Python使用遗传算法解决最大流问题

本文为大家分享了Python遗传算法解决最大流问题，供大家参考，具体内容如下
Generate_matrix    
def Generate_matrix(x,y):
 import numpy as np
 import random
 return np.ceil(np.array([random.random()*10 for i in range(x*y)]).reshape(x,y))

Max_road    
def Max_road(A,degree,start):
 
 import random
 import numpy as np
 import copy
 
 def change(M,number,start): # number 控制变异程度 start 控制变异量
  x , y = M.shape
  for i in range(start,x):
   Line = zip(range(len(M[i])),M[i])
   index_0 = [t[0] for t in Line if t[1]==0] # 获取 0 所对应的下标    
   index_1 = [t[0] for t in Line if t[1]==1] # 获取 1 所对应的下标
   M[i][random.sample(index_0,number)[0]]=1 # 随机改变序列中 number 个值 0->1
   M[i][random.sample(index_1,number)[0]]=0 # 随机改变序列中 number 个值 1->0
  return M
 
 x,y = A.shape
 
 n=x
 generation = y
 
 #初始化一个有 n 中情况的解决方案矩阵
 init_solve = np.zeros([n,x+y-2])
 init=[1]*(x-1)+[0]*(y-1)
 for i in range(n) :
  random.shuffle(init)
  init_solve[i,:] = init # 1 表示向下走 0 表示向右走
 solve = copy.copy(init_solve)
 
 for loop in range(generation):
  Sum = [A[0,0]]*n # 用于记录每一种方案的总流量
  for i in range(n):
   j=0;k=0;
   for m in solve[i,:]:
    if m==1:
     k=k+1
    else:
     j=j+1  
    Sum[i] = Sum[i] + A[k,j]
 
  Sum_index = zip(range(len(Sum)),Sum)
  sort_sum_index = sorted(Sum_index,key = lambda d : d[1] , reverse =True) # 将 方案 按照流量总和排序
 
  Max = sort_sum_index[0][1] # 最大流量
  #print Max
  solve_index_half = [a[0] for a in sort_sum_index[:n/2]] # 保留排序后方案的一半
  solve = np.concatenate([solve[solve_index_half],solve[solve_index_half]]) # 将保留的一半方案 进行复制 ，复制部分用于变异
  change(solve,int((x+y-2)*degree)+1 ,start) # 变异
 
 return solve[0] , Max

Draw_road    
def Draw_road(road,A):
 
 import pylab as plt
 import seaborn
 seaborn.set()
 
 x , y =A.shape
 
 # 将下移和右移映射到绘图坐标上
 Road = [(1,x)] # 初始坐标
 j=1;k=x;
 for m in road:
  if m==1:
   k=k-1
  else:
   j=j+1
  Road.append((j,k))
 
 # print Road
 
 for i in range(len(road)):  
  plt.plot([Road[i][0],Road[i+1][0]],[Road[i][1],Road[i+1][1]])

实际运行的例子
    
In [119]: A = Generate_matrix(4,6)
 
In [120]: A
Out[120]:
array([[ 10., 1., 7., 10., 8., 8.],
  [ 4., 8., 8., 4., 8., 2.],
  [ 9., 8., 8., 3., 9., 8.],
  [ 7., 2., 5., 9., 3., 8.]])
 
In [121]: road , M=Max_road(A,0.1,2)
 

In [122]: Draw_road(road,A)

较大规模的情况

In [105]: A=Generate_matrix(40,60) In [106]: road , M=Max_road(A,0.1,4) In [107]: roadOut[107]:array([0.,0.,0.,1.,1.,0.,0.,0.,0.,0.,0.,0.,0.,  1.,0.,0.,0.,1.,0.,0.,1.,0.,1.,1.,1.,1.,  1.,0.,0.,0.,0.,0.,1.,0.,0.,1.,0.,0.,0.,  1.,0.,0.,0.,1.,0.,1.,0.,0.,1.,0.,0.,1.,  0.,0.,0.,1.,0.,0.,1.,1.,1.,1.,0.,0.,0.,  0.,0.,0.,1.,0.,1.,1.,1.,1.,0.,1.,0.,1.,  1.,1.,0.,1.,0.,1.,0.,1.,0.,1.,0.,0.,1.,  0.,1.,0.,0.,1.,0.,1.]) In [108]: Draw_road(road,A)

In [109]: A=generate_Matrix(100,200)In [110]: road , M=Max_road(A,0.1,10)In [111]: draw_road(road,A)

以上就是本文的全部内容，希望对大家的学习有所帮助