简介

遗传算法（Genetic Algorithm，GA）最早是由美国的 John holland于20世纪70年代提出,该算法是根据大自然中生物体进化规律而设计提出的。是模拟达尔文生物进化论的自然选择和遗传学机理的生物进化过程的计算模型，是一种通过模拟自然进化过程搜索最优解的方法。该算法通过数学的方式,利用计算机仿真运算,将问题的求解过程转换成类似生物进化中的染色体基因的交叉、变异等过程。在求解较为复杂的组合优化问题时,相对一些常规的优化算法,通常能够较快地获得较好的优化结果。遗传算法已被人们广泛地应用于组合优化、机器学习、信号处理、自适应控制和人工生命等领域。

由来

遗传算法





基本代码实现

代码

项目代码结构

基本代码和数据集

import random
import math
import numpy as np
import matplotlib.pyplot as pltclass GA(object):def __init__(self, num_city, num_total, iteration, data):self.num_city = num_cityself.num_total = num_totalself.scores = []self.iteration = iterationself.location = dataself.ga_choose_ratio = 0.2self.mutate_ratio = 0.05# fruits中存每一个个体是下标的listself.dis_mat = self.compute_dis_mat(num_city, data)self.fruits = self.greedy_init(self.dis_mat,num_total,num_city)# 显示初始化后的最佳路径scores = self.compute_adp(self.fruits)sort_index = np.argsort(-scores)init_best = self.fruits[sort_index[0]]init_best = self.location[init_best]# 存储每个iteration的结果，画出收敛图self.iter_x = [0]self.iter_y = [1. / scores[sort_index[0]]]def random_init(self, num_total, num_city):tmp = [x for x in range(num_city)]result = []for i in range(num_total):random.shuffle(tmp)result.append(tmp.copy())return resultdef greedy_init(self, dis_mat, num_total, num_city):start_index = 0result = []for i in range(num_total):rest = [x for x in range(0, num_city)]# 所有起始点都已经生成了if start_index >= num_city:start_index = np.random.randint(0, num_city)result.append(result[start_index].copy())continuecurrent = start_indexrest.remove(current)# 找到一条最近邻路径result_one = [current]while len(rest) != 0:tmp_min = math.inftmp_choose = -1for x in rest:if dis_mat[current][x] < tmp_min:tmp_min = dis_mat[current][x]tmp_choose = xcurrent = tmp_chooseresult_one.append(tmp_choose)rest.remove(tmp_choose)result.append(result_one)start_index += 1return result# 计算不同城市之间的距离def compute_dis_mat(self, num_city, location):dis_mat = np.zeros((num_city, num_city))for i in range(num_city):for j in range(num_city):if i == j:dis_mat[i][j] = np.infcontinuea = location[i]b = location[j]tmp = np.sqrt(sum([(x[0] - x[1]) ** 2 for x in zip(a, b)]))dis_mat[i][j] = tmpreturn dis_mat# 计算路径长度def compute_pathlen(self, path, dis_mat):try:a = path[0]b = path[-1]except:import pdbpdb.set_trace()result = dis_mat[a][b]for i in range(len(path) - 1):a = path[i]b = path[i + 1]result += dis_mat[a][b]return result# 计算种群适应度def compute_adp(self, fruits):adp = []for fruit in fruits:if isinstance(fruit, int):import pdbpdb.set_trace()length = self.compute_pathlen(fruit, self.dis_mat)adp.append(1.0 / length)return np.array(adp)def swap_part(self, list1, list2):index = len(list1)list = list1 + list2list = list[::-1]return list[:index], list[index:]def ga_cross(self, x, y):len_ = len(x)assert len(x) == len(y)path_list = [t for t in range(len_)]order = list(random.sample(path_list, 2))order.sort()start, end = order# 找到冲突点并存下他们的下标,x中存储的是y中的下标,y中存储x与它冲突的下标tmp = x[start:end]x_conflict_index = []for sub in tmp:index = y.index(sub)if not (index >= start and index < end):x_conflict_index.append(index)y_confict_index = []tmp = y[start:end]for sub in tmp:index = x.index(sub)if not (index >= start and index < end):y_confict_index.append(index)assert len(x_conflict_index) == len(y_confict_index)# 交叉tmp = x[start:end].copy()x[start:end] = y[start:end]y[start:end] = tmp# 解决冲突for index in range(len(x_conflict_index)):i = x_conflict_index[index]j = y_confict_index[index]y[i], x[j] = x[j], y[i]assert len(set(x)) == len_ and len(set(y)) == len_return list(x), list(y)def ga_parent(self, scores, ga_choose_ratio):sort_index = np.argsort(-scores).copy()sort_index = sort_index[0:int(ga_choose_ratio * len(sort_index))]parents = []parents_score = []for index in sort_index:parents.append(self.fruits[index])parents_score.append(scores[index])return parents, parents_scoredef ga_choose(self, genes_score, genes_choose):sum_score = sum(genes_score)score_ratio = [sub * 1.0 / sum_score for sub in genes_score]rand1 = np.random.rand()rand2 = np.random.rand()for i, sub in enumerate(score_ratio):if rand1 >= 0:rand1 -= subif rand1 < 0:index1 = iif rand2 >= 0:rand2 -= subif rand2 < 0:index2 = iif rand1 < 0 and rand2 < 0:breakreturn list(genes_choose[index1]), list(genes_choose[index2])def ga_mutate(self, gene):path_list = [t for t in range(len(gene))]order = list(random.sample(path_list, 2))start, end = min(order), max(order)tmp = gene[start:end]# np.random.shuffle(tmp)tmp = tmp[::-1]gene[start:end] = tmpreturn list(gene)def ga(self):# 获得优质父代scores = self.compute_adp(self.fruits)# 选择部分优秀个体作为父代候选集合parents, parents_score = self.ga_parent(scores, self.ga_choose_ratio)tmp_best_one = parents[0]tmp_best_score = parents_score[0]# 新的种群fruitsfruits = parents.copy()# 生成新的种群while len(fruits) < self.num_total:# 轮盘赌方式对父代进行选择gene_x, gene_y = self.ga_choose(parents_score, parents)# 交叉gene_x_new, gene_y_new = self.ga_cross(gene_x, gene_y)# 变异if np.random.rand() < self.mutate_ratio:gene_x_new = self.ga_mutate(gene_x_new)if np.random.rand() < self.mutate_ratio:gene_y_new = self.ga_mutate(gene_y_new)x_adp = 1. / self.compute_pathlen(gene_x_new, self.dis_mat)y_adp = 1. / self.compute_pathlen(gene_y_new, self.dis_mat)# 将适应度高的放入种群中if x_adp > y_adp and (not gene_x_new in fruits):fruits.append(gene_x_new)elif x_adp <= y_adp and (not gene_y_new in fruits):fruits.append(gene_y_new)self.fruits = fruitsreturn tmp_best_one, tmp_best_scoredef run(self):BEST_LIST = Nonebest_score = -math.infself.best_record = []for i in range(1, self.iteration + 1):tmp_best_one, tmp_best_score = self.ga()self.iter_x.append(i)self.iter_y.append(1. / tmp_best_score)if tmp_best_score > best_score:best_score = tmp_best_scoreBEST_LIST = tmp_best_oneself.best_record.append(1./best_score)print(i,1./best_score)print(1./best_score)return self.location[BEST_LIST], 1. / best_score# 读取数据
def read_tsp(path):lines = open(path, 'r').readlines()assert 'NODE_COORD_SECTION\n' in linesindex = lines.index('NODE_COORD_SECTION\n')data = lines[index + 1:-1]tmp = []for line in data:line = line.strip().split(' ')if line[0] == 'EOF':continuetmpline = []for x in line:if x == '':continueelse:tmpline.append(float(x))if tmpline == []:continuetmp.append(tmpline)data = tmpreturn datadata = read_tsp('data/st70.tsp')data = np.array(data)
data = data[:, 1:]
Best, Best_path = math.inf, Nonemodel = GA(num_city=data.shape[0], num_total=25, iteration=500, data=data.copy())
path, path_len = model.run()
if path_len < Best:Best = path_lenBest_path = path
# 加上一行因为会回到起点
fig, axs = plt.subplots(2, 1, sharex=False, sharey=False)
axs[0].scatter(Best_path[:, 0], Best_path[:,1])
Best_path = np.vstack([Best_path, Best_path[0]])
axs[0].plot(Best_path[:, 0], Best_path[:, 1])
axs[0].set_title('规划结果')
iterations = range(model.iteration)
best_record = model.best_record
axs[1].plot(iterations, best_record)
axs[1].set_title('收敛曲线')
plt.show()

这里需要导入数据集
st70.tsp

NAME: st70
TYPE: TSP
COMMENT: 70-city problem (Smith/Thompson)
DIMENSION: 70
EDGE_WEIGHT_TYPE : EUC_2D
NODE_COORD_SECTION
1 64 96
2 80 39
3 69 23
4 72 42
5 48 67
6 58 43
7 81 34
8 79 17
9 30 23
10 42 67
11 7 76
12 29 51
13 78 92
14 64 8
15 95 57
16 57 91
17 40 35
18 68 40
19 92 34
20 62 1
21 28 43
22 76 73
23 67 88
24 93 54
25 6 8
26 87 18
27 30 9
28 77 13
29 78 94
30 55 3
31 82 88
32 73 28
33 20 55
34 27 43
35 95 86
36 67 99
37 48 83
38 75 81
39 8 19
40 20 18
41 54 38
42 63 36
43 44 33
44 52 18
45 12 13
46 25 5
47 58 85
48 5 67
49 90 9
50 41 76
51 25 76
52 37 64
53 56 63
54 10 55
55 98 7
56 16 74
57 89 60
58 48 82
59 81 76
60 29 60
61 17 22
62 5 45
63 79 70
64 9 100
65 17 82
66 74 67
67 10 68
68 48 19
69 83 86
70 84 94
EOF

运行截图


使用遗传算法解决旅行家问题

基本代码和数据集


# -*- encoding: utf-8 -*-
import numpy as np
import pandas as pd
from Draw import *class TSP(object):citys = np.array([])  # 城市数组citys_name = np.array([])  #城市名字数组pop_size = 50  # 种群大小c_rate = 0.7  # 交叉率m_rate = 0.05  # 突变率pop = np.array([])  # 种群数组fitness = np.array([])  # 适应度数组（距离）city_size = -1  # 标记城市数目ga_num = 200  # 最大迭代次数best_dist = -1  # 记录目前最优距离best_gen = []  # 记录目前最优旅行方案dw = Draw()  # 绘图类#初始化数据def __init__(self, c_rate, m_rate, pop_size, ga_num):self.fitness = np.zeros(self.pop_size)self.c_rate = c_rateself.m_rate = m_rateself.pop_size = pop_sizeself.ga_num = ga_numdef init(self):tsp = selftsp.load_Citys2()  # 加载城市数据，调用City2tsp.pop = tsp.creat_pop(tsp.pop_size)  # 创建种群tsp.fitness = tsp.get_fitness(tsp.pop)  # 计算初始种群适应度tsp.dw.bound_x = [np.min(tsp.citys[:, 0]), np.max(tsp.citys[:, 0])]  # 计算绘图时的X界，min，maxtsp.dw.bound_y = [np.min(tsp.citys[:, 1]), np.max(tsp.citys[:, 1])]  # 计算绘图时的Y界tsp.dw.set_xybound(tsp.dw.bound_x, tsp.dw.bound_y)  # 设置边界def creat_pop(self, size):pop = []for i in range(size):gene = np.arange(self.citys.shape[0])  # 问题的解，基因，种群中的个体：[0，...，city_size]np.random.shuffle(gene)  # 打乱数组[0，...，city_size]pop.append(gene)   # 加入种群#array数组return np.array(pop)def get_fitness(self, pop):d = np.array([])  # 适应度记录数组for i in range(pop.shape[0]):#行gen = pop[i]  # 取其中一条基因（编码解，个体）dis = self.gen_distance(gen)  # 计算此基因优劣（距离长短）dis = self.best_dist / dis  # 当前最优距离除以当前pop[i]（个体）距离；越近适应度越高，最优适应度为1d = np.append(d, dis)  # 保存适应度pop[i]     d=d.append(dis)return ddef get_local_fitness(self, gen, i):'''计算地i个城市的邻域交换基因数组中任意两个值组成的解集：称为邻域。计算领域内所有可能的适应度:param gen:城市路径:param i:第i城市:return:第i城市的局部适应度'''di = 0fi = 0if i == 0:di = self.ct_distance(self.citys[gen[0]], self.citys[gen[-1]])else:di = self.ct_distance(self.citys[gen[i]], self.citys[gen[i - 1]])od = []for j in range(self.city_size):if i != j:#交换基因数组中任意两个值组成的解集：称为邻域。计算领域内所有可能的适应度od.append(self.ct_distance(self.citys[gen[i]], self.citys[gen[i - 1]]))mind = np.min(od)fi = di - mindreturn fidef EO(self, gen):# 极值优化，传统遗传算法性能不好，这里混合EO# 其会在整个基因的领域内，寻找一个最佳变换以更新基因local_fitness = []for g in range(self.city_size):f = self.get_local_fitness(gen, g)local_fitness.append(f)max_city_i = np.argmax(local_fitness)maxgen = np.copy(gen)if 1 < max_city_i < self.city_size - 1:for j in range(max_city_i):maxgen = np.copy(gen)jj = max_city_iwhile jj < self.city_size:gen1 = self.exechange_gen(maxgen, j, jj)d = self.gen_distance(maxgen)d1 = self.gen_distance(gen1)if d > d1:maxgen = gen1[:]jj += 1gen = maxgenreturn gendef exechange_gen(self, gen, i, j):# 函数：交换基因中i,j值c = gen[j]gen[j] = gen[i]gen[i] = creturn gendef select_pop(self, pop):# 选择种群，优胜劣汰,策略1：低于平均的要替换改变best_f_index = np.argmax(self.fitness)#av表示平均数av = np.median(self.fitness, axis=0)for i in range(self.pop_size):if i != best_f_index and self.fitness[i] < av:pi = self.cross(pop[best_f_index], pop[i])pi = self.mutate(pi)pop[i, :] = pi[:]return popdef select_pop2(self, pop):# 选择种群，优胜劣汰，策略2：轮盘赌，适应度低的替换的概率大probility = self.fitness / self.fitness.sum()idx = np.random.choice(np.arange(self.pop_size), size=self.pop_size, replace=True, p=probility)n_pop = pop[idx, :]return n_popdef cross(self, parent1, parent2):"""交叉p1,p2的部分基因片段"""#交叉率大于设定的，退出，返回parent1if np.random.rand() > self.c_rate:return parent1#在index1与index2进行交叉基因片段index1 = np.random.randint(0, self.city_size - 1)index2 = np.random.randint(index1, self.city_size - 1)tempGene = parent2[index1:index2]  # 交叉的基因片段，例如：[20,24]#newGene用来储存newGene = []p1len = 0#对parent1的数据进行遍历for g in parent1:#若等于索引值，直接加上交叉的基因片段if p1len == index1:newGene.extend(tempGene)  # 插入基因片段#如果g不在交叉的基因片段，也加上，避免重复。if g not in tempGene:newGene.append(g)p1len += 1newGene = np.array(newGene)#检查一下是不是城市的数量if newGene.shape[0] != self.city_size:print('c error')return self.creat_pop(1)# return parent1return newGenedef mutate(self, gene):"""突变"""if np.random.rand() > self.m_rate:return gene#随机生成两个索引节点，#np.random.randint返回一个随机整型数，范围从低（包括）到高（不包括），即[low, high)。index1 = np.random.randint(0, self.city_size - 1)index2 = np.random.randint(index1, self.city_size - 1)newGene = self.reverse_gen(gene, index1, index2)if newGene.shape[0] != self.city_size:print('m error')return self.creat_pop(1)return newGenedef reverse_gen(self, gen, i, j):# 函数：翻转基因中i到j之间的基因片段#i>=j,j=33,生成的index1，index2发生错误。if i >= j:return genif j > self.city_size - 1:return gen#先做一个备份parent1parent1 = np.copy(gen)#tempGene为parent1的i-jtempGene = parent1[i:j]newGene = []p1len = 0#对parent1进行遍历，for g in parent1:if p1len == i:newGene.extend(tempGene[::-1])  # 插入基因片段(步长为-1，倒着插入)if g not in tempGene:newGene.append(g) #如果g不在tempGene，追加上p1len += 1return np.array(newGene)def evolution(self):# 主程序：迭代进化种群tsp = self#ga_num 最大迭代次数x_data = []y_data = []for i in range(self.ga_num):#最好的索引，argmax返回的是最大数的索引best_f_index = np.argmax(tsp.fitness)worst_f_index = np.argmin(tsp.fitness)#本地最好的路线，将种群（最好的索引），local_best_gen是个1*34local_best_gen = tsp.pop[best_f_index]#最优的距离local_best_dist = tsp.gen_distance(local_best_gen)if i == 0:#第一个，初始化，以下两个存着最好的tsp.best_gen = local_best_gentsp.best_dist = tsp.gen_distance(local_best_gen)#出现更优秀的路程if local_best_dist < tsp.best_dist:tsp.best_dist = local_best_dist # 记录最优值（距离值）tsp.best_gen = local_best_gen  # 记录最个体基因（1*34）的基因，一个路线# 绘图tsp.dw.ax.cla()tsp.re_draw()#相当于sleep（0.001）tsp.dw.plt.pause(0.001)else:tsp.pop[worst_f_index] = self.best_gen#打印出基因代数和距离print('gen:%d evo,best dist :%s' % (i, self.best_dist))x_data.append(i)y_data.append(self.best_dist)# 设置数据图的标题tsp.pop = tsp.select_pop(tsp.pop)  # 选择淘汰种群tsp.fitness = tsp.get_fitness(tsp.pop)  # 计算种群适应度for j in range(self.pop_size):r = np.random.randint(0, self.pop_size - 1)if j != r:tsp.pop[j] = tsp.cross(tsp.pop[j], tsp.pop[r])  # 交叉种群中第j,r个体的基因tsp.pop[j] = tsp.mutate(tsp.pop[j])  # 突变种群中第j个体的基因tsp.best_dist = tsp.gen_distance(self.best_gen)  # 记录最优值plt.title('TSP问题：34城市旅游')# 第一个列表代表横坐标的值，第二个代表纵坐标的值plt.plot(x_data, y_data)# 设置两条坐标轴的标签plt.xlabel("经度")plt.ylabel("纬度")# print(x_data)# print(y_data)def load_Citys2(self, file='china.csv', delm=';'):# 中国34城市经纬度#分delimiter隔符。header头，从哪里开始读data = pd.read_csv(file, delimiter=delm, header=None).values#所有行，第1-2列self.citys = data[:, 1:]#第0列，所有行self.citys_name = data[:, 0]#城市数量shape[0]为行数；shape[0]为列数self.city_size = data.shape[0]def gen_distance(self, gen):# 计算基因所代表的总旅行距离#传入的数据为种群数distance = 0.0for i in range(-1, len(self.citys) - 1):index1, index2 = gen[i], gen[i + 1]city1, city2 = self.citys[index1], self.citys[index2]#距离公式distance += np.sqrt((city1[0] - city2[0]) ** 2 + (city1[1] - city2[1]) ** 2)return distancedef ct_distance(self, city1, city2):# 计算2城市之间的距离d = np.sqrt((city1[0] - city2[0]) ** 2 + (city1[1] - city2[1]) ** 2)return ddef draw_citys_way(self, gen):'''根据一条基因gen绘制一条旅行路线:param gen::return:'''tsp = selfdw = self.dwm = gen.shape[0]#多少行tsp.dw.set_xybound(tsp.dw.bound_x, tsp.dw.bound_y)for i in range(m):if i < m - 1:#获得基因地点的代数值best_i = tsp.best_gen[i]next_best_i = tsp.best_gen[i + 1]#城市best_icity = tsp.citys[best_i]next_best_icity = tsp.citys[next_best_i]dw.draw_line(best_icity, next_best_icity)#首位相连start = tsp.citys[tsp.best_gen[0]]end = tsp.citys[tsp.best_gen[-1]]dw.draw_line(end, start)def draw_citys_name(self, gen, size=5):'''根据一条基因gen（路线）绘制对应城市名称'''tsp = selfm = gen.shape[0]tsp.dw.set_xybound(tsp.dw.bound_x, tsp.dw.bound_y)for i in range(m):c = gen[i]best_icity = tsp.citys[c]tsp.dw.draw_text(best_icity[0], best_icity[1], tsp.citys_name[c], 10)def re_draw(self):# 重绘图；每次迭代后绘制一次，动态展示。tsp = selftsp.dw.draw_points(tsp.citys[:, 0], tsp.citys[:, 1])tsp.draw_citys_name(tsp.pop[0], 8)tsp.draw_citys_way(self.best_gen)def main():#tsp = TSP(0.5, 0.1, 100, 500)tsp.init()tsp.evolution()tsp.re_draw()tsp.dw.plt.show()if __name__ == '__main__':main()


import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
import matplotlib.animation as animationclass Draw(object):#边界值bound_x = []bound_y = []def __init__(self):self.fig, self.ax = plt.subplots()self.plt = pltself.set_font()def draw_line(self, p_from, p_to):#画线函数#储存两个点的坐标line1 = [(p_from[0], p_from[1]), (p_to[0], p_to[1])]#zip匹配(line1_xs, line1_ys) = zip(*line1)self.ax.add_line(Line2D(line1_xs, line1_ys, linewidth=1, color='blue'))def draw_points(self, pointx, pointy):#画点self.ax.plot(pointx, pointy, 'ro')#设置边界def set_xybound(self, x_bd, y_bd):self.ax.axis([x_bd[0], x_bd[1], y_bd[0], y_bd[1]])def draw_text(self, x, y, text, size=8):#写入文本self.ax.text(x, y, text, fontsize=size)def set_font(self, ft_style='SimHei'):plt.rcParams['font.sans-serif'] = [ft_style]  #用来正常显示中文标签

import matplotlib.pyplot as plt  # 调用matplotlib中的子模块pyplot绘制折线图# 解决中文显示问题
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False# 定义2个列表分别作为X轴、Y轴数据
x_data = [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, 52, 53, 54, 55, 56,57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83,84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108,109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130,131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152,153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174,175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196,197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218,219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240,241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262,263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284,285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306,307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328,329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350,351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372,373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394,395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416,417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438,439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460,461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482,483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499]
y_data = [564.3572005522793, 525.8139896243653, 428.1402039165018, 395.73743500834706, 394.06860429583867,373.684464645136, 365.60282673151573, 345.53960499838325, 331.2057904610075, 318.760364597339,303.162734978924, 301.42654142792907, 324.64583395454457, 301.42654142792907, 286.65204026600344,286.65204026600344, 282.273279917727, 282.273279917727, 280.1240489659227, 280.1240489659227,263.21414723204833, 254.22777921677803, 254.22777921677803, 250.71667881027474, 250.71667881027474,250.50756156870992, 246.24627654938107, 243.8041742198946, 240.15416946358778, 233.2661303383399,233.2661303383399, 239.59565159058116, 245.4156684272969, 228.28636969404505, 223.25718187742706,234.39093411202532, 228.28636969404505, 228.28636969404505, 228.28636969404505, 228.28636969404505,223.25718187742706, 223.25718187742706, 223.25718187742706, 223.25718187742706, 223.25718187742706,223.25718187742706, 237.62255381361274, 218.7219498855295, 218.7219498855295, 218.7219498855295,218.7219498855295, 213.88717907524358, 213.88717907524358, 213.88717907524358, 213.88717907524358,213.88717907524358, 213.88717907524358, 210.38478374497757, 209.33239248439264, 209.33239248439264,206.78401520265885, 204.6494179326049, 202.52449291907507, 202.52449291907507, 209.40591607095607,202.52449291907507, 202.52449291907507, 196.47995538838418, 196.47995538838418, 190.37500614252744,190.37500614252744, 189.59159577864688, 189.59159577864688, 208.0505225509335, 188.16445411312182,188.16445411312182, 183.3306118846393, 183.3306118846393, 183.3306118846393, 180.91006531329387,180.91006531329387, 180.91006531329387, 180.91006531329387, 180.1372614132791, 180.1372614132791,173.88941629266455, 173.88941629266455, 176.59810679235267, 170.69606582130436, 170.69606582130436,170.69606582130436, 170.69606582130436, 170.69606582130436, 168.07668182016852, 168.07668182016852,168.07668182016852, 168.07668182016852, 168.07668182016852, 168.07668182016852, 168.07668182016852,168.07668182016852, 167.8576491945162, 167.8576491945162, 167.8576491945162, 167.8576491945162,167.8576491945162, 167.8576491945162, 167.8576491945162, 167.8576491945162, 167.8576491945162,167.8576491945162, 167.8576491945162, 167.8576491945162, 167.8576491945162, 177.3790464315465,167.8576491945162, 167.8576491945162, 167.8576491945162, 167.8576491945162, 167.8576491945162,167.8576491945162, 167.8576491945162, 167.8576491945162, 167.61076548111026, 167.61076548111026,164.97138190423385, 164.97138190423385, 164.97138190423385, 164.97138190423385, 164.97138190423385,164.72449819082792, 164.54586334812686, 164.54586334812686, 199.208730578168, 164.54586334812686,164.54586334812686, 164.54586334812686, 164.54586334812686, 164.29897963472092, 164.29897963472092,164.29897963472092, 164.29897963472092, 164.29897963472092, 164.29897963472092, 164.29897963472092,164.29897963472092, 164.29897963472092, 185.88553720859375, 164.29897963472092, 164.29897963472092,164.29897963472092, 164.29897963472092, 164.29897963472092, 164.29897963472092, 164.29897963472092,164.29897963472092, 164.29897963472092, 164.29897963472092, 164.29897963472092, 164.29897963472092,164.29897963472092, 164.29897963472092, 164.29897963472092, 162.57964890814006, 164.29897963472092,162.57964890814006, 158.7673551900737, 158.7673551900737, 158.7673551900737, 158.7673551900737,158.7673551900737, 158.7673551900737, 158.7673551900737, 158.7673551900737, 158.7673551900737,158.7673551900737, 158.7673551900737, 158.7673551900737, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 165.4458885670924, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 191.02831038858773, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 171.65859112307524, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 164.0340772847696, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 179.9211681457678, 179.9211681457678,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,163.66825012378013, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 171.91025362935008, 158.1419649942265, 158.1419649942265,209.80381193148267, 191.60574674226325, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 175.8142105909829, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,167.026358254871, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 176.6464998788, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 167.23953199487363, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 192.04319689552514,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 163.16329458342935, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 200.09613901232325, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 161.73403495002682, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 170.9199683340315,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,194.74385775914007, 176.00797889997622, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 161.17029153503222, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265, 158.1419649942265,158.1419649942265, 158.1419649942265, 158.1419649942265, 200.08345964477837]# 设置数据图的标题
plt.title('迭代代数与距离的关系')# 第一个列表代表横坐标的值，第二个代表纵坐标的值
plt.plot(x_data, y_data)
# 设置两条坐标轴的标签
plt.xlabel("迭代代数")
plt.ylabel("距离/KM")# 调用show()函数显示图形
plt.show()


北京 ;116.46;39.92
天津 ;117.2;39.13
上海 ;121.48;31.22
重庆 ;106.54;29.59
拉萨 ;91.11;29.97
乌鲁木齐 ;87.68;43.77
银川 ;106.27;38.47
呼和浩特 ;111.65;40.82
南宁  ;108.33;22.84
哈尔滨  ;126.63;45.75
长春  ;125.35;43.88
沈阳  ;123.38;41.8
石家庄  ;114.48;38.03
太原  ;112.53;37.87
西宁 ;101.74;36.56
济南 ;117;36.65
郑州 ;113.6;34.76
南京;118.78;32.04
合肥;117.27;31.86
杭州;120.19;30.26
福州;119.3;26.08
南昌;115.89;28.68
长沙;113;28.21
武汉;114.31;30.52
广州;113.23;23.16
台北;121.5;25.05
海口;110.35;20.02
兰州;103.73;36.03
西安;108.95;34.27
成都;104.06;30.67
贵阳;106.71;26.57
昆明;102.73;25.04
香港;114.1;22.2
澳门;113.33;22.13

运行截图

运行视频展示

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小结

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