python编码函数_Python实现遗传算法(二进制编码)求函数最优值方式

目标函数

s2eiiqutfhb.jpg

编码方式

本程序采用的是二进制编码精确到小数点后五位,经过计算可知对于

tyy2j4mhnk0.jpg 其编码长度为18,对于

teyfqdl4iyy.jpg 其编码长度为15,因此每个基于的长度为33。

参数设置

c5rc5ob5owd.jpg

算法步骤

设计的程序主要分为以下步骤:1、参数设置;2、种群初始化;3、用轮盘赌方法选择其中一半较好的个体作为父代;4、交叉和变异;5、更新最优解;6、对最有个体进行自学习操作;7结果输出。其算法流程图为:

python编码函数_Python实现遗传算法(二进制编码)求函数最优值方式_第1张图片

算法结果

由程序输出可知其最终优化结果为38.85029,

3ovrmhyfo14.jpg

输出基因编码为[1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 1 1]。

代码

import numpy as np

import random

import math

import copy

class Ind():

def __init__(self):

self.fitness = 0

self.x = np.zeros(33)

self.place = 0

self.x1 = 0

self.x2 = 0

def Cal_fit(x, upper, lower): #计算适应度值函数

Temp1 = 0

for i in range(18):

Temp1 += x[i] * math.pow(2, i)

Temp2 = 0

for i in range(18, 33, 1):

Temp2 += math.pow(2, i - 18) * x[i]

x1 = lower[0] + Temp1 * (upper[0] - lower[0])/(math.pow(2, 18) - 1)

x2 = lower[1] + Temp2 * (upper[1] - lower[1])/(math.pow(2, 15) - 1)

if x1 > upper[0]:

x1 = random.uniform(lower[0], upper[0])

if x2 > upper[1]:

x2 = random.uniform(lower[1], upper[1])

return 21.5 + x1 * math.sin(4 * math.pi * (x1)) + x2 * math.sin(20 * math.pi * x2)

def Init(G, upper, lower, Pop): #初始化函数

for i in range(Pop):

for j in range(33):

G[i].x[j] = random.randint(0, 1)

G[i].fitness = Cal_fit(G[i].x, upper, lower)

G[i].place = i

def Find_Best(G, Pop):

Temp = copy.deepcopy(G[0])

for i in range(1, Pop, 1):

if G[i].fitness > Temp.fitness:

Temp = copy.deepcopy(G[i])

return Temp

def Selection(G, Gparent, Pop, Ppool): #选择函数

fit_sum = np.zeros(Pop)

fit_sum[0] = G[0].fitness

for i in range(1, Pop, 1):

fit_sum[i] = G[i].fitness + fit_sum[i - 1]

fit_sum = fit_sum/fit_sum.max()

for i in range(Ppool):

rate = random.random()

Gparent[i] = copy.deepcopy(G[np.where(fit_sum > rate)[0][0]])

def Cross_and_Mutation(Gparent, Gchild, Pc, Pm, upper, lower, Pop, Ppool): #交叉和变异

for i in range(Ppool):

place = random.sample([_ for _ in range(Ppool)], 2)

parent1 = copy.deepcopy(Gparent[place[0]])

parent2 = copy.deepcopy(Gparent[place[1]])

parent3 = copy.deepcopy(parent2)

if random.random() < Pc:

num = random.sample([_ for _ in range(1, 32, 1)], 2)

num.sort()

if random.random() < 0.5:

for j in range(num[0], num[1], 1):

parent2.x[j] = parent1.x[j]

else:

for j in range(0, num[0], 1):

parent2.x[j] = parent1.x[j]

for j in range(num[1], 33, 1):

parent2.x[j] = parent1.x[j]

num = random.sample([_ for _ in range(1, 32, 1)], 2)

num.sort()

num.sort()

if random.random() < 0.5:

for j in range(num[0], num[1], 1):

parent1.x[j] = parent3.x[j]

else:

for j in range(0, num[0], 1):

parent1.x[j] = parent3.x[j]

for j in range(num[1], 33, 1):

parent1.x[j] = parent3.x[j]

for j in range(33):

if random.random() < Pm:

parent1.x[j] = (parent1.x[j] + 1) % 2

if random.random() < Pm:

parent2.x[j] = (parent2.x[j] + 1) % 2

parent1.fitness = Cal_fit(parent1.x, upper, lower)

parent2.fitness = Cal_fit(parent2.x, upper, lower)

Gchild[2 * i] = copy.deepcopy(parent1)

Gchild[2 * i + 1] = copy.deepcopy(parent2)

def Choose_next(G, Gchild, Gsum, Pop): #选择下一代函数

for i in range(Pop):

Gsum[i] = copy.deepcopy(G[i])

Gsum[2 * i + 1] = copy.deepcopy(Gchild[i])

Gsum = sorted(Gsum, key = lambda x: x.fitness, reverse = True)

for i in range(Pop):

G[i] = copy.deepcopy(Gsum[i])

G[i].place = i

def Decode(x): #解码函数

Temp1 = 0

for i in range(18):

Temp1 += x[i] * math.pow(2, i)

Temp2 = 0

for i in range(18, 33, 1):

Temp2 += math.pow(2, i - 18) * x[i]

x1 = lower[0] + Temp1 * (upper[0] - lower[0]) / (math.pow(2, 18) - 1)

x2 = lower[1] + Temp2 * (upper[1] - lower[1]) / (math.pow(2, 15) - 1)

if x1 > upper[0]:

x1 = random.uniform(lower[0], upper[0])

if x2 > upper[1]:

x2 = random.uniform(lower[1], upper[1])

return x1, x2

def Self_Learn(Best, upper, lower, sPm, sLearn): #自学习操作

num = 0

Temp = copy.deepcopy(Best)

while True:

num += 1

for j in range(33):

if random.random() < sPm:

Temp.x[j] = (Temp.x[j] + 1)%2

Temp.fitness = Cal_fit(Temp.x, upper, lower)

if Temp.fitness > Best.fitness:

Best = copy.deepcopy(Temp)

num = 0

if num > sLearn:

break

return Best

if __name__ == '__main__':

upper = [12.1, 5.8]

lower = [-3, 4.1]

Pop = 100

Ppool = 50

G_max = 300

Pc = 0.8

Pm = 0.1

sPm = 0.05

sLearn = 20

G = np.array([Ind() for _ in range(Pop)])

Gparent = np.array([Ind() for _ in range(Ppool)])

Gchild = np.array([Ind() for _ in range(Pop)])

Gsum = np.array([Ind() for _ in range(Pop * 2)])

Init(G, upper, lower, Pop) #初始化

Best = Find_Best(G, Pop)

for k in range(G_max):

Selection(G, Gparent, Pop, Ppool) #使用轮盘赌方法选择其中50%为父代

Cross_and_Mutation(Gparent, Gchild, Pc, Pm, upper, lower, Pop, Ppool) #交叉和变异生成子代

Choose_next(G, Gchild, Gsum, Pop) #选择出父代和子代中较优秀的个体

Cbest = Find_Best(G, Pop)

if Best.fitness < Cbest.fitness:

Best = copy.deepcopy(Cbest) #跟新最优解

else:

G[Cbest.place] = copy.deepcopy(Best)

Best = Self_Learn(Best, upper, lower, sPm, sLearn)

print(Best.fitness)

x1, x2 = Decode(Best.x)

print(Best.x)

print([x1, x2])

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