python实现遗传算法（旅行商问题）

àì夳堔傛蜴生んèń 2022-05-31 02:48 253阅读 0赞

网上找到一篇不错的论文：

[http://www.doc88.com/p-9078235973437.html][http_www.doc88.com_p-9078235973437.html]

然后我用python对其做了算法实现，贴代码：

from matplotlib import pyplot as plt
    import numpy as np
    import random
    
    def coordinate_init(size):
        # 产生坐标字典
        coordinate_dict = {}
        coordinate_dict[0] = (-size, 0)  # 起点是（-size，0）
        up=1
        for i in range(1, size + 1):  # 顺序标号随机坐标
            x=np.random.uniform(-size,size)
            if np.random.randint(0,2)==up:
                y=np.sqrt(size**2-x**2)
            else:
                y=-np.sqrt(size**2-x**2)
            coordinate_dict[i]=(x,y)
        coordinate_dict[size + 1] = (-size, 0)  # 终点是（-size,0),构成一个圆
        return coordinate_dict
    
    
    def distance_matrix(coordinate_dict, size):  # 生成距离矩阵
        d = np.zeros((size + 2, size + 2))
        for i in range(size + 1):
            for j in range(size + 1):
                if (i == j):
                    continue
                if (d[i][j] != 0):
                    continue
                x1 = coordinate_dict[i][0]
                y1 = coordinate_dict[i][1]
                x2 = coordinate_dict[j][0]
                y2 = coordinate_dict[j][1]
                distance = np.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)
                if (i == 0):
                    d[i][j] = d[size + 1][j] = d[j][i] = d[j][size + 1] = distance
                else:
                    d[i][j] = d[j][i] = distance
        return d
    
    
    def path_length(d_matrix, path_list, size):  # 计算路径长度
        length = 0
        for i in range(size + 1):
            length += d_matrix[path_list[i]][path_list[i + 1]]
        return length
    
    def shuffle(my_list):#起点和终点不能打乱
        temp_list=my_list[1:-1]
        np.random.shuffle(temp_list)
        shuffle_list=my_list[:1]+temp_list+my_list[-1:]
        return shuffle_list
    def product_len_probability(my_list,d_matrix,size,p_num):
        len_list=[]
        pro_list=[]
        path_len_pro=[]
        for path in my_list:
            len_list.append(path_length(d,path,size))
        max_len=max(len_list)+1e-10
        gen_best_length=min(len_list)
        gen_best_length_index=len_list.index(gen_best_length)
        mask_list=np.ones(p_num)*max_len-np.array(len_list)
        sum_len=np.sum(mask_list)
        for i in range(p_num):
            if(i==0):
                pro_list.append(mask_list[i]/sum_len)
            elif(i==p_num-1):
                pro_list.append(1)
            else:
                pro_list.append(pro_list[i-1]+mask_list[i]/sum_len)
        for i in range(p_num):
            path_len_pro.append([my_list[i],len_list[i],pro_list[i]])
        return my_list[gen_best_length_index],gen_best_length,path_len_pro
    
    def choose_cross(population,p_num):
        jump=np.random.random()
        if jump<population[0][2]:
            return 0
        low=1
        high=p_num
        mid=int((low+high)/2)
        #二分搜索
        while(low<high):
            if jump>population[mid][2]:
                low=mid
                mid=int((low+high)/2)
            elif jump<population[mid-1][2]:
                high=mid
                mid = int((low + high) / 2)
            else:
                return mid
    def veriation(my_list,size):#变异
        ver_1=np.random.randint(1,size+1)
        ver_2=np.random.randint(1,size+1)
        while ver_2==ver_1:#直到ver_2与ver_1不同
            ver_2 = np.random.randint(1, size+1)
        my_list[ver_1],my_list[ver_2]=my_list[ver_2],my_list[ver_1]
        return my_list
    
    
    
    
    
    
    size=50
    p_num=100#种群个体数量
    gen=2000#进化代数
    pm=0.1#变异率
    coordinate_dict=coordinate_init(size)
    d=distance_matrix(coordinate_dict,size)
    print(coordinate_dict)
    path_list=list(range(size+2))
    print(path_list)#打印初始化的路径
    population=[0]*p_num#种群矩阵
    #建立初始种群
    for i in range(p_num):
        population[i]=shuffle(path_list)
    gen_best,gen_best_length,population=product_len_probability(population,d,size,p_num)
    print(population)#这个列表的每一项中有三项，第一项是路径，第二项是长度，第三项是使用时转盘的概率
    son_list=[0]*p_num
    best_path=gen_best#最好路径初始化
    best_path_length=gen_best_length#最好路径长度初始化
    every_gen_best=[]
    every_gen_best.append(gen_best_length)
    for i in range(gen):#迭代gen代
        son_num=0
        while son_num<p_num:#产生p_num数量子代，杂交与变异
            father_index = choose_cross(population, p_num)
            mother_index = choose_cross(population, p_num)
            father=population[father_index][0]
            mother=population[mother_index][0]
            son1=father.copy()
            son2=mother.copy()
            prduct_set=np.random.randint(1,p_num+1)
            father_cross_set=set(father[1:prduct_set])
            mother_cross_set=set(mother[1:prduct_set])
            cross_complete=1
            for j in range(1,size+1):
                if son1[j] in mother_cross_set:
                    son1[j]=mother[cross_complete]
                    cross_complete+=1
                    if cross_complete>prduct_set:
                        break
            if np.random.random()<pm:#变异
                son1=veriation(son1,size)
            son_list[son_num]=son1
            son_num+=1
            if son_num==p_num: break
            cross_complete=1
            for j in range(1,size+1):
                if son2[j] in father_cross_set:
                    son2[j]=father[cross_complete]
                    cross_complete+=1
                    if cross_complete>prduct_set:
                        break
            if np.random.random()<pm:#变异
                son2=veriation(son2,size)
            son_list[son_num]=son2
            son_num+=1
        gen_best, gen_best_length,population=product_len_probability(son_list,d,size,p_num)
        if(gen_best_length<best_path_length):
            best_path=gen_best
            best_path_length=gen_best_length
        every_gen_best.append(gen_best_length)
    x=[]
    y=[]
    for point in best_path:
        x.append(coordinate_dict[point][0])
        y.append(coordinate_dict[point][1])
    print(gen_best)#最后一代最优路径
    print(gen_best_length)#最后一代最优路径长度
    print(best_path)#史上最优路径
    print(best_path_length)#史上最优路径长度
    plt.figure(1)
    plt.subplot(211)
    plt.plot(every_gen_best)
    plt.subplot(212)
    plt.scatter(x,y)
    plt.plot(x,y)
    plt.grid()
    plt.show()

输出：

{0: (-50, 0), 1: (-48.49424982314113, -12.17816628605375), 2: (9.111061342180996, 49.162877877713946), 3: (-5.177802487038939, 49.73118097738293), 4: (-28.11906419040516, -41.34390195731257), 5: (-38.917605610534636, 31.391399674797604), 6: (47.49580752251565, 15.62524456717865), 7: (-6.1349940624823915, 49.622191082753545), 8: (-7.114661421590306, -49.49122743331524), 9: (-45.98755124771604, -19.62511478281569), 10: (-10.907208159626194, 48.79582779462383), 11: (11.535613615138459, 48.651100897330494), 12: (16.69100207851993, -47.131841143910805), 13: (49.92190405424485, 2.7934737512229932), 14: (21.635620902506773, 45.07660045037793), 15: (34.80965114207605, 35.89273167880879), 16: (-10.556283772662766, 48.8729462270387), 17: (-34.26986662576967, -36.40846387108302), 18: (29.108362245849747, -40.65345308045048), 19: (38.62445512198866, -31.751401016797416), 20: (0.6666921470255147, 49.99555501823232), 21: (33.397971470527224, -37.209884461710566), 22: (-12.979918591843784, 48.28583346437243), 23: (-5.747924357032666, 49.66851483169021), 24: (47.17922013912872, -16.556605541705437), 25: (26.763758657317197, -42.233887135011365), 26: (-42.271695978747516, 26.70400193005425), 27: (4.4298597129327035, 49.803376822498045), 28: (-23.768133125153255, 43.989497016276424), 29: (-36.36374544900421, -34.317313661183114), 30: (-42.41586057800746, 26.474417300991394), 31: (-5.10843255646467, 49.73835458492824), 32: (10.132932983122302, -48.96247204910667), 33: (-33.00921929564278, -37.55517862415468), 34: (33.06877220376812, 37.50275063159092), 35: (-6.947638052481068, 49.514950524985046), 36: (-6.315644697890875, -49.599522498205594), 37: (41.3780628679112, -28.06877113981281), 38: (-27.811302751680987, -41.55155158660554), 39: (-16.79218725418388, -47.095885671897335), 40: (-19.86513495419905, -45.88438092915125), 41: (3.641422053024421, -49.867224160080816), 42: (-11.270990243754596, -48.713086321082024), 43: (-5.685945775992117, -49.67564816519737), 44: (32.73452125193285, -37.79485571353272), 45: (-31.139436980627934, -39.119502355340636), 46: (-47.652625926583255, -15.140252385648182), 47: (-26.642952144042653, -42.31020091006722), 48: (44.9791425162565, 21.83750760737788), 49: (36.73862125617772, -33.9156852826996), 50: (-15.430519955614422, 47.55942655141445), 51: (-50, 0)}
    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51]
    [[[0, 13, 46, 26, 47, 11, 7, 4, 16, 3, 44, 49, 22, 41, 9, 27, 35, 39, 37, 25, 29, 8, 30, 32, 20, 1, 42, 33, 15, 38, 23, 10, 34, 45, 50, 21, 28, 6, 40, 36, 17, 19, 43, 31, 48, 5, 14, 2, 24, 12, 18, 51], 3378.9736954709733, 0.008003801880142453], [[0, 17, 28, 45, 46, 31, 33, 12, 9, 36, 38, 48, 22, 43, 34, 37, 30, 15, 39, 26, 1, 5, 35, 6, 8, 49, 13, 3, 44, 29, 47, 18, 21, 25, 14, 2, 4, 24, 41, 11, 20, 32, 40, 10, 16, 7, 50, 42, 23, 19, 27, 51], 3173.5751430670653, 0.019749436265361], [[0, 6, 50, 3, 19, 32, 20, 48, 21, 5, 46, 12, 33, 8, 44, 15, 37, 49, 18, 39, 4, 25, 22, 36, 1, 26, 2, 29, 27, 47, 7, 41, 43, 28, 10, 23, 30, 40, 9, 13, 45, 34, 24, 35, 17, 14, 11, 38, 31, 42, 16, 51], 3317.665833989199, 0.028870109448754372], [[0, 17, 47, 32, 28, 23, 42, 14, 26, 1, 48, 46, 4, 11, 50, 29, 33, 8, 13, 41, 49, 22, 21, 16, 30, 2, 27, 12, 6, 45, 39, 35, 37, 24, 44, 43, 15, 25, 40, 38, 18, 7, 5, 34, 20, 9, 10, 19, 36, 31, 3, 51], 3101.8879988284825, 0.041921698931360954], [[0, 46, 44, 36, 21, 49, 22, 33, 41, 18, 39, 42, 28, 2, 1, 48, 26, 47, 8, 13, 10, 11, 37, 12, 14, 43, 27, 15, 34, 16, 29, 9, 20, 23, 38, 40, 24, 45, 50, 32, 5, 35, 19, 31, 17, 4, 3, 25, 6, 7, 30, 51], 3081.407712551679, 0.05534638647141202], [[0, 24, 46, 31, 20, 18, 49, 12, 44, 22, 27, 36, 4, 14, 19, 48, 3, 35, 38, 39, 25, 26, 50, 16, 23, 8, 37, 15, 13, 43, 11, 34, 33, 7, 41, 17, 47, 28, 29, 30, 42, 40, 32, 45, 2, 6, 10, 1, 9, 5, 21, 51], 2966.771950346533, 0.07085944228983285], [[0, 18, 38, 10, 50, 3, 17, 6, 40, 43, 24, 7, 15, 11, 34, 44, 45, 21, 32, 47, 33, 39, 30, 20, 19, 22, 26, 9, 48, 42, 8, 28, 41, 2, 36, 5, 13, 31, 27, 1, 23, 29, 35, 12, 37, 16, 25, 49, 14, 46, 4, 51], 3247.5580001563394, 0.08125729960342595], [[0, 25, 32, 1, 38, 26, 36, 19, 47, 22, 10, 44, 8, 50, 42, 11, 13, 35, 37, 2, 15, 23, 46, 12, 16, 24, 34, 20, 48, 21, 27, 17, 45, 7, 33, 29, 31, 30, 14, 43, 9, 3, 41, 18, 5, 39, 4, 40, 28, 6, 49, 51], 3373.3805991351646, 0.08936299329063527], [[0, 14, 4, 8, 43, 48, 32, 25, 17, 38, 47, 33, 2, 1, 9, 34, 27, 49, 21, 46, 22, 31, 15, 19, 35, 42, 23, 28, 36, 24, 29, 3, 39, 50, 5, 30, 40, 41, 20, 16, 44, 13, 11, 6, 10, 26, 18, 7, 45, 12, 37, 51], 3054.827829933213, 0.10327189782052813], [[0, 46, 32, 34, 8, 4, 5, 6, 40, 2, 24, 22, 21, 15, 10, 30, 35, 3, 13, 37, 19, 41, 12, 26, 27, 7, 28, 42, 36, 45, 18, 29, 14, 38, 16, 39, 43, 47, 11, 1, 25, 17, 33, 31, 50, 49, 9, 20, 48, 44, 23, 51], 3086.2185154955982, 0.11660894492387508], [[0, 42, 18, 13, 27, 1, 32, 12, 16, 47, 21, 35, 6, 10, 8, 19, 36, 44, 48, 50, 46, 30, 11, 45, 4, 29, 14, 17, 41, 7, 20, 34, 9, 49, 25, 22, 43, 28, 40, 38, 3, 15, 37, 24, 23, 33, 39, 31, 5, 2, 26, 51], 3144.6353149636698, 0.1288817884263013], [[0, 33, 9, 49, 40, 31, 41, 5, 23, 42, 10, 2, 7, 8, 26, 21, 14, 50, 22, 3, 25, 16, 6, 34, 11, 15, 1, 20, 48, 27, 4, 36, 28, 32, 47, 18, 38, 39, 17, 12, 44, 19, 45, 24, 43, 37, 46, 30, 29, 13, 35, 51], 3060.7609188186675, 0.14268260736071517], [[0, 47, 39, 35, 11, 32, 6, 29, 18, 31, 28, 26, 46, 48, 24, 37, 19, 12, 21, 14, 40, 41, 42, 20, 13, 3, 10, 4, 23, 30, 34, 45, 49, 8, 50, 2, 22, 1, 15, 5, 17, 44, 25, 7, 36, 27, 43, 38, 9, 16, 33, 51], 3066.739675138409, 0.15637450875663955], [[0, 1, 8, 4, 2, 5, 3, 25, 44, 46, 47, 23, 26, 22, 39, 29, 12, 6, 13, 7, 32, 40, 15, 45, 31, 43, 50, 33, 18, 16, 49, 38, 17, 42, 20, 48, 14, 30, 19, 27, 11, 9, 21, 36, 41, 34, 10, 24, 37, 35, 28, 51], 3131.07919281141, 0.16889430988324786], [[0, 42, 32, 39, 24, 20, 25, 1, 35, 11, 34, 7, 19, 45, 38, 29, 6, 2, 8, 30, 4, 28, 50, 26, 21, 46, 9, 12, 27, 15, 48, 10, 41, 36, 22, 16, 17, 23, 44, 43, 47, 31, 37, 18, 40, 13, 49, 14, 33, 3, 5, 51], 3039.412900751468, 0.183084034712995], [[0, 9, 21, 34, 39, 2, 38, 50, 1, 16, 7, 3, 45, 48, 29, 18, 41, 8, 46, 49, 12, 5, 22, 23, 33, 31, 15, 17, 26, 36, 44, 27, 19, 25, 43, 24, 10, 40, 28, 35, 6, 13, 11, 37, 20, 14, 4, 42, 32, 47, 30, 51], 3098.2625905815694, 0.19620166979457832], [[0, 16, 23, 4, 11, 37, 13, 6, 17, 43, 47, 29, 35, 40, 33, 8, 30, 25, 48, 19, 41, 5, 21, 26, 15, 24, 50, 46, 42, 32, 2, 12, 31, 7, 38, 9, 28, 3, 10, 34, 36, 18, 39, 44, 45, 20, 27, 14, 22, 49, 1, 51], 2969.1429606855563, 0.21167153191249544], [[0, 21, 17, 5, 3, 29, 6, 16, 15, 41, 31, 40, 44, 39, 30, 8, 19, 11, 38, 46, 18, 47, 24, 4, 1, 33, 28, 42, 9, 48, 14, 49, 27, 23, 45, 25, 2, 37, 20, 32, 26, 10, 7, 12, 50, 36, 13, 35, 43, 34, 22, 51], 3678.9063735703367, 0.21421133304330559], [[0, 34, 21, 29, 50, 3, 44, 46, 30, 31, 38, 25, 36, 27, 2, 42, 49, 15, 37, 47, 48, 13, 32, 26, 6, 16, 17, 20, 11, 43, 19, 4, 1, 5, 39, 22, 14, 24, 41, 33, 10, 23, 40, 12, 7, 45, 18, 35, 9, 28, 8, 51], 3410.682348723798, 0.2216374849446873], [[0, 37, 16, 27, 36, 31, 7, 44, 41, 12, 32, 20, 25, 35, 30, 48, 19, 45, 18, 14, 39, 33, 42, 5, 47, 8, 21, 10, 6, 13, 22, 9, 11, 28, 2, 4, 23, 3, 24, 43, 34, 49, 50, 1, 15, 26, 46, 29, 17, 40, 38, 51], 3083.9118547768117, 0.23501655346422595], [[0, 21, 15, 29, 7, 38, 41, 22, 5, 25, 26, 3, 20, 46, 30, 49, 13, 35, 36, 2, 39, 45, 17, 18, 11, 34, 8, 14, 33, 40, 10, 1, 50, 47, 16, 4, 37, 31, 28, 48, 12, 42, 9, 43, 32, 19, 23, 44, 27, 6, 24, 51], 3475.266796272603, 0.24126614310490935], [[0, 48, 12, 38, 21, 42, 4, 8, 15, 35, 39, 17, 37, 14, 22, 11, 50, 27, 26, 46, 19, 24, 16, 32, 30, 10, 5, 43, 41, 31, 44, 13, 29, 2, 18, 23, 7, 36, 40, 20, 45, 33, 34, 25, 9, 49, 47, 28, 6, 3, 1, 51], 3171.0573296629104, 0.25305764556430427], [[0, 32, 24, 30, 13, 47, 15, 39, 50, 35, 42, 41, 43, 22, 27, 5, 36, 12, 31, 23, 7, 21, 18, 25, 8, 48, 37, 44, 3, 14, 9, 33, 6, 28, 10, 38, 1, 16, 4, 29, 49, 46, 34, 2, 45, 11, 19, 20, 26, 40, 17, 51], 3058.4277743615517, 0.2669009683803984], [[0, 39, 43, 20, 49, 8, 34, 14, 13, 21, 27, 1, 15, 12, 22, 5, 42, 46, 50, 32, 47, 36, 23, 4, 45, 16, 19, 44, 41, 9, 2, 37, 29, 30, 31, 35, 38, 11, 18, 3, 28, 10, 48, 7, 24, 33, 17, 26, 40, 25, 6, 51], 3244.693006449372, 0.27735101849892657], [[0, 13, 4, 20, 3, 19, 2, 48, 16, 38, 45, 24, 14, 46, 32, 35, 1, 28, 15, 41, 25, 50, 9, 26, 10, 47, 33, 8, 18, 12, 27, 43, 17, 11, 21, 42, 5, 7, 49, 31, 40, 39, 44, 6, 22, 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0.9839614332023872], [[0, 44, 49, 30, 28, 39, 40, 17, 50, 3, 9, 6, 42, 4, 18, 19, 33, 10, 38, 1, 8, 26, 11, 7, 27, 21, 12, 15, 35, 5, 45, 13, 22, 48, 41, 32, 24, 14, 34, 43, 46, 47, 36, 16, 37, 29, 20, 25, 2, 31, 23, 51], 2937.925337289444, 1]]
    [0, 9, 46, 26, 16, 1, 38, 33, 29, 17, 45, 4, 47, 42, 36, 43, 40, 39, 8, 41, 32, 12, 25, 21, 49, 19, 18, 44, 37, 24, 48, 6, 13, 34, 15, 11, 7, 23, 20, 27, 2, 14, 35, 3, 10, 22, 31, 50, 28, 5, 30, 51]
    673.8118727243583
    [0, 9, 46, 1, 29, 33, 45, 17, 38, 4, 47, 8, 36, 43, 40, 39, 42, 41, 12, 32, 21, 19, 49, 25, 18, 44, 37, 24, 48, 6, 13, 34, 15, 11, 20, 27, 2, 14, 3, 10, 16, 35, 7, 22, 31, 23, 50, 28, 5, 26, 30, 51]
    522.7587332118794

还有张图：

![SouthEast][]

效果的话，只能算差强人意了。很明显最优路径是一个圈，没有交叉的，然而史上最优路径也不是一个圈，更不用说最后一代了。算法本身的缺陷吧，要做更多的调优和设计更好的算子，才能有一定概率得到最优解吧。

缺点如下：

1、早熟。这是最大的缺点，即算法对新空间的探索能力是有限的，也容易收敛到局部最优解。  
2、大量计算。涉及到大量个体的计算，当问题复杂时，计算时间是个问题。  
3、处理规模小。目前对于维数较高的问题，还是很难处理和优化的。  
4、难于处理非线性约束。对非线性约束的处理，大部分算法都是添加惩罚因子，这是一笔不小的开支。  
5、稳定性差。因为算法属于随机类算法，需要多次运算，结果的可靠性差，不能稳定的得到解。

最大优点：不需要知道怎么去解决一个问题，需要知道是，用什么方式对可行解编码，使得它能被遗传算法机制所利用。

整体来看，是不如模拟退火算法的，毕竟模拟退火在参数不错的条件下，得到全局最优解的概率收敛到1。而遗传算法只能说得到不错的解，至于是不是最优解，看运气了。。。以上。

[http_www.doc88.com_p-9078235973437.html]: http://www.doc88.com/p-9078235973437.html
[SouthEast]: /images/20220531/a919f0c968954199b96b013834de30d5.png