基于模拟退火算法解决旅行商问题(Python代码)
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2022-06-26 17:07:13
大家好!本文为大家提供了模拟退火算法解决TSP的一种python实现...
大家好!本文为大家提供了模拟退火算法解决TSP的一种python实现。有兴趣的同学可以看看“遗传算法解决TSP问题”,你会发现二者产生新解的方式一样,但选择新解的方式不同。
import math
import random
import numpy as np
import matplotlib.pyplot as plt
# 随机生成城市信息
nCity = 10
City = np.random.uniform(-10, 10, [nCity, 2])
Dis = {}
for i in range(nCity):
for j in range(nCity):
if i > j:
dis = ((City[i][0] - City[j][0]) ** 2 + (City[i][1] - City[j][1]) ** 2) ** 0.5
Dis[(i, j)] = dis
Dis[(j, i)] = dis
Data_BestFit =[] #用于保存每一代蚂蚁的最优适应度
#适应度计算函数 适应值 = 路径距离
def Cal_Fit(X):
total_dis = Dis[(X[-1],X[0])]
for i in range(nCity-1):
total_dis += Dis[(X[i],X[i+1])]
return total_dis
def SAA_TSP():
# 定义参数
T0 = 100 # 初始温度
T1 = 0.1 # 最终温度
a = 0.99 # 温度衰减系数
Markov = 100 # 马尔科夫链
Pm = 0.3 # 变异概率
Pc = 0.7 # 交叉概率
# 初始化解
Best_X = None
Best_Fit = math.inf
X = np.zeros([Markov,nCity])
Fit = np.zeros([Markov])
for i in range(Markov):
X[i] = np.random.permutation(nCity)
Fit[i] = Cal_Fit(X[i])
if Fit[i] < Best_Fit:
Best_Fit = Fit[i]
Best_X = X[i].copy()
# 降温过程
T = T0
while T >= T1:
for i in range(Markov):
# 变异、交叉产生新解
x = X[i].copy()
if random.random() < Pm:
point1 = int(random.random() * nCity)
point2 = int(random.random() * nCity)
while point1 == point2:
point1 = int(random.random() * nCity)
point2 = int(random.random() * nCity)
x[point1],x[point2] = x[point2],x[point1]
if random.random() < Pc:
point = int(random.random()*nCity)
temp1 = list(x[0:point])
temp2 = list(x[point:nCity])
temp2.extend(temp1)
x = np.array(temp2.copy())
# 计算新解适应值并判断是否接受
fit = Cal_Fit(x)
delta = fit - Fit[i]
if delta <= 0:
Fit[i] = fit
X[i] = x
if Fit[i] < Best_Fit:
Best_Fit = Fit[i]
Best_X = X[i].copy()
# 是否接受恶化解
elif random.random() < math.exp(-delta/T):
Fit[i] = fit
X[i] = x.copy()
Data_BestFit.append(Best_Fit)
T *= a # 降温
return Best_X, Best_Fit
# 绘制路径与迭代曲线
def Draw_City(City, X ,Best_Fit):
X = list(X)
X.append(X[0])
coor_x = []
coor_y = []
for i in X:
i = int(i)
coor_x.append(City[i][0])
coor_y.append(City[i][1])
plt.plot(coor_x, coor_y, 'r-o')
plt.title('TSP with Simulated Annealing Algorithm\n'+'total_dis = '+str(round(Best_Fit,3)))
plt.show()
plt.plot(range(len(Data_BestFit)), Data_BestFit)
plt.title('Iteration_BestFit')
plt.xlabel('iteration')
plt.ylabel('fitness')
plt.show()
if __name__ == '__main__':
Best_X, Best_Fit = SAA_TSP()
Draw_City(City,Best_X, Best_Fit)
本文地址:https://blog.csdn.net/qq_44936034/article/details/112686933