启发式退火求解att48.tsp的最优路径

对于TSP问题，启发式退火算法可以用来求解最优路径。这里给出一个使用启发式退火算法求解att48.tsp最优路径的示例代码（使用Python实现）：

import math
import random

# 读取att48.tsp文件中的城市坐标
with open("att48.tsp", "r") as f:
    lines = f.readlines()[6:-1]
    coords = [tuple(map(float, line.strip().split()[1:])) for line in lines]

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

# 计算当前路径的总距离
def total_distance(path):
    return sum(distance(coords[path[i]], coords[path[i+1]])
               for i in range(len(path)-1)) + distance(coords[path[-1]], coords[path[0]])

# 启发式退火算法求解TSP问题
def solve_tsp():
    # 初始温度
    T = 10000
    # 温度下降速度
    cooling_rate = 0.003
    # 当前路径
    current_path = list(range(len(coords)))
    # 当前路径的总距离
    current_distance = total_distance(current_path)
    # 最优路径
    best_path = current_path
    # 最优路径的总距离
    best_distance = current_distance

    # 迭代直到温度降至极低
    while T > 1:
        # 随机交换两个城市
        i, j = random.sample(range(len(coords)), 2)
        new_path = current_path.copy()
        new_path[i], new_path[j] = new_path[j], new_path[i]
        # 计算新路径的总距离
        new_distance = total_distance(new_path)
        # 计算能量差
        delta_E = new_distance - current_distance
        # 如果新路径更优，则接受新路径
        if delta_E < 0 or random.random() < math.exp(-delta_E / T):
            current_path = new_path
            current_distance = new_distance
            # 如果当前路径更优，则更新最优路径
            if current_distance < best_distance:
                best_path = current_path
                best_distance = current_distance
        # 温度下降
        T *= 1 - cooling_rate
    
    return best_path, best_distance

# 输出最优路径和总距离
best_path, best_distance = solve_tsp()
print("Best path:", best_path)
print("Total distance:", best_distance)

该代码使用了随机交换两个城市的方式来产生新的路径，然后根据能量差和温度来决定是否接受新路径。通过不断降温，算法能够逐渐收敛到最优路径。