最大流問題 （使用遺傳算法解決 --Python 實現）

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 控制變異程度  start 控制變異量 
        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]  # 獲取 0  所對應的下標              
            index_1 = [t[0] for t in Line if t[1]==1]  # 獲取 1  所對應的下標
            M[i][random.sample(index_0,number)[0]]=1   # 隨機改變序列中 number 個值 0->1
            M[i][random.sample(index_1,number)[0]]=0   # 隨機改變序列中 number 個值 1->0
        return M

    x,y = A.shape


    n=x
    generation = y

    #初始化一個有 n 中情況的解決方案矩陣
    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 # 用於記錄每一種方案的總流量

        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)  # 將 方案 按照流量總和排序

        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]]    #  保留排序後方案的一半

        solve = np.concatenate([solve[solve_index_half],solve[solve_index_half]])  # 將保留的一半方案 進行復制 ，複製部分用於變異

        change(solve,int((x+y-2)*degree)+1 ,start)  #  變異

    return solve[0] , Max

Draw_road

def Draw_road(road,A):

    import pylab as plt
    import seaborn
    seaborn.set()

    x , y =A.shape    

    # 將下移和右移映射到繪圖座標上
    Road = [(1,x)]  #  初始座標
    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]])

實際運行的例子

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)

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較大規模的情況

In [105]: A = Generate_matrix(40,60)

In [106]: road , M=Max_road(A,0.1,4)

In [107]: road
Out[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)

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