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())