用python来编写TSP问题
import math
from os import path
import numpy as np
import matplotlib.pyplot as plt
class TSPInstance:
'''
设计一个类,实现从文件读入一个旅行商问题的实例
文件格式为:
city number
best known tour length
list of city position (index x y)
best known tour (city index starts from 1)
以文件01eil51.txt为例:
第一行51为城市数
第二行426为最优解的路径长度
第三行开始的51行为各个城市的序号、x坐标和y坐标
最后是最优解的访问城市系列(注意里面城市序号从1开始,而python的sequence是从0开始)
Eil51Tour.png是最优解的城市访问顺序图
'''
def __init__(self, file_name):
'''
从文件file_name读入旅行商问题的数据
'''
self.file_name=file_name
a= open(file_name)
# 城市数量
self.city_num = a.readline()
# 返回坐标 51行,3列
self.city = np.zeros((int(self.city_num), 3))
# x坐标
self.x = np.zeros(int(self.city_num))
# y坐标
self.y = np.zeros(int(self.city_num))
# 城市ID
self.id = np.zeros(int(self.city_num))
b = a.readlines()
for i, content in enumerate(b):
if i in range(1, 52 ):
# 单行赋值
self.city[i-1] = content.strip('\n').split(' ')
self.x[i-1] = self.city[i-1][1]
self.y[i-1] = self.city[i-1][2]
for i, content in enumerate(b):
if i in range(53, 104):
self.id[i - 53] = content.strip('\n')
@property
def citynum(self):
'''
返回城市数
'''
return self.city_num
@property
def optimalval(self):
'''
返回最优路径长度
'''
c = 0
i = 1
s = open(self.file_name)
str = s.readlines()
for content in str:
if i == 2:
c = content
i = i + 1
return c
@property
def optimaltour(self):
'''
返回最优路径
'''
tour = np.array(self.id)
return tour
def __getitem__(self, n):
'''
返回城市n的坐标,由x和y构成的tuple:(x,y)
'''
(x, y) = (self.x[n-1], self.y[n-1])
return (x, y)
def get_distance(self, n, m):
'''
返回城市n、m间的整数距离(四舍五入)
'''
u=int(self.x[n-1] - self.x[m-1])
v=int(self.y[n-1] - self.y[m-1])
dis = math.sqrt(pow(u,2) + pow(v,2))
return int(dis+0.5)
def evaluate(self, tour):
'''
返回访问系列tour所对应的路径程度
'''
dis = 0
for i in range(50):
dis += self.get_distance(int(tour[i]), int(tour[i + 1]))
dis += self.get_distance(int(tour[50]), int(tour[0]))
return dis
def plot_tour(self, tour):
'''
画出访问系列tour所对应的路径路
'''
for i in range(51):
x0,y0 = self.__getitem__(i)
plt.scatter(int(x0),int(y0),s=10,c='c')
#记住坐标点的画法
for i in range(len(tour)-1):
x1,y1 = self.__getitem__(int(tour[i]))
x,y = self.__getitem__(int(tour[i+1]))
plt.plot([x1,x],[y1,y],c='b')
x2,y2 = self.__getitem__(int(tour[0]))
x3,y3 = self.__getitem__(int(tour[len(tour)-1]))
plt.plot([x2,x3],[y2,y3],c='b')
plt.xlabel('x label')
plt.ylabel('y label')
plt.title("City access sequence diagram")
plt.plot()
plt.show()
if __name__ == "__main__":
file_name = path.dirname(__file__) + "/1.txt"
instance = TSPInstance(file_name)
print(instance.citynum)
print(instance.evaluate(instance.optimaltour))
print(instance.optimaltour)
print(instance.__getitem__(2))
print(instance.get_distance(0, 1))
instance.plot_tour(instance.optimaltour)
'''
output:
51
426
[ 1. 22. 8. 26. 31. 28. 3. 36. 35. 20. 2. 29. 21. 16. 50.
34. 30. 9. 49. 10. 39. 33. 45. 15. 44. 42. 40. 19. 41. 13.
25. 14. 24. 43. 7. 23. 48. 6. 27. 51. 46. 12. 47. 18. 4.
17. 37. 5. 38. 11. 32.]
(49.0, 49.0)
14
'''
其实解决TSP问题有很多方法,比如模拟退火算法,贪心算法,回溯算法等等。希望各位博友可以把你们的解决方法出现在评论区。