标准遗传算法（二进制编码 python实现）

代码地址：https://github.com/guojun007/binary_sga

种群初始化:

​​binary_sga​​​/​​population_init​​/population_init.py

#种群初始化函数
def population_init(population, N, V, nbits):
#自变量个数V并没有用到
del population[:]
for i in xrange(N):
tempIndividual=[]
for j in nbits:
tempVal=[]
for k in xrange(j):
tempVal.append(random.randint(0, 1))
tempIndividual.append(tempVal)
population.append(tempIndividual)

选择操作：（轮盘赌选择）

​​binary_sga​​​/​​selection​​/selection.py

#!/usr/bin/env python
#encoding:UTF-8
import copy
import random
#轮盘赌选择法
def selection(population, xbin):
s=sum(xbin)
temp=[k*1.0/s for k in xbin]
temp2=[]

s2=0
for k in temp:
s2=s2+k
temp2.append(s2)

temp3=[]
for _ in xrange(len(population)):
r=random.random()
for i in xrange(len(temp2)):
if r<=temp2[i]:
temp3.append(i)
break

temp4=[]
temp5=[]
for i in temp3:
temp4.append(copy.deepcopy(population[i]))
temp5.append(xbin[i])
population[:]=temp4
xbin[:]=temp5

交叉操作：（单点交叉）

​​binary_sga​​​/​​crossover​​/crossover.py

#二进制编码,单点交叉
def crossover(population, alfa, nbits):
for i in xrange(len(population), 2):
for j in xrange(len(nbits)):
r=random.random()
if r<alfa:
p=random.randint(1, nbits[j]-1)
population[i][j][p:], population[i+1][j][p:]=population[i+1][j][p:], population[i][j][p:]

变异操作：

​​binary_sga​​​/​​mutation​​/mutation.py

def mutation(population, belta, nbits):
for i in xrange(len(population)):
for j in xrange(len(nbits)):
for k in xrange(nbits[j]):
r=random.random()
if r<belta:
population[i][j][k]^=1

二进制个体解码操作：

​​binary_sga​​​/​​decode​​/decode.py

#种群个体解码
def decode(population, population_real, minBinVal, maxBinVal, nbits):
del population_real[:]

def iner(valList):
L=len(valList)
s=0
for i in valList:
s=s+i*(2**(L-1))
L=L-1
return s

for i in population:
temp=[]
for j in i:
temp.append(iner(j))

for j in xrange(len(temp)):
temp[j]=temp[j]*(maxBinVal[j]-minBinVal[j])*1.0/(2**(nbits[j])-1)+minBinVal[j]
population_real.append(temp)

测试函数部分：

​​binary_sga​​​/​​function​​/object_fun.py

#对偶问题， 转化为求最大值
#二维　Rastrigin测试函数
def object_fun(p):
import math
x=p[0]
y=p[1]
object_value=20.0+x**2+y**2-10.0*(math.cos(2*math.pi*x)+math.cos(2*math.pi*y))
return 100.0-object_value

"""
#求最大值,无需转化
#二维　Schaffer测试函数
def object_fun(p):
import math
x=p[0]
y=p[1]
object_value =0.5-((math.sin( math.sqrt(x**2+y**2) ))**2-0.5)/(1+0.001*(x**2+y**2))**2
return object_value
"""

主函数部分：

​​binary_sga​​/sga.py

N=200
V=2
nbits=(17, 17)
maxBinVal=(-5, -5)
minBinVal=(5, 5)
population=[]
population_real=[]
alfa=0.9
belta=0.05

#目标函数值列表
xbin=[]


def per_run():
population_init(population, N, V, nbits)

for i in xrange(200):
decode(population, population_real, minBinVal, maxBinVal, nbits)
eval_fun(population_real, xbin)
selection(population, xbin)
crossover(population, alfa, nbits)
mutation(population, belta, nbits)

decode(population, population_real, minBinVal, maxBinVal, nbits)
eval_fun(population_real, xbin)
return 100.0-max(xbin)

Ｎ为个体种群数。

Ｖ为自变量个数。

nbits 各个自变量二进制编码的长度。

maxBinVal　各个自变量　上限。minBinVal　各个自变量　下限。种群个体　二进制编码　列表　population。
种群个体　实数解码　　列表　population_real。alfa=0.9　　交叉概率。
belta=0.05　变异概率。