# DEAP/deap

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 # 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 . """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 systematicaly, 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