使用退火求解TSP优化问题代码

以下是使用退火算法求解TSP问题的Python代码：

import random
import math

# 计算路径长度
def distance(path, cities):
    distance = 0
    for i in range(len(path) - 1):
        distance += math.sqrt((cities[path[i]][0] - cities[path[i+1]][0])**2 + 
                              (cities[path[i]][1] - cities[path[i+1]][1])**2)
    return distance

# 交换路径中两个城市的位置
def swap(path, i, j):
    path[i], path[j] = path[j], path[i]
    return path

# 退火算法求解TSP问题
def tsp(cities, T, cooling_rate):
    # 初始化路径
    path = list(range(len(cities)))
    random.shuffle(path)
    best_path = path
    # 初始温度
    temp = T
    # 循环直到温度降至停止温度
    while temp > 1:
        # 随机交换两个城市的位置，得到新路径
        i, j = random.sample(range(len(cities)), 2)
        new_path = swap(path, i, j)
        # 计算新路径的长度
        new_distance = distance(new_path, cities)
        old_distance = distance(path, cities)
        # 计算接受新路径的概率
        accept_prob = math.exp(-(new_distance - old_distance) / temp)
        # 根据概率接受或拒绝新路径
        if accept_prob > random.random():
            path = new_path
        # 更新最优路径
        if distance(path, cities) < distance(best_path, cities):
            best_path = path
        # 降温
        temp *= cooling_rate
    return best_path

其中，cities是一个二维数组，表示每个城市的坐标；T是初始温度；cooling_rate是温度下降系数。使用该函数求解TSP问题，返回的是最优路径。