基于模拟退火算法解决旅行商问题(Python代码)

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)