本节向您介绍使用遗传算法实现解决方案。

生成位模式

以下示例显示了如何根据 One Max 问题生成一个包含15个字符串的位串。

如下所示导入必要的软件包 -

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)

现在，使用正确的参数创建工具箱 -

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

初始化工具箱

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)

注册计算操作符 -

toolbox.register("evaluate", eval_func)

现在，注册交叉运算符 -

toolbox.register("mate", tools.cxTwoPoint)

注册一个可变运算符 -

toolbox.register("mutate", tools.mutFlipBit, indpb = 0.05)

定义育种操作符 -

toolbox.register("select", tools.selTournament, tournsize = 3)
return toolbox
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')

评估整个人口 -

fitnesses = list(map(toolbox.evaluate, population))
for ind, fit in zip(population, fitnesses):
   ind.fitness.values = fit
print('\nEvaluated', len(population), 'individuals')

经过几代人的创建和迭代 -

for g in range(num_generations):
   print("\n- Generation", g)

选择下一代个人 -

offspring = toolbox.select(population, len(population))

现在，克隆选定的个人 -

offspring = list(map(toolbox.clone, offspring))

对后代应用交叉和变异 -

for child1, child2 in zip(offspring[::2], offspring[1::2]):
   if random.random() < probab_crossing:
   toolbox.mate(child1, child2)

删除孩子的适应值

del child1.fitness.values
del child2.fitness.values

现在，应用突变 -

for mutant in offspring:
   if random.random() < probab_mutating:
   toolbox.mutate(mutant)
   del mutant.fitness.values

评估与无效的健身个体 -

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')

现在，用下一代个体替代人口 -

population[:] = offspring

打印当代人的统计数据 -

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")

打印最终输出 -

   best_ind = tools.selBest(population, 1)[0]
   print('\nBest individual:\n', best_ind)
   print('\nNumber of ones:', sum(best_ind))
Following would be the output:
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

这是遗传编程中最著名的问题之一。 所有符号回归问题都使用任意数据分布，并尝试用符号公式来拟合最准确的数据。 通常，像 RMSE (均方根误差)这样的度量用于度量个体的适应度。 这是一个经典的回归问题，这里我们使用方程: 5x3-6x2 + 8x = 1。 我们需要按照上述示例中的所有步骤进行操作，但主要部分是创建基元集，因为它们是个人的构建基块，因此可以开始评估。 这里将使用经典的基元集。

以下 Python 代码详细解释了这一点 -

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)
   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.expr)
   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)