The number of children to produce at each generation.
:param cxpb: The probability that an offspring is produced by crossover.
:param mutpb: The probability that an offspring is produced by mutation.
:param ngen: The number of generation.
:param stats: A :class:`~deap.tools.Statistics` object that is updated
inplace, optional.
:param halloffame: A :class:`~deap.tools.HallOfFame` object that will
contain the best individuals, optional.
:param verbose: Whether or not to log the statistics.
:returns: The final population
:returns: A class:`~deap.tools.Logbook` with the statistics of the
evolution.
The algorithm takes in a population and evolves it in place using the
:func:`varOr` function. It returns the optimized population and a
:class:`~deap.tools.Logbook` with the statistics of the evolution. The
logbook will contain the generation number, the number of evaluations for
each generation and the statistics if a :class:`~deap.tools.Statistics` is
given as argument. The *cxpb* and *mutpb* arguments are passed to the
:func:`varOr` function. The pseudocode goes as follow ::
evaluate(population)
for g in range(ngen):
offspring = varOr(population, toolbox, lambda_, cxpb, mutpb)
evaluate(offspring)
population = select(population + offspring, mu)
First, the individuals having an invalid fitness are evaluated. Second,
the evolutionary loop begins by producing *lambda_* offspring from the
population, the offspring are generated by the :func:`varOr` function. The
offspring are then evaluated and the next generation population is
selected from both the offspring **and** the population. Finally, when
*ngen* generations are done, the algorithm returns a tuple with the final
population and a :class:`~deap.tools.Logbook` of the evolution.
This function expects :meth:`toolbox.mate`, :meth:`toolbox.mutate`,
:meth:`toolbox.select` and :meth:`toolbox.evaluate` aliases to be
registered in the toolbox. This algorithm uses the :func:`varOr`
variation.
"""
logbook = tools.Logbook()
logbook.header = ['gen', 'nevals'] + (stats.fields if stats else [])
# Evaluate the individuals with an invalid fitness
invalid_ind = [ind for ind in population if not ind.fitness.valid]
fitnesses = toolbox.map(toolbox.evaluate, invalid_ind)
for ind, fit in zip(invalid_ind, fitnesses):
ind.fitness.values = fit
if halloffame is not None:
halloffame.update(population)
record = stats.compile(population) if stats is not None else {}
logbook.record(gen=0, nevals=len(invalid_ind), **record)
if verbose:
print(logbook.stream)
# Begin the generational process
for gen in range(1, ngen + 1):
# Vary the population
offspring = varOr(population, toolbox, lambda_, 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
# Update the hall of fame with the generated individuals
if halloffame is not None:
halloffame.update(offspring)
# Select the next generation population
population[:] = toolbox.select(population + offspring, mu)
# Update the statistics with the new population
record = stats.compile(population) if stats is not None else {}
logbook.record(gen=gen, nevals=len(invalid_ind), **record)
if verbose:
print(logbook.stream)
return population, logbook
[docs]def eaMuCommaLambda(population, toolbox, mu, lambda_, cxpb, mutpb, ngen,
stats=None, halloffame=None, verbose=__debug__):
r"""This is the :math:`(\mu~,~\lambda)` evolutionary algorithm.
:param population: A list of individuals.
:param toolbox: A :class:`~deap.base.Toolbox` that contains the evolution
operators.
:param mu: The number of individuals to select for the next generation.
:param lambda\_: The number of children to produce at each generation.
:param cxpb: The probability that an offspring is produced by crossover.
:param mutpb: The probability that an offspring is produced by mutation.
:param ngen: The number of generation.
:param stats: A :class:`~deap.tools.Statistics` object that is updated
inplace, optional.
:param halloffame: A :class:`~deap.tools.HallOfFame` object that will
contain the best individuals, optional.
:param verbose: Whether or not to log the statistics.
:returns: The final population
:returns: A class:`~deap.tools.Logbook` with the statistics of the
evolution
The algorithm takes in a population and evolves it in place using the
:func:`varOr` function. It returns the optimized population and a
:class:`~deap.tools.Logbook` with the statistics of the evolution. The
logbook will contain the generation number, the number of evaluations for
each generation and the statistics if a :class:`~deap.tools.Statistics` is
given as argument. The *cxpb* and *mutpb* arguments are passed to the
:func:`varOr` function. The pseudocode goes as follow ::
evaluate(population)
for g in range(ngen):
offspring = varOr(population, toolbox, lambda_, cxpb, mutpb)
evaluate(offspring)
population = select(offspring, mu)
First, the individuals having an invalid fitness are evaluated. Second,
the evolutionary loop begins by producing *lambda_* offspring from the
population, the offspring are generated by the :func:`varOr` function. The
offspring are then evaluated and the next generation population is
selected from **only** the offspring. Finally, when
*ngen* generations are done, the algorithm returns a tuple with the final
population and a :class:`~deap.tools.Logbook` of the evolution.
.. note::
Care must be taken when the lambda:mu ratio is 1 to 1 as a
non-stochastic selection will result in no selection at all as the
operator selects *lambda* individuals from a pool of *mu*.
This function expects :meth:`toolbox.mate`, :meth:`toolbox.mutate`,
:meth:`toolbox.select` and :meth:`toolbox.evaluate` aliases to be
registered in the toolbox. This algorithm uses the :func:`varOr`
variation.
"""
assert lambda_ >= mu, "lambda must be greater or equal to mu."
# Evaluate the individuals with an invalid fitness
invalid_ind = [ind for ind in population if not ind.fitness.valid]
fitnesses = toolbox.map(toolbox.evaluate, invalid_ind)
for ind, fit in zip(invalid_ind, fitnesses):
ind.fitness.values = fit
if halloffame is not None:
halloffame.update(population)
logbook = tools.Logbook()
logbook.header = ['gen', 'nevals'] + (stats.fields if stats else [])
record = stats.compile(population) if stats is not None else {}
logbook.record(gen=0, nevals=len(invalid_ind), **record)
if verbose:
print(logbook.stream)
# Begin the generational process
for gen in range(1, ngen + 1):
# Vary the population
offspring = varOr(population, toolbox, lambda_, 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
# Update the hall of fame with the generated individuals
if halloffame is not None:
halloffame.update(offspring)
# Select the next generation population
population[:] = toolbox.select(offspring, mu)
# Update the statistics with the new population
record = stats.compile(population) if stats is not None else {}
logbook.record(gen=gen, nevals=len(invalid_ind), **record)
if verbose:
print(logbook.stream)
return population, logbook
[docs]def eaGenerateUpdate(toolbox, ngen, halloffame=None, stats=None,
verbose=__debug__):
"""This is algorithm implements the ask-tell model proposed in
[Colette2010]_, where ask is called `generate` and tell is called `update`.
:param toolbox: A :class:`~deap.base.Toolbox` that contains the evolution
operators.
:param ngen: The number of generation.
:param stats: A :class:`~deap.tools.Statistics` object that is updated
inplace, optional.
:param halloffame: A :class:`~deap.tools.HallOfFame` object that will
contain the best individuals, optional.
:param verbose: Whether or not to log the statistics.
:returns: The final population
:returns: A class:`~deap.tools.Logbook` with the statistics of the
evolution
The algorithm generates the individuals using the :func:`toolbox.generate`
function and updates the generation method with the :func:`toolbox.update`
function. It returns the optimized population and a
:class:`~deap.tools.Logbook` with the statistics of the evolution. The
logbook will contain the generation number, the number of evaluations for
each generation and the statistics if a :class:`~deap.tools.Statistics` is
given as argument. The pseudocode goes as follow ::
for g in range(ngen):
population = toolbox.generate()
evaluate(population)
toolbox.update(population)
This function expects :meth:`toolbox.generate` and :meth:`toolbox.evaluate` aliases to be
registered in the toolbox.
.. [Colette2010] Collette, Y., N. Hansen, G. Pujol, D. Salazar Aponte and
R. Le Riche (2010). On Object-Oriented Programming of Optimizers -
Examples in Scilab. In P. Breitkopf and R. F. Coelho, eds.:
Multidisciplinary Design Optimization in Computational Mechanics,
Wiley, pp. 527-565;
"""
logbook = tools.Logbook()
logbook.header = ['gen', 'nevals'] + (stats.fields if stats else [])
for gen in range(ngen):
# Generate a new population
population = toolbox.generate()
# Evaluate the individuals
fitnesses = toolbox.map(toolbox.evaluate, population)
for ind, fit in zip(population, fitnesses):
ind.fitness.values = fit
if halloffame is not None:
halloffame.update(population)
# Update the strategy with the evaluated individuals
toolbox.update(population)
record = stats.compile(population) if stats is not None else {}
logbook.record(gen=gen, nevals=len(population), **record)
if verbose:
print(logbook.stream)
return population, logbook
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