吉吉:

(I)实现功能

求解函数 f(x) = x + 10*sin(5*x) + 7*cos(4*x) 在区间[0, 9] 的最大值;

(II)代码:

#求解函数 f(x) = x + 10*sin(5*x) + 7*cos(4*x) 在区间[0,9]的最大值。

import math

import random

class GA():

#initalise

def __init__(self, length, count):

#length of chromosome

self.length = length

#number of chromosome

self.count = count

# randomly get initial population

self.population = self.get_population(length, count)

def get_population(self, length, count):

# get a list of count numbers chromosome (length : length)

return [self.get_chromosome(length) for i in range(count)]

def get_chromosome(self, length):

#randomly get a chromosome which length is length

# a bit ( 0, 1 ) represent a gene

chromosome = 0

for i in range(length):

chromosome |= ( 1 << i ) * random.randint(0, 1)

return chromosome

def evolve(self, retain_rate = 0.2, random_select_rate = 0.5, mutation_rate =
0.01 ):

#进化函数

parents = self.selection(retain_rate, random_select_rate)

self.crossover(parents)

self.mutation(mutation_rate)

def fitness(self, chromosome):#适应条件

# decode and compute fitness function

x = self.decode(chromosome)

return x + 10 * math.sin(5 * x) + 7 * math.cos(4 * x)

def selection(self, retain_rate, random_select_rate):

#英语不好表达了,我就用汉语了

#通过适应度大小从大到小进行排序,最后生成的仍然是二进制的列表

graded = [(self.fitness(chromosome), chromosome) for chromosome in
self.population]

graded = [x[1] for x in sorted(graded, reverse=True)]

# 选出适应性强的染色体,挑选20%作为父类

retain_length = int(len(graded) * retain_rate)

parents = graded[:retain_length]

# 从剩余的80%里面选出适应性不强,但是幸存的染色体(概率0.5)

for chromosome in graded[retain_length:]:

if random.random() < random_select_rate:

parents.append(chromosome)

return parents

def crossover(self, parents):

#交叉产生后代

# 新出生的孩子,最终会被加入存活下来的父母之中,形成新一代的种群。

children = []

#需要繁殖的数量

target_count = len(self.population) - len(parents)

while len(children) < target_count:

malelocation = random.randint(0, len(parents) - 1)

femalelocation = random.randint(0, len(parents) - 1)

male = parents[malelocation]

female = parents[femalelocation]

if malelocation != femalelocation:

#随机选择交叉点

cross_pos = random.randint(0, self.length)

#生成掩码,方便位运算

mask = 0

for i in range(cross_pos):

mask |= (1 << i )

#孩子将获得父亲在交叉点前的基因和母亲在交叉点后(包括交叉点)的基因

child = (male & mask) | (female & ~mask)

children.append(child)

#经过繁殖后,孩子和父母的数量与原始种群数量相等,在这里可以更新种群。

self.population = parents + children

def mutation(self, rate):#变异函数

#对种群中的所有个体,随机改变某个个体中的某个基因

for i in range(len(self.population)):

if random.random() < rate:

j = random.randint(0, self.length)

self.population[i] ^= 1 << j #^是异或运算

def decode(self, chromosome):

#将二进制还原成十进制

return chromosome * 9.0 / (2**self.length-1)

def result(self):

#获得当前最优的个体值

graded = [(self.fitness(chromosome), chromosome) for chromosome in
self.population]

graded = [ x[1] for x in sorted(graded, reverse = True)]

return ga.decode(graded[0])

if __name__ == "__main__":

#染色体长度为17,群落数量是300

ga = GA(17, 300)

for x in range(200):

ga.evolve()

print(ga.result())

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