python DEAP学习2（遗传算法） 最大值问题

One Max Problem

This is the first complete example built with DEAP. It will help new users to overview some of the framework possibilities. The problem is very simple, we search for a 1 filled list individual. This problem is widely used in the evolutionary computation community since it is very simple and it illustrates well the potential of evolutionary algorithms.

了解DEAP整体框架之后，我们来看一个简单的例子。

Setting Things Up

Here we use the one max problem to show how simple can be an evolutionary algorithm with DEAP. The first thing to do is to elaborate the structures of the algorithm. It is pretty obvious in this case that an individual that can contain a series of booleans is the most interesting kind of structure available. DEAP does not contain any explicit individual structure since it is simply a container of attributes associated with a fitness. Instead, it provides a convenient method for creating types called the creator.

这里我们用最大值问题来展示一下利用DEAP做遗传算法有多简单。

First of all, we need to import some modules.

import randomfrom deap import basefrom deap import creatorfrom deap import tools

Creator

The creator is a class factory that can build at run-time new classes that inherit from a base classe. It is very useful since an individual can be any type of container from list to n-ary tree. The creator allows build complex new structures convenient for evolutionary computation.

Let see an example of how to use the creator to setup an individual that contains an array of booleans and a maximizing fitness. We will first need to import the deap.base and deap.creator modules.

The creator defines at first a single function create() that is used to create types. The create() function takes at least 2 arguments plus additional optional arguments. The first argument name is the actual name of the type that we want to create. The second argument base is the base classe that the new type created should inherit from. Finally the optional arguments are members to add to the new type, for example a fitness for an individual or speed for a particle.

creator.create("FitnessMax", base.Fitness, weights=(1.0,))creator.create("Individual", list, fitness=creator.FitnessMax)

The first line creates a maximizing fitness by replacing, in the base type Fitness, the pure virtual weights attribute by (1.0,) that means to maximize a single objective fitness. The second line creates an Individual class that inherits the properties of list and has a fitness attribute of the type FitnessMax that was just created.

在Fitness内，weights属性为1表示求最大化，注意1.0后面有一个逗号，即使是在求解单目标问题，weights也需要迭代。

In this last step, two things are of major importance. The first is the comma（逗号） following the 1.0 in the weights declaration, even when implementing a single objective fitness, the weights (and values) must be iterable. We won’t repeat it enough, in DEAP single objective is a special case of multiobjective. The second important thing is how the just created FitnessMax can be used directly as if it was part of the creator. This is not magic.

Toolbox

A Toolbox can be found in the base module. It is intended to store functions with their arguments. The toolbox contains two methods, register() andunregister() that are used to do the tricks.

toolbox = base.Toolbox()# Attribute generator toolbox.register("attr_bool", random.randint, 0, 1)#参数：函数名、方法、参数# Structure initializerstoolbox.register("individual", tools.initRepeat, creator.Individual,     toolbox.attr_bool, 100)toolbox.register("population", tools.initRepeat, list, toolbox.individual)

In this code block we registered a generation function and two initialization functions. The generator toolbox.attr_bool() when called, will draw a random integer between 0 and 1. The two initializers for their part will produce respectively initialized individuals and populations.

上面的代码我们创建了三个函数，toolbox.attr_bool()将随机生成0和1的序列，后面来个将分别产生个体和总体。（不太明白为什么要产生总体...）

Again, looking a little closer shows that there is no magic. The registration of tools in the toolbox only associates an alias to an already existing function and freezes part of its arguments. This allows to call the alias as if the majority of the (or every) arguments have already been given. For example, theattr_bool() generator is made from the randint() that takes two arguments a and b, with a <= n <= b, where n is the returned integer. Here, we fix a = 0 and b= 1.

It is the same thing for the initializers. This time, the initRepeat() is frozen with predefined arguments. In the case of the individual() method, initRepeat()takes 3 arguments, a class that is a container – here the Individual is derived from a list –, a function to fill the container and the number of times the function shall be repeated. When called, the individual() method will thus return an individual initialized with what would be returned by 100 calls to theattr_bool() method. Finally, the population() method uses the same paradigm, but we don’t fix the number of individuals that it should contain.

toolbox.register("individual", tools.initRepeat, creator.Individual, toolbox.attr_bool, 100)

individual指向tools.initRepeat，tools.initRepeat有三个参数，分别是creator.Individual、toolbox.attr_bool,100。调用individual的时候，将使用toolbox.attr_bool方法重复100次填充creator.Individual。

The Evaluation Function

The evaluation function is pretty simple in this case, we need to count the number of ones in the individual. This is done by the following lines of code.

def evalOneMax(individual):    return sum(individual),

The returned value must be an iterable of length equal to the number of objectives (weights).

在这个问题中，我们的目标是求取最大值。

The Genetic Operators

There is two way of using operators, the first one, is to simply call the function from the tools module and the second one is to register them with their argument in a toolbox as for the initialization methods. The most convenient way is to register them in the toolbox, because it allows to easily switch between operators if desired. The toolbox method is also used in the algorithms, see the One Max Problem: Short Version for an example.

Registering the operators and their default arguments in the toolbox is done as follow.

toolbox.register("evaluate", evalOneMax)toolbox.register("mate", tools.cxTwoPoint)#交配toolbox.register("mutate", tools.mutFlipBit, indpb=0.05)#变异，0.05为变异概率toolbox.register("select", tools.selTournament, tournsize=3)#选择，3是什么？

三个操作算子，分别是交配、变异、选择。

The evaluation is given the alias evaluate. Having a single argument being the individual to evaluate we don’t need to fix any, the individual will be given later in the algorithm. The mutation, for its part, needs an argument to be fixed (the independent probability of each attribute to be mutated indpb). In the algorithms the mutate() function is called with the signature mutant, = toolbox.mutate(mutant). This is the most convenient way because each mutation takes a different number of arguments, having those arguments fixed in the toolbox leave open most of the possibilities to change the mutation (or crossover, or selection, or evaluation) operator later in your researches.

Evolving the Population

Once the representation and the operators are chosen, we have to define an algorithm. A good habit to take is to define the algorithm inside a function, generally named main().

Creating the Population

Before evolving it, we need to instantiate a population. This step is done effortless using the method we registered in the toolbox.

def main():    pop = toolbox.population(n=300)

创建种群，pop是一个list，包含300个体。

pop will be a list composed of 300 individuals, n is the parameter left open earlier in the toolbox. The next thing to do is to evaluate this brand new population.

# Evaluate the entire population    fitnesses = list(map(toolbox.evaluate, pop))    for ind, fit in zip(pop, fitnesses):        ind.fitness.values = fit

We first map() the evaluation function to every individual, then assign their respective fitness. Note that the order in fitnesses and population are the same.

map（）对可迭代函数'iterable'中的每一个元素应用‘function’方法，将结果作为list返回。

map（）举例：

def add100(x):      return x+100h=[1,2,3]map(add100,h)[101,102,103]

The Appeal of Evolution

The evolution of the population is the last thing to accomplish. Let say that we want to evolve for a fixed number of generation NGEN, the evolution will then begin with a simple for statement.

# Begin the evolution    for g in range(NGEN):        print("-- Generation %i --" % g)

Is that simple enough? Lets continue with more complicated things, selecting, mating and mutating the population. The crossover and mutation operators provided within DEAP usually take respectively 2 and 1 individual(s) on input and return 2 and 1 modified individual(s), they also modify inplace these individuals.

In a simple GA, the first step is to select the next generation.

第一步选择子代，然后克隆被选择的子代，toolbox.clone保证我们拥有独立的子代，而不是只保存子代的引用。

# Select the next generation individuals        offspring = toolbox.select(pop, len(pop))        # Clone the selected individuals        offspring = list(map(toolbox.clone, offspring))

This step creates an offspring list that is an exact copy of the selected individuals. The toolbox.clone() method ensure that we don’t own a reference to the individuals but an completely independent instance.

Next, a simple GA would replace the parents by the produced children directly in the population. This is what is done by the following lines of code, where a crossover is applied with probability CXPB and a mutation with probability MUTPB. The del statement simply invalidate the fitness of the modified individuals.

第二步使子代的基因交叉、变异产生新的子代，删除交叉和变异后的子代。

 # Apply crossover and mutation on the offspring        for child1, child2 in zip(offspring[::2], offspring[1::2]):            if random.random() < CXPB:                toolbox.mate(child1, child2)                del child1.fitness.values                del child2.fitness.values        for mutant in offspring:            if random.random() < MUTPB:                toolbox.mutate(mutant)                del mutant.fitness.values

The population now needs to be re-evaluated, we then apply the evaluation as seen earlier, but this time only on the individuals with an invalid fitness.

第三步重新评估个体。

 # Evaluate the individuals with an invalid fitness        invalid_ind = [ind for ind in offspring if not ind.fitness.valid]#不懂....        fitnesses = map(toolbox.evaluate, invalid_ind)        for ind, fit in zip(invalid_ind, fitnesses):            ind.fitness.values = fit

And finally, last but not least, we replace the old population by the offspring.

最后我们拥有了全新的子代。

 pop[:] = offspring

This is the end of the evolution part, it will continue until the predefined number of generation are accomplished.

Although, some statistics may be gathered on the population, the following lines print the min, max, mean and standard deviation of the population.

这就是进化的过程，它会不断进化直到达到预设的进化代数。

# Gather all the fitnesses in one list and print the stats        fits = [ind.fitness.values[0] for ind in pop]                length = len(pop)        mean = sum(fits) / length        sum2 = sum(x*x for x in fits)        std = abs(sum2 / length - mean**2)**0.5                print("  Min %s" % min(fits))        print("  Max %s" % max(fits))        print("  Avg %s" % mean)        print("  Std %s" % std)

A Statistics object has been defined to facilitate how statistics are gathered. It is not presented here so that we can focus on the core and not the gravitating helper objects of DEAP.

The complete examples/ga/onemax.

完整的代码如下：

#    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/>.#    example which maximizes the sum of a list of integers#    each of which can be 0 or 1import randomfrom deap import basefrom deap import creatorfrom deap import toolscreator.create("FitnessMax", base.Fitness, weights=(1.0,))creator.create("Individual", list, fitness=creator.FitnessMax)toolbox = base.Toolbox()# Attribute generator #                      define 'attr_bool' to be an attribute ('gene')#                      which corresponds to integers sampled uniformly#                      from the range [0,1] (i.e. 0 or 1 with equal#                      probability)toolbox.register("attr_bool", random.randint, 0, 1)# Structure initializers#                         define 'individual' to be an individual#                         consisting of 100 'attr_bool' elements ('genes')toolbox.register("individual", tools.initRepeat, creator.Individual,     toolbox.attr_bool, 100)# define the population to be a list of individualstoolbox.register("population", tools.initRepeat, list, toolbox.individual)# the goal ('fitness') function to be maximizeddef evalOneMax(individual):    return sum(individual),#----------# Operator registration#----------# register the goal / fitness functiontoolbox.register("evaluate", evalOneMax)# register the crossover operatortoolbox.register("mate", tools.cxTwoPoint)# register a mutation operator with a probability to# flip each attribute/gene of 0.05toolbox.register("mutate", tools.mutFlipBit, indpb=0.05)# operator for selecting individuals for breeding the next# generation: each individual of the current generation# is replaced by the 'fittest' (best) of three individuals# drawn randomly from the current generation.toolbox.register("select", tools.selTournament, tournsize=3)#----------def main():    random.seed(64)    # create an initial population of 300 individuals (where    # each individual is a list of integers)    pop = toolbox.population(n=300)    # CXPB  is the probability with which two individuals    #       are crossed    #    # MUTPB is the probability for mutating an individual    #    # NGEN  is the number of generations for which the    #       evolution runs    CXPB, MUTPB, NGEN = 0.5, 0.2, 40        print("Start of evolution")        # Evaluate the entire population    fitnesses = list(map(toolbox.evaluate, pop))    for ind, fit in zip(pop, fitnesses):        ind.fitness.values = fit        print("  Evaluated %i individuals" % len(pop))        # Begin the evolution    for g in range(NGEN):        print("-- Generation %i --" % g)                # Select the next generation individuals        offspring = toolbox.select(pop, len(pop))        # Clone the selected individuals        offspring = list(map(toolbox.clone, offspring))            # Apply crossover and mutation on the offspring        for child1, child2 in zip(offspring[::2], offspring[1::2]):            # cross two individuals with probability CXPB            if random.random() < CXPB:                toolbox.mate(child1, child2)                # fitness values of the children                # must be recalculated later                del child1.fitness.values                del child2.fitness.values        for mutant in offspring:            # mutate an individual with probability MUTPB            if random.random() < MUTPB:                toolbox.mutate(mutant)                del mutant.fitness.values            # Evaluate the individuals with an invalid fitness        invalid_ind = [ind for ind in offspring if not ind.fitness.valid]        fitnesses = map(toolbox.evaluate, invalid_ind)        for ind, fit in zip(invalid_ind, fitnesses):            ind.fitness.values = fit                print("  Evaluated %i individuals" % len(invalid_ind))                # The population is entirely replaced by the offspring        pop[:] = offspring                # Gather all the fitnesses in one list and print the stats        fits = [ind.fitness.values[0] for ind in pop]                length = len(pop)        mean = sum(fits) / length        sum2 = sum(x*x for x in fits)        std = abs(sum2 / length - mean**2)**0.5                print("  Min %s" % min(fits))        print("  Max %s" % max(fits))        print("  Avg %s" % mean)        print("  Std %s" % std)        print("-- End of (successful) evolution --")        best_ind = tools.selBest(pop, 1)[0]    print("Best individual is %s, %s" % (best_ind, best_ind.fitness.values))if __name__ == "__main__":    main()