TSP的python解法 tsp问题python

TSP问题是指在给定的一些城市之间，求解访问每个城市一次并回到起始城市的最短路径。其中，TSP问题是一个NP难问题，因此需要使用一些高效的算法来解决。模拟退火算法是其中一种常用的算法之一，可以用来求解TSP问题。以下是一个使用Python实现的TSP问题的模拟退火算法解法：

# -*- coding: utf-8 -*-
import numpy as np
import math
import random

# 计算两个城市之间的距离
def distance(city1, city2):
    return math.sqrt((city1[0] - city2[0]) ** 2 + (city1[1] - city2[1]) ** 2)

# 计算路径长度
def path_length(path, cities):
    length = 0
    for i in range(len(path) - 1):
        length += distance(cities[path[i]], cities[path[i+1]])
    length += distance(cities[path[-1]], cities[path[0]])
    return length

# 模拟退火算法求解TSP问题
def tsp_simulated_annealing(cities, T=10000, alpha=0.99, stopping_T=1e-8, stopping_iter=100000):
    # 初始化路径
    path = list(range(len(cities)))
    # 初始化温度
    temperature = T
    # 记录最优路径和长度
    best_path, best_length = path, path_length(path, cities)
    # 迭代次数
    iter_num = 0
    # 迭代
    while temperature > stopping_T and iter_num < stopping_iter:
        # 生成新路径
        new_path = path.copy()
        # 随机交换两个城市的位置
        rand1 = random.randint(0, len(cities) - 1)
        rand2 = random.randint(0, len(cities) - 1)
        while rand1 == rand2:
            rand2 = random.randint(0, len(cities) - 1)
        new_path[rand1], new_path[rand2] = new_path[rand2], new_path[rand1]
        # 计算路径长度差
        delta = path_length(new_path, cities) - path_length(path, cities)
        # 判断是否接受新路径
        if delta < 0 or math.exp(-delta / temperature) > random.random():
            path = new_path
        # 更新最优路径
        if path_length(path, cities) < best_length:
            best_path, best_length = path.copy(), path_length(path, cities)
        # 降温
        temperature *= alpha
        # 迭代次数加1
        iter_num += 1
    return best_path, best_length

# 测试
if __name__ == '__main__':
    # 随机生成10个城市
    cities = np.random.rand(10, 2)
    # 求解TSP问题
    best_path, best_length = tsp_simulated_annealing(cities)
    print('最优路径：', best_path)
    print('最短路径长度：', best_length)