遗传算法解决旅行商问题

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import numpy as np
import matplotlib.pyplot as plt
import matplotlib
import math
import random
import time

start = time.time()

matplotlib.rcParams['font.family'] = 'STSong'

'''
数据载入
---------
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
'''
city_name = []
city_condition = []
with open('data.txt','r',encoding='UTF-8') as f:
lines = f.readlines()
for line in lines:
line = line.split('\n')[0]
line = line.split(',')
city_name.append(line[0])
city_condition.append([float(line[1]), float(line[2])])
city_condition = np.array(city_condition)

# 距离矩阵
city_count = len(city_name)
Distance = np.zeros([city_count, city_count])
for i in range(city_count):
for j in range(city_count):
Distance[i][j] = math.sqrt(
(city_condition[i][0] - city_condition[j][0]) ** 2 + (city_condition[i][1] - city_condition[j][1]) ** 2)
# 种群数
count = 200
# 改良次数
improve_count = 500
# 进化次数
iteration = 200
# 设置强者的定义概率,即种群前20%为强者
retain_rate = 0.2
# 变异率
mutation_rate = 0.1
# 设置起点
index = [i for i in range(city_count)]

#总距离
def get_total_distance(path_new):
distance = 0
for i in range(city_count - 1):
# count为30,意味着回到了开始的点,此时的值应该为0.
distance += Distance[int(path_new[i])][int(path_new[i + 1])]
distance += Distance[int(path_new[-1])][int(path_new[0])]
return distance

# 改良
#思想:随机生成两个城市,任意交换两个城市的位置,如果总距离减少,就改变染色体。
def improve(x):
i = 0
distance = get_total_distance(x)
while i < improve_count:
# randint [a,b]
u = random.randint(0, len(x) - 1)
v = random.randint(0, len(x) - 1)
if u != v:
new_x = x.copy()
## 随机交叉两个点,t为中间数
t = new_x[u]
new_x[u] = new_x[v]
new_x[v] = t
new_distance = get_total_distance(new_x)
if new_distance < distance:
distance = new_distance
x = new_x.copy()
else:
continue
i += 1

# 适应度评估,选择,迭代一次选择一次
def selection(population):
# 对总距离从小到大进行排序
graded = [[get_total_distance(x), x] for x in population]
graded = [x[1] for x in sorted(graded)]
# 选出适应性强的染色体
retain_length = int(len(graded) * retain_rate)
#适应度强的集合,直接加入选择中
parents = graded[:retain_length]
## 轮盘赌算法选出K个适应性不强的个体,保证种群的多样性
s = graded[retain_length:]
# 挑选的不强的个数
k = count * 0.2
# 存储适应度
a = []
for i in range(0, len(s)):
a.append(get_total_distance(s[i]))
sum = np.sum(a)
b = np.cumsum(a / sum)
while k > 0: # 迭代一次选择k条染色体
t = random.random()
for h in range(1, len(b)):
if b[h - 1] < t <= b[h]:
parents.append(s[h])
k -= 1
break
return parents

# 交叉繁殖
def crossover(parents):
# 生成子代的个数,以此保证种群稳定
target_count = count - len(parents)
# 孩子列表
children = []
while len(children) < target_count:
male_index = random.randint(0, len(parents) - 1)
female_index = random.randint(0, len(parents) - 1)
#在适应度强的中间选择父母染色体
if male_index != female_index:
male = parents[male_index]
female = parents[female_index]

left = random.randint(0, len(male) - 2)
right = random.randint(left + 1, len(male) - 1)

# 交叉片段
gene1 = male[left:right]
gene2 = female[left:right]

#得到原序列通过改变序列的染色体,并复制出来备用。
child1_c = male[right:] + male[:right]
child2_c = female[right:] + female[:right]
child1 = child1_c.copy()
child2 = child2_c.copy()

#已经改变的序列=>去掉交叉片段后的序列
for o in gene2:
child1_c.remove(o)
for o in gene1:
child2_c.remove(o)

#交换交叉片段
child1[left:right] = gene2
child2[left:right] = gene1

child1[right:] = child1_c[0:len(child1) - right]
child1[:left] = child1_c[len(child1) - right:]

child2[right:] = child2_c[0:len(child1) - right]
child2[:left] = child2_c[len(child1) - right:]

children.append(child1)
children.append(child2)

return children

# 变异
def mutation(children):
#children现在包括交叉和优质的染色体
for i in range(len(children)):
if random.random() < mutation_rate:
child = children[i]
#产生随机数
u = random.randint(0, len(child) - 4)
v = random.randint(u + 1, len(child) - 3)
w = random.randint(v + 1, len(child) - 2)
child = child[0:u] + child[v:w] + child[u:v] + child[w:]
children[i] = child
return children

# 得到最佳纯输出结果
def get_result(population):
graded = [[get_total_distance(x), x] for x in population]
graded = sorted(graded)
return graded[0][0], graded[0][1]

# 使用改良圈算法初始化种群
population = []
for i in range(count):
# 随机生成个体
x = index.copy()
#随机排序
random.shuffle(x)
improve(x)
population.append(x)

#主函数:
register = []
i = 0
distance, result_path = get_result(population)
register.append(distance)
while i < iteration:
# 选择繁殖个体群
parents = selection(population)
# 交叉繁殖
children = crossover(parents)
# 变异操作
children = mutation(children)
# 更新种群
population = parents + children
distance, result_path = get_result(population)
register.append(distance)
i = i + 1

print("迭代",iteration,"次后,最优值是:",distance)
print("最优路径:",result_path)
end = time.time()
print("Time used:",end - start)

## 路线图绘制
X = []
Y = []
for index in result_path:
X.append(city_condition[index, 0])
Y.append(city_condition[index, 1])
X.append(X[0])
Y.append(Y[0])
#画图
fig = plt.figure()
ax2 = fig.add_subplot()
ax2.set_title('最佳轨迹图')
for i in range(len(x)):
plt.annotate(result_path[i], xy = (X[i], Y[i]), xytext = (X[i]+0.3, Y[i]+0.3))
plt.plot(X, Y, '-o')
plt.xlabel('经度')
plt.ylabel('纬度')
plt.show()

## 距离迭代图
fig = plt.figure()
ax3 = fig.add_subplot()
ax3.set_title('距离迭代图')
plt.plot(list(range(len(register))), register)
plt.xlabel('迭代次数')
plt.ylabel('距离值')
plt.show()
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