python实现遗传算法（旅行商问题）

网上找到一篇不错的论文：

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 jumppopulation[mid][2]:
            low=mid
            mid=int((low+high)/2)
        elif jumpprduct_set:
                    break
        if np.random.random()prduct_set:
                    break
        if np.random.random()

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, 34, 37, 23, 29, 30, 36, 51], 3378.300115470454, 0.2853670912714936], [[0, 9, 28, 37, 40, 44, 25, 17, 21, 13, 34, 23, 4, 41, 24, 35, 18, 22, 20, 10, 1, 47, 19, 5, 12, 8, 45, 7, 15, 6, 2, 14, 29, 32, 48, 33, 26, 3, 30, 36, 11, 16, 42, 43, 50, 49, 46, 38, 31, 39, 27, 51], 3157.416478592869, 0.2974070948976855], [[0, 22, 31, 19, 33, 3, 20, 10, 39, 36, 48, 16, 12, 7, 9, 13, 1, 17, 28, 29, 26, 35, 37, 38, 50, 27, 2, 42, 25, 21, 8, 5, 41, 40, 24, 18, 49, 46, 44, 11, 45, 30, 15, 14, 43, 32, 6, 34, 47, 23, 4, 51], 3216.353140613106, 0.3083734243664552], [[0, 3, 46, 6, 31, 21, 4, 7, 15, 12, 37, 45, 13, 22, 11, 36, 41, 38, 32, 42, 43, 1, 49, 33, 14, 25, 44, 18, 10, 35, 34, 50, 2, 29, 23, 17, 5, 19, 27, 40, 16, 30, 47, 9, 20, 48, 28, 26, 8, 39, 24, 51], 3184.9374081533933, 0.31991206755171775], [[0, 47, 26, 2, 8, 9, 28, 1, 16, 20, 6, 44, 25, 50, 17, 10, 41, 37, 34, 22, 38, 19, 18, 46, 4, 23, 33, 42, 31, 32, 14, 35, 39, 43, 3, 5, 40, 45, 29, 49, 15, 24, 7, 48, 12, 30, 36, 21, 11, 13, 27, 51], 3272.375021457225, 0.3298578226674326], [[0, 27, 7, 24, 32, 43, 37, 25, 38, 47, 2, 31, 6, 9, 35, 18, 10, 41, 34, 20, 5, 40, 50, 26, 19, 22, 14, 46, 15, 33, 23, 12, 49, 8, 45, 29, 21, 39, 44, 30, 13, 16, 11, 42, 36, 48, 1, 28, 3, 17, 4, 51], 3185.2347749618457, 0.3413910485954809], [[0, 18, 36, 14, 3, 27, 40, 17, 16, 10, 29, 25, 20, 50, 35, 12, 31, 21, 43, 1, 47, 49, 48, 8, 34, 6, 4, 46, 37, 42, 33, 28, 11, 44, 26, 38, 13, 32, 24, 5, 23, 22, 45, 19, 7, 30, 15, 39, 2, 41, 9, 51], 3266.259824054999, 0.3514482068547272], [[0, 6, 40, 13, 11, 21, 41, 34, 16, 32, 12, 4, 27, 44, 8, 37, 17, 36, 35, 28, 48, 7, 1, 38, 20, 50, 26, 9, 42, 24, 5, 15, 22, 23, 2, 45, 18, 25, 10, 14, 30, 46, 19, 39, 31, 29, 49, 33, 47, 3, 43, 51], 3186.161956434656, 0.3629645419248193], [[0, 50, 32, 40, 20, 13, 4, 2, 45, 47, 28, 1, 49, 9, 48, 46, 41, 23, 14, 3, 33, 31, 19, 8, 7, 12, 38, 29, 24, 44, 17, 11, 21, 22, 36, 35, 15, 42, 43, 39, 37, 27, 16, 5, 30, 34, 10, 6, 25, 26, 18, 51], 3512.636551564206, 0.368533350890954], [[0, 5, 15, 3, 33, 10, 21, 36, 42, 28, 20, 13, 40, 12, 38, 35, 17, 41, 26, 49, 32, 24, 6, 34, 31, 9, 4, 16, 47, 44, 39, 37, 45, 19, 27, 48, 1, 46, 8, 2, 18, 29, 11, 7, 23, 43, 25, 22, 30, 50, 14, 51], 3114.9866033468174, 0.38134631754207415], [[0, 20, 47, 21, 35, 44, 14, 3, 34, 27, 28, 38, 10, 48, 7, 40, 5, 24, 11, 16, 12, 32, 39, 13, 45, 8, 30, 49, 18, 22, 29, 42, 1, 36, 19, 2, 17, 4, 25, 15, 46, 26, 43, 37, 33, 23, 6, 31, 9, 41, 50, 51], 3384.9026964436503, 0.3892421082979777], [[0, 35, 23, 29, 1, 27, 3, 15, 31, 21, 16, 33, 7, 13, 32, 19, 45, 14, 11, 30, 28, 26, 20, 24, 22, 4, 37, 40, 9, 12, 44, 2, 46, 41, 50, 34, 38, 43, 39, 5, 6, 8, 25, 49, 47, 17, 42, 10, 18, 36, 48, 51], 3098.9653656401274, 0.4023469406283873], [[0, 31, 33, 30, 2, 9, 12, 15, 25, 11, 14, 50, 29, 43, 27, 49, 37, 8, 6, 42, 19, 41, 48, 13, 24, 1, 23, 45, 39, 3, 28, 44, 40, 10, 4, 22, 32, 5, 46, 17, 26, 7, 20, 34, 36, 18, 38, 16, 47, 35, 21, 51], 3391.205282373086, 0.41012791450451835], [[0, 2, 7, 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522.7587332118794

还有张图：

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。