# This file is part of DEAP.

#

# 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

# the License, or (at your option) any later version.

#

# DEAP is distributed in the hope that it will be useful,

# but WITHOUT ANY WARRANTY; without even the implied warranty of

# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the

# GNU Lesser General Public License for more details.

#

# You should have received a copy of the GNU Lesser General Public

# License along with DEAP. If not, see <http://www.gnu.org/licenses/>.

"""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

import tools

def varAnd(population, toolbox, cxpb, mutpb):

"""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* beceause of its propention 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

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 evalutions 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

def varOr(population, toolbox, lambda_, cxpb, mutpb):

"""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

:returns: A class:`~deap.tools.Logbook` with the statistics of the

evolution

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* beceause 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 xrange(lambda_):

op_choice = random.random()

if op_choice < cxpb: # Apply crossover

ind1, ind2 = map(toolbox.clone, 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

def eaMuPlusLambda(population, toolbox, mu, lambda_, cxpb, mutpb, ngen,

stats=None, halloffame=None, verbose=__debug__):

"""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 evalutions 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

def eaMuCommaLambda(population, toolbox, mu, lambda_, cxpb, mutpb, ngen,

stats=None, halloffame=None, verbose=__debug__):

"""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 evalutions 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

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 evalutions 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)

.. [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 xrange(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