进化算法及Python实现（使用DEAP库）

进化算法介绍

进化算法（也叫演化算法，Evolutionary Algorithms）包括遗传算法(Genetic Algorithms)、遗传规划（Genetic Programming）、进化策略(Evolution Strategies)和进化规划(Evolution Programming)4种典型方法。第一类方法比较成熟，现已广泛应用，进化策略和进化规划在科研和实际问题中的应用也越来越广泛。

算法优点

• 泛用性强，对连续变量和离散变量都能适用；
• 不需要导数信息，因此不要求适应度函数的连续和可微性质(或者说不需要问题内在机理的相关信息)；
• 可以在解空间内大范围并行搜索；
• 不容易陷入局部最优；
• 高度并行化，并且容易与其他优化方法整合。

算法缺点

• 对于凸优化问题，相对基于梯度的优化方法（例如梯度下降法，牛顿/拟牛顿法）收敛速度更慢；
• 进化算法需要在搜索空间投放大量个体来搜索最优解。对于高维问题，由于搜索空间随维度指数级膨胀，需要投放的个体数也大幅增长，会导致收敛速度变慢；
• 设计编码方式、适应度函数以及变异规则需要大量经验。

DEAP库介绍

话不多说，先上网址：

https://deap.readthedocs.io/en/master/

原文介绍：

DEAP is a novel evolutionary computation framework for rapid prototyping and testing of ideas. It seeks to make algorithms explicit and data structures transparent. It works in perfect harmony with parallelisation mechanism such as multiprocessing and SCOOP. The following documentation presents the key concepts and many features to build your own evolutions.

使用DEAP实现EA

首先，安装DEAP

pip install deap

之后，引入以下包：

import random

from deap import base
from deap import creator
from deap import tools

最后，给出完整代码：

import random

import numpy

from deap import algorithms
from deap import base
from deap import creator
from deap import tools

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

toolbox = base.Toolbox()

toolbox.register("attr_bool", random.randint, 0, 1)
toolbox.register("individual", tools.initRepeat, creator.Individual, toolbox.attr_bool, n=100)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)

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

def cxTwoPointCopy(ind1, ind2):
    """Execute a two points crossover with copy on the input individuals. The
    copy is required because the slicing in numpy returns a view of the data,
    which leads to a self overwriting in the swap operation. It prevents
    ::

        >>> import numpy
        >>> a = numpy.array((1,2,3,4))
        >>> b = numpy.array((5,6,7,8))
        >>> a[1:3], b[1:3] = b[1:3], a[1:3]
        >>> print(a)
        [1 6 7 4]
        >>> print(b)
        [5 6 7 8]
    """
    size = len(ind1)
    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].copy(), ind1[cxpoint1:cxpoint2].copy()

    return ind1, ind2


toolbox.register("evaluate", evalOneMax)
toolbox.register("mate", cxTwoPointCopy)
toolbox.register("mutate", tools.mutFlipBit, indpb=0.05)
toolbox.register("select", tools.selTournament, tournsize=3)

def main():
    random.seed(64)

    pop = toolbox.population(n=300)

    # Numpy equality function (operators.eq) between two arrays returns the
    # equality element wise, which raises an exception in the if similar()
    # check of the hall of fame. Using a different equality function like
    # numpy.array_equal or numpy.allclose solve this issue.
    hof = tools.HallOfFame(1, similar=numpy.array_equal)

    stats = tools.Statistics(lambda ind: ind.fitness.values)
    stats.register("avg", numpy.mean)
    stats.register("std", numpy.std)
    stats.register("min", numpy.min)
    stats.register("max", numpy.max)

    algorithms.eaSimple(pop, toolbox, cxpb=0.5, mutpb=0.2, ngen=40, stats=stats,
                        halloffame=hof)

    return pop, stats, hof

if __name__ == "__main__":
    main()