安装必要的包
为了使用遗传算法在 Python 中解决问题，我们将使用一个强大的 GA 包叫做 DEAP。这是一个新式进化计算框架的库，用于快速原型设计和测试想法。我们可以在命令提示符下使用以下命令来安装这个包：
pip install deap
如果你使用的是 Anaconda 环境，可以使用以下命令来安装 deap：
conda install -c conda-forge deap
使用遗传算法实现解决方案
本节解释了如何使用遗传算法实现解决方案。
生成比特模式
下面的例子展示了如何生成一个比特字符串，该字符串包含 15 个 1，基于 One Max 问题。
导入必要的包
import random
from deap import base, creator, tools
定义评估函数
这是创建遗传算法的第一步。
def eval_func(individual):
target_sum = 15
return len(individual) - abs(sum(individual) - target_sum),
创建带有正确参数的工具箱
def create_toolbox(num_bits):
creator.create("FitnessMax", base.Fitness, weights=(1.0,))
creator.create("Individual", list, fitness=creator.FitnessMax)
toolbox = base.Toolbox()
toolbox.register("attr_bool", random.randint, 0, 1)
toolbox.register("individual", tools.initRepeat, creator.Individual,
toolbox.attr_bool, num_bits)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)
toolbox.register("evaluate", eval_func)
toolbox.register("mate", tools.cxTwoPoint)
toolbox.register("mutate", tools.mutFlipBit, indpb = 0.05)
toolbox.register("select", tools.selTournament, tournsize = 3)
return toolbox
主函数
if __name__ == "__main__":
num_bits = 45
toolbox = create_toolbox(num_bits)
random.seed(7)
population = toolbox.population(n = 500)
probab_crossing, probab_mutating = 0.5, 0.2
num_generations = 10
print('\nEvolution process starts')
fitnesses = list(map(toolbox.evaluate, population))
for ind, fit in zip(population, fitnesses):
ind.fitness.values = fit
print('\nEvaluated', len(population), 'individuals')
for g in range(num_generations):
print("\n- Generation", g)
offspring = toolbox.select(population, len(population))
offspring = list(map(toolbox.clone, offspring))
for child1, child2 in zip(offspring[::2], offspring[1::2]):
if random.random() < probab_crossing:
toolbox.mate(child1, child2)
del child1.fitness.values
del child2.fitness.values
for mutant in offspring:
if random.random() < probab_mutating:
toolbox.mutate(mutant)
del mutant.fitness.values
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', len(invalid_ind), 'individuals')
population[:] = offspring
fits = [ind.fitness.values[0] for ind in population]
length = len(population)
mean = sum(fits) / length
sum2 = sum(x*x for x in fits)
std = abs(sum2 / length - mean**2)**0.5
print('Min =', min(fits), ', Max =', max(fits))
print('Average =', round(mean, 2), ', Standard deviation =', round(std, 2))
print("\n- Evolution ends")
best_ind = tools.selBest(population, 1)[0]
print('\nBest individual:\n', best_ind)
print('\nNumber of ones:', sum(best_ind))
输出示例
Evolution process starts
Evaluated 500 individuals
- Generation 0
Evaluated 295 individuals
Min = 32.0 , Max = 45.0
Average = 40.29 , Standard deviation = 2.61
- Generation 1
Evaluated 292 individuals
Min = 34.0 , Max = 45.0
Average = 42.35 , Standard deviation = 1.91
- Generation 2
Evaluated 277 individuals
Min = 37.0 , Max = 45.0
Average = 43.39 , Standard deviation = 1.46
… … … …
- Generation 9
Evaluated 299 individuals
Min = 40.0 , Max = 45.0
Average = 44.12 , Standard deviation = 1.11
- Evolution ends
Best individual:
[0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1,
1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0,
1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1]
Number of ones: 15
符号回归问题
这是遗传编程中已知的最佳问题之一。所有的符号回归问题都使用任意的数据分布，并试图用符号公式拟合最准确的数据。通常，使用 RMSE（均方根误差）这样的度量来衡量个体的适应度。这是一个经典的回归问题，这里我们使用方程 5x^3-6x^2+8x=1。我们需要遵循上面例子中的所有步骤，但主要的部分是创建原始集合，因为它们是个体的基础，所以评估可以开始。在这里我们将使用经典的一组原始。
Python 代码详解
import operator
import math
import random
import numpy as np
from deap import algorithms, base, creator, tools, gp
def division_operator(numerator, denominator):
if denominator == 0:
return 1
return numerator / denominator
def eval_func(individual, points):
func = toolbox.compile(expr=individual)
mse = [(func(x) - (5*x**3 - 6*x**2 + 8*x)) ** 2 for x in points]
return math.fsum(mse) / len(points),
def create_toolbox():
pset = gp.PrimitiveSet("MAIN", 1)
pset.addPrimitive(operator.add, 2)
pset.addPrimitive(operator.sub, 2)
pset.addPrimitive(operator.mul, 2)
pset.addPrimitive(division_operator, 2)
pset.addPrimitive(operator.neg, 1)
pset.addPrimitive(math.cos, 1)
pset.addPrimitive(math.sin, 1)
pset.addEphemeralConstant("rand101", lambda: random.randint(-1,1))
pset.renameArguments(ARG0 = 'x')
creator.create("FitnessMin", base.Fitness, weights = (-1.0,))
creator.create("Individual", gp.PrimitiveTree, fitness=creator.FitnessMin)
toolbox = base.Toolbox()
toolbox.register("expr", gp.genHalfAndHalf, pset=pset, min_=1, max_=2)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)
toolbox.register("compile", gp.compile, pset = pset)
toolbox.register("evaluate", eval_func, points = [x/10. for x in range(-10,10)])
toolbox.register("select", tools.selTournament, tournsize = 3)
toolbox.register("mate", gp.cxOnePoint)
toolbox.register("expr_mut", gp.genFull, min_=0, max_=2)
toolbox.register("mutate", gp.mutUniform, expr = toolbox.expr_mut, pset = pset)
toolbox.decorate("mate", gp.staticLimit(key = operator.attrgetter("height"), max_value = 17))
toolbox.decorate("mutate", gp.staticLimit(key = operator.attrgetter("height"), max_value = 17))
return toolbox
if __name__ == "__main__":
random.seed(7)
toolbox = create_toolbox()
population = toolbox.population(n = 450)
hall_of_fame = tools.HallOfFame(1)
stats_fit = tools.Statistics(lambda x: x.fitness.values)
stats_size = tools.Statistics(len)
mstats = tools.MultiStatistics(fitness=stats_fit, size = stats_size)
mstats.register("avg", np.mean)
mstats.register("std", np.std)
mstats.register("min", np.min)
mstats.register("max", np.max)
probab_crossover = 0.4
probab_mutate = 0.2
number_gen = 10
population, log = algorithms.eaSimple(population, toolbox,
probab_crossover, probab_mutate, number_gen,
stats = mstats, halloffame = hall_of_fame, verbose = True)
注意，所有的基本步骤与生成比特模式时使用的步骤相同。这个程序将在 10 代之后给我们输出 min, max, std（标准偏差）。