最大流问题 （使用遗传算法解决 --Python 实现）

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]: AOut[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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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)

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