数学建模第三日资料汇总（第二题非理想条件下的解）

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第二问在不考虑曲线不闭合以及权重为3，9的情况下我们得到一下结果：

from random import*
import numpy as np
from math import*
from matplotlib import pyplot as pltcitys = np.loadtxt("data.csv",dtype=int,delimiter=",")
hospitals = np.loadtxt("hospital.csv",dtype=int,delimiter=",")number_of_citys = 25
distance = np.zeros((number_of_citys,number_of_citys))
for i in range(number_of_citys):for j in range(number_of_citys):distance[i][j] = sqrt((citys[i][0]-citys[j][0])**2+(citys[i][1]-citys[j][1])**2)
#由城市坐标计算距离矩阵#初始化参数
iteration1 = 4000                #外循环迭代次数
T0 = 10000000                      #初始温度，取大些
Tf = 1e-8                           #截止温度，可以不用
alpha = 0.98                     #温度更新因子
iteration2 = 2000                 #内循环迭代次数
fbest = 0                        #最佳距离#初始化初解
x = []
for i in range(25):x.append(i)
np.random.shuffle(x)
x = np.array(x)
for j in range(len(x) - 1):fbest = fbest +3 * distance[x[j]][x[j + 1]] - 9 * (hospitals[x[j]])
fbest = fbest + 3 * distance[x[-1]][x[0]] - 9 * (hospitals[x[-1]])
xbest = x.copy()
f_now = fbest
x_now = xbest.copy()for i in range(iteration1):for k in range(iteration2):#生成新解x1 = [0 for q in range(number_of_citys)]n1,n2 = randint(0,number_of_citys-1),randint(0,number_of_citys-1)n = [n1,n2]n.sort()n1,n2 = n#n1为0单独写if n1 > 0:x1[0:n1] = x_now[0:n1]x1[n1:n2+1] = x_now[n2:n1-1:-1]x1[n2+1:number_of_citys] = x_now[n2+1:number_of_citys]else:x1[0:n1] = x_now[0:n1]x1[n1:n2+1] = x_now[n2::-1]x1[n2+1:number_of_citys] = x_now[n2+1:number_of_citys]s = 0;for j in range(len(x1) - 1):s = s + 3*distance[x1[j]][x1[j + 1]] - 9 *(hospitals[x[j]])s = s + 3*distance[x1[-1]][x1[0]] - 9 *(hospitals[x[-1]])#判断是否更新解if s <= f_now:f_now = sx_now = x1.copy()if s > f_now:deltaf = s - f_nowif random() < exp(-deltaf/T0):f_now = sx_now = x1.copy()if s < fbest:fbest = sxbest = x1.copy()T0 = alpha * T0                #更新温度# if T0 < Tf:                  #停止准则为最低温度时可以取消注释#     break#打印最佳路线和最佳距离
print(xbest)
print(fbest)#绘制结果
plt.title('SA_TSP')
plt.xlabel('x')
plt.ylabel('y')
plt.plot(citys[...,0],citys[...,1],'ob',ms = 3)
plt.plot(citys[xbest,0],citys[xbest,1])
plt.plot([citys[xbest[-1],0],citys[xbest[0],0]],[citys[xbest[-1],1],citys[xbest[0],1]],ms = 2)
plt.show()

结果如下：

[6, 9, 20, 7, 16, 2, 4, 22, 14, 11, 5, 1, 19, 13, 3, 12, 24, 15, 21, 10, 8, 23, 0, 17, 18]
-112324.8118531057[20, 7, 16, 2, 4, 22, 14, 11, 5, 1, 19, 13, 3, 12, 24, 15, 21, 8, 10, 23, 0, 17, 18, 6, 9]
-112324.8118531057[9, 6, 18, 17, 0, 23, 10, 8, 21, 15, 24, 12, 3, 13, 19, 1, 5, 11, 14, 22, 4, 2, 16, 7, 20]
-112324.8118531057[15, 24, 12, 3, 13, 19, 1, 5, 11, 14, 22, 4, 2, 16, 7, 20, 9, 6, 18, 17, 0, 23, 10, 8, 21]
-112324.8118531057[18, 6, 9, 20, 7, 16, 2, 4, 22, 14, 11, 5, 1, 19, 13, 3, 12, 24, 15, 21, 8, 10, 23, 0, 17]
-112324.81185310568[23, 0, 17, 18, 6, 9, 20, 7, 16, 2, 4, 22, 14, 11, 5, 1, 19, 13, 3, 12, 24, 15, 21, 8, 10]
-112324.8118531057

图像：

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