Python实现遗传算法(二进制编码)求函数最优值方式

目标函数

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 其编码长度为18，对于 其编码长度为15，因此每个基于的长度为33。

参数设置

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：

算法结果

由程序输出可知其最终优化结果为38.85029，

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])

来源：https://blog.csdn.net/zhenguipa8450/article/details/78938303