一、遗传算法介绍

遗传算法是通过模拟大自然中生物进化的历程，来解决问题的。大自然中一个种群经历过若干代的自然选择后，剩下的种群必定是适应环境的。把一个问题所有的解看做一个种群，经历过若干次的自然选择以后，剩下的解中是有问题的最优解的。当然，只能说有最优解的概率很大。这里，我们用遗传算法求一个函数的最大值。
f(x) = 10 * sin( 5x ) + 7 * cos( 4x ), 0 <= x <= 10

1、将自变量x进行编码

取基因片段的长度为10, 则10位二进制位可以表示的范围是0到1023。基因与自变量转变的公式是x = b2d(individual) * 10 / 1023。构造初始的种群pop。每个个体的基因初始值是[0, 1, 0, 1, 0, 1, 0, 1, 0, 1]

2、计算目标函数值

根据自变量与基因的转化关系式，求出每个个体的基因对应的自变量，然后将自变量代入函数f（x），求出每个个体的目标函数值。

3、适应度函数

适应度函数是用来评估个体适应环境的能力，是进行自然选择的依据。本题的适应度函数直接将目标函数值中的负值变成0. 因为我们求的是最大值，所以要使目标函数值是负数的个体不适应环境，使其繁殖后代的能力为0.适应度函数的作用将在自然选择中体现。

4、自然选择

自然选择的思想不再赘述，操作使用轮盘赌算法。其具体步骤：

假设种群中共5个个体，适应度函数计算出来的个体适应性列表是fitvalue = [1 ,3, 0, 2, 4] ，totalvalue = 10 ，如果将fitvalue画到圆盘上，值的大小表示在圆盘上的面积。在转动轮盘的过程中，单个模块的面积越大则被选中的概率越大。选择的方法是将fitvalue转化为[1 ， 4 ，4 , 6 ，10], fitvalue / totalvalue = [0.1 , 0.4 , 0.4 , 0.6 , 1.0] . 然后产生5个0-1之间的随机数，将随机数从小到大排序，假如是[0.05 , 0.2 , 0.7 , 0.8 ,0.9]，则将0号个体、1号个体、4号个体、4号个体、4号个体拷贝到新种群中。自然选择的结果使种群更符合条件了。

5、繁殖

假设个体a、b的基因是

a = [1, 0, 0, 0, 0, 1, 1, 1, 0, 0]

b = [0, 0, 0, 1, 1, 0, 1, 1, 1, 1]

这两个个体发生基因交换的概率pc = 0.6.如果要发生基因交换，则产生一个随机数point表示基因交换的位置，假设point = 4,则：

a = [1, 0, 0, 0, 0, 1, 1, 1, 0, 0]

b = [0, 0, 0, 1,1, 0, 1, 1, 1, 1]

交换后为：

a = [1, 0, 0, 0, 1, 0, 1, 1, 1, 1]

b = [0, 0, 0, 1, 0, 1, 1, 1, 0, 0]

6、突变

遍历每一个个体，基因的每一位发生突变（0变为1,1变为0）的概率为0.001.突变可以增加解空间

二、代码

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def b2d(b): #将二进制转化为十进制 x∈[0,10]

t = 0

for j in range(len(b)):

t += b[j] * (math.pow(2, j))

t = t * 10 / 1023

return t

popsize = 50 #种群的大小

#用遗传算法求函数最大值：

#f(x)=10*sin(5x)+7*cos(4x) x∈[0,10]

chromlength = 10 #基因片段的长度

pc = 0.6 #两个个体交叉的概率

pm = 0.001; #基因突变的概率

results = [[]]

bestindividual = []

bestfit = 0

fitvalue = []

tempop = [[]]

pop = [[0, 1, 0, 1, 0, 1, 0, 1, 0, 1] for i in range(popsize)]

for i in range(100): #繁殖100代

objvalue = calobjvalue(pop) #计算目标函数值

fitvalue = calfitvalue(objvalue); #计算个体的适应值

[bestindividual, bestfit] = best(pop, fitvalue) #选出最好的个体和最好的函数值

results.append([bestfit,b2d(bestindividual)]) #每次繁殖，将最好的结果记录下来

selection(pop, fitvalue) #自然选择，淘汰掉一部分适应性低的个体

crossover(pop, pc) #交叉繁殖

mutation(pop, pc) #基因突变

results.sort()

print(results[-1]) #打印函数最大值和对应的

来自CODE的代码片

GA.py

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def best(pop, fitvalue): #找出适应函数值中最大值，和对应的个体

px = len(pop)

bestindividual = []

bestfit = fitvalue[0]

for i in range(1,px):

if(fitvalue[i] > bestfit):

bestfit = fitvalue[i]

bestindividual = pop[i]

return [bestindividual, bestfit]

来自CODE的代码片

best.py

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def calfitvalue(objvalue):#转化为适应值，目标函数值越大越好，负值淘汰。

fitvalue = []

temp = 0.0

Cmin = 0;

for i in range(len(objvalue)):

if(objvalue[i] + Cmin > 0):

temp = Cmin + objvalue[i]

else:

temp = 0.0

fitvalue.append(temp)

return fitvalue

来自CODE的代码片

calfitvalue.py

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import math

def decodechrom(pop): #将种群的二进制基因转化为十进制（0,1023）

temp = [];

for i in range(len(pop)):

t = 0;

for j in range(10):

t += pop[i][j] * (math.pow(2, j))

temp.append(t)

return temp

def calobjvalue(pop): #计算目标函数值

temp1 = [];

objvalue = [];

temp1 = decodechrom(pop)

for i in range(len(temp1)):

x = temp1[i] * 10 / 1023 #（0,1023）转化为（0,10）

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

return objvalue #目标函数值objvalue[m] 与个体基因 pop[m] 对应

来自CODE的代码片

calobjvalue.py

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import random

def crossover(pop, pc): #个体间交叉，实现基因交换

poplen = len(pop)

for i in range(poplen - 1):

if(random.random() < pc):

cpoint = random.randint(0,len(pop[0]))

temp1 = []

temp2 = []

temp1.extend(pop[i][0 : cpoint])

temp1.extend(pop[i+1][cpoint : len(pop[i])])

temp2.extend(pop[i+1][0 : cpoint])

temp2.extend(pop[i][cpoint : len(pop[i])])

pop[i] = temp1

pop[i+1] = temp2

来自CODE的代码片

crossover.py

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import random

def mutation(pop, pm): #基因突变

px = len(pop)

py = len(pop[0])

for i in range(px):

if(random.random() < pm):

mpoint = random.randint(0,py-1)

if(pop[i][mpoint] == 1):

pop[i][mpoint] = 0

else:

pop[i][mpoint] = 1

来自CODE的代码片

mutation.py

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import random

def sum(fitvalue):

total = 0

for i in range(len(fitvalue)):

total += fitvalue[i]

return total

def cumsum(fitvalue):

for i in range(len(fitvalue)):

t = 0;

j = 0;

while(j <= i):

t += fitvalue[j]

j = j + 1

fitvalue[i] = t;

def selection(pop, fitvalue): #自然选择（轮盘赌算法）

newfitvalue = []

totalfit = sum(fitvalue)

for i in range(len(fitvalue)):

newfitvalue.append(fitvalue[i] / totalfit)

cumsum(newfitvalue)

ms = [];

poplen = len(pop)

for i in range(poplen):

ms.append(random.random()) #random float list ms

ms.sort()

fitin = 0

newin = 0

newpop = pop

while newin < poplen:

if(ms[newin] < newfitvalue[fitin]):

newpop[newin] = pop[fitin]

newin = newin + 1

else:

fitin = fitin + 1

pop = newpop

来自CODE的代码片

selection.py

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python实现的遗传算法实例（一）

一、遗传算法介绍

1、将自变量x进行编码

2、计算目标函数值

3、适应度函数

4、自然选择

5、繁殖

6、突变

二、代码

来自CODE的代码片

GA.py

来自CODE的代码片

best.py

来自CODE的代码片

calfitvalue.py

来自CODE的代码片

calobjvalue.py

来自CODE的代码片

crossover.py

来自CODE的代码片

mutation.py

来自CODE的代码片

selection.py

python实现的遗传算法实例（一）相关推荐

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