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import math
import random
import time,os
from matplotlib.pyplot import *
import numpy as np
class Evolution():
def __init__(self, lower_bound, upper_bound, chromosome_size, population, mutation_rate, retain_rate, formula):
self.lower_bound = lower_bound
self.upper_bound = upper_bound
self.chromosome_size = chromosome_size
self.num = population
self.mutation_rate = mutation_rate
self.retain_rate = retain_rate
self.formula = formula
self.best = 0
self.population = self.Gene_population()
def Gene_population(self):
"""
获取初始种群（一个含有 self.num 个长度为 self.chromosome_size 的染色体的列表）
"""
return [self.Gene_chromosome() for i in xrange(self.num)]
def Evolve(self, random_select_rate=0.5):
"""
进化
对当前一代种群依次进行选择、交叉并生成新一代种群，然后对新一代种群进行变异
"""
parents = self.Selection(random_select_rate)
self.Crossover(parents)
self.Mutation()
def Gene_chromosome(self):
"""
随机生成长度为 self.chromosome_size 的染色体，每个基因的取值是 0 或 1
这里用一个 bit 表示一个基因
"""
chromosome = 0
for i in xrange(self.chromosome_size):
chromosome |= (1 << i) * random.randint(0, 1)
return chromosome
def Fitness(self, chromosome):
"""
计算适应度，将染色体解码为定义域之间的数字，代入函数计算
因为是求最大值，所以数值越大，适应度越高
"""
x = self.Decode(chromosome)
return eval(self.formula)
def Selection(self, random_select_rate):
"""
选择
先对适应度从大到小排序，选出存活的染色体
再进行随机选择，选出适应度虽然小，但是幸存下来的个体
"""
graded = [x for y,x in sorted([(y, x) for y, x in [(self.Fitness(chromosome), chromosome) for chromosome in self.population]],reverse = True)]
retain_chromosome_size = int(len(graded) * self.retain_rate)
parents = graded[:retain_chromosome_size]
for chromosome in graded[retain_chromosome_size:]:
if random.random() < random_select_rate:
parents.append(chromosome)
return parents
def Crossover(self, parents):
"""
染色体的交叉、繁殖，生成新一代的种群
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 = []
target_num = len(self.population) - len(parents)
while len(children) < target_num:
male = random.randint(0, len(parents)-1)
female = random.randint(0, len(parents)-1)
if male != female:
cross_pos = random.randint(0, self.chromosome_size)
mask = 0
for i in xrange(cross_pos):
mask |= (1 << i)
male = parents[male]
female = parents[female]
child = ((male & mask) | (female & ~mask)) & ((1 << self.chromosome_size) - 1)
children.append(child)
self.population = parents + children
def Mutation(self):
"""
变异
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 xrange(len(self.population)):
if random.randint(0, 100) < self.mutation_rate * 100:
j = random.randint(0, self.chromosome_size-1)
self.population[i] ^= 1 << j
def Decode(self, chromosome):
"""
解码染色体，将二进制转化为属于定义域的实数
"""
return self.lower_bound + chromosome * (self.upper_bound - self.lower_bound) / (2 ** self.chromosome_size - 1.0)
def Result(self):
"""
获得当前代的最优值，这里取的是函数取最大值时 x 的值。
"""
global x
graded = sorted([(yi, xi) for yi, xi in [(self.Fitness(chromosome), chromosome) for chromosome in self.population]],reverse = True)
chromosome = [xi for yi,xi in graded]
fitness = [yi for yi,xi in graded]
if self.best < fitness[0]:
self.best = fitness[0]
os.system('cls')
print '历史最优出现在第',x,'代, 个体为 '+ bin(chromosome[0])[2:] + ' 最优适应度 ' + str(self.Decode(chromosome[0])) + ' ,其值为 ' + str(fitness[0])
xi = [self.Decode(i) for i in chromosome]
self.PlotAndSave(xi, fitness)
return '最优个体为 '+ bin(chromosome[0])[2:] + ' 最优适应度 ' + str(self.Decode(chromosome[0])) + ' ,其值为 ' + str(fitness[0])
def PlotAndSave(self, chromosome, fitness):
x = np.arange(self.lower_bound, self.upper_bound, 0.0001)
y = eval(self.formula.replace('math','np'))
plot(x,y)
plot(chromosome, fitness, 'o')
savefig('Best.jpg')
close('all')
time.clock()
lower_bound = 0
upper_bound = 9
chromosome_size = 17
population = 200
mutation_rate = 0.1
generations = 2000
retain_rat = 0.2
formula = 'x + 10 * math.sin(5 * x) + 7 * math.cos(4 * x)'
gene = Evolution(lower_bound, upper_bound, chromosome_size, population, mutation_rate, retain_rat, formula)
for x in xrange(generations):
gene.Evolve()
print '\r进化到第',x,'代',gene.Result(),
print '花费时间',int(time.clock()),'S'
os.system('pause')
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