退火算法旅行商问题python程序

退火算法是一种基于模拟退火过程的优化算法，常用于解决旅行商问题（Traveling Salesman Problem，TSP）。TSP是一个经典的组合优化问题，目标是找到一条最短路径，使得旅行商能够访问所有城市并回到起始城市。

以下是一个使用Python实现的退火算法解决TSP的示例程序：

import random
import math

# 计算两个城市之间的距离
def distance(city1, city2):
    x1, y1 = city1
    x2, y2 = city2
    return math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)

# 计算路径的总长度
def path_length(path, cities):
    total_length = 0
    for i in range(len(path)):
        city1 = cities[path[i]]
        city2 = cities[path[(i + 1) % len(path)]]
        total_length += distance(city1, city2)
    return total_length

# 生成初始解
def generate_initial_solution(num_cities):
    return list(range(num_cities))

# 生成新解
def generate_neighbor_solution(solution):
    new_solution = solution.copy()
    index1 = random.randint(0, len(solution) - 1)
    index2 = random.randint(0, len(solution) - 1)
    new_solution[index1], new_solution[index2] = new_solution[index2], new_solution[index1]
    return new_solution

# 判断是否接受新解
def accept_new_solution(old_length, new_length, temperature):
    if new_length < old_length:
        return True
    else:
        probability = math.exp((old_length - new_length) / temperature)
        return random.random() < probability

# 退火算法
def simulated_annealing(cities, initial_temperature, cooling_rate, max_iterations):
    current_solution = generate_initial_solution(len(cities))
    best_solution = current_solution.copy()
    current_length = path_length(current_solution, cities)
    best_length = current_length
    temperature = initial_temperature

    for i in range(max_iterations):
        new_solution = generate_neighbor_solution(current_solution)
        new_length = path_length(new_solution, cities)

        if accept_new_solution(current_length, new_length, temperature):
            current_solution = new_solution
            current_length = new_length

        if current_length < best_length:
            best_solution = current_solution.copy()
            best_length = current_length

        temperature *= cooling_rate

    return best_solution, best_length

# 示例用法
cities = [(0, 0), (1, 2), (3, 1), (5, 2), (6, 0)]
initial_temperature = 100
cooling_rate = 0.99
max_iterations = 1000

best_solution, best_length = simulated_annealing(cities, initial_temperature, cooling_rate, max_iterations)
print("最短路径:", best_solution)
print("路径长度:", best_length)

以上是一个简单的退火算法解决TSP的Python程序示例。程序首先定义了一些辅助函数，如计算城市之间的距离、计算路径长度等。然后，通过生成初始解和生成新解的方式进行迭代优化，根据一定的概率接受新解或者保留当前解。最后输出找到的最短路径和路径长度。