使用优化后的退火算法对att48求解最优路径

为了使用优化后的退火算法求解att48问题的最优路径，我们需要进行以下步骤：

1. 定义问题：att48问题是一个旅行商问题（TSP），它需要找到一个最短的路径，以使旅行商能够访问48个城市一次。

2. 定义邻域结构：我们可以定义两个城市之间的交换为邻域结构，即将路径中的两个城市交换位置。

3. 定义能量函数：能量函数可以定义为路径长度，即从起点开始，经过所有城市一次后返回起点所需的距离。

4. 初始化：我们可以使用随机算法来初始化路径，即随机生成一组路径。

5. 退火过程：在退火过程中，我们会接受一些较差的解，以避免陷入局部最优解。我们可以使用Metropolis准则来接受这些较差的解。

6. 终止条件：在退火过程中，我们需要设置一个终止条件。这可以是迭代次数、温度阈值或能量值的变化率。

7. 输出结果：在退火过程结束后，我们可以输出路径的最短长度和路径本身。

总之，使用优化后的退火算法对att48求解最优路径的过程是一个较为复杂的过程，需要注意算法的参数设置和调优，也需要考虑到算法的时间复杂度和空间复杂度。

相关问题

使用优化后的退火算法对att48求解最优路径并绘图python代码

以下是使用优化后的退火算法对att48求解最优路径并绘图的Python 代码，其中部分代码参考了其他开源项目：

import math
import random
import matplotlib.pyplot as plt

# 定义城市坐标
city_coordinates = [
    (6734, 1453), (2233, 10), (5530, 1424), (401, 841), (3082, 1644), 
    (7608, 4458), (7573, 3716), (7265, 1268), (6898, 1885), (1112, 2049), 
    (5468, 2606), (5989, 2873), (4706, 2674), (4612, 2035), (6347, 2683), 
    (6107, 669), (7611, 5184), (7462, 3590), (7732, 4723), (5900, 3561), 
    (4483, 3369), (6101, 1110), (5199, 2182), (1633, 2809), (4307, 2322), 
    (675, 1006), (7555, 4819), (7541, 3981), (3177, 756), (7352, 4506), 
    (7545, 2801), (3245, 3305), (6426, 3173), (4608, 1198), (23, 2216), 
    (7248, 3779), (7762, 4595), (7392, 2244), (3484, 2829), (6271, 2135), 
    (4985, 140), (1916, 1569), (7280, 4899), (7509, 3239), (10, 2676), 
    (6807, 2993), (5185, 3258)
]

# 定义距离矩阵
def distance_matrix(city_coordinates):
    n = len(city_coordinates)
    matrix = [[0] * n for i in range(n)]
    for i in range(n):
        for j in range(n):
            if i != j:
                x1, y1 = city_coordinates[i]
                x2, y2 = city_coordinates[j]
                matrix[i][j] = math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)
    return matrix

distance = distance_matrix(city_coordinates)

# 邻域结构：交换两个城市的位置
def swap_cities(path):
    n = len(path)
    i, j = random.sample(range(n), 2)
    new_path = path[:]
    new_path[i], new_path[j] = new_path[j], new_path[i]
    return new_path

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

# 优化后的退火算法
def simulated_annealing(distance, max_iterations=50000, start_temperature=10000, cooling_rate=0.99):
    n = len(distance)
    current_path = random.sample(range(n), n)
    current_length = path_length(current_path, distance)
    best_path = current_path[:]
    best_length = current_length
    temperature = start_temperature

    for i in range(max_iterations):
        new_path = swap_cities(current_path)
        new_length = path_length(new_path, distance)
        delta = new_length - current_length
        if delta < 0 or random.random() < math.exp(-delta/temperature):
            current_path = new_path[:]
            current_length = new_length
        if current_length < best_length:
            best_path = current_path[:]
            best_length = current_length
        temperature *= cooling_rate

    return best_path, best_length

# 绘制最优路径
def plot_path(city_coordinates, path):
    x = [city_coordinates[path[i]][0] for i in range(len(path))]
    y = [city_coordinates[path[i]][1] for i in range(len(path))]
    x.append(city_coordinates[path[0]][0])
    y.append(city_coordinates[path[0]][1])
    plt.plot(x, y, marker='o')
    plt.show()

# 求解最优路径
best_path, best_length = simulated_annealing(distance)
print('最优路径:', best_path)
print('最短距离:', best_length)

# 绘制最优路径
plot_path(city_coordinates, best_path)

运行代码后，会输出最优路径和最短距离，并绘制最优路径的图像。

使用优化后的退火算法对att48.tsp求解最优路径并绘图python代码

以下是使用优化后的退火算法对att48.tsp求解最优路径并绘图的Python代码：

import math
import random
import matplotlib.pyplot as plt

# 读取tsp文件
def read_tsp_file(filename):
    coordinates = []
    with open(filename, 'r') as f:
        lines = f.readlines()
        for line in lines:
            if line.startswith('DIMENSION'):
                n = int(line.split()[-1])
            elif line.startswith('NODE_COORD_SECTION'):
                for i in range(n):
                    line = lines[i+1].strip().split()
                    coordinates.append((float(line[1]), float(line[2])))
    return coordinates

# 定义距离矩阵
def distance_matrix(city_coordinates):
    n = len(city_coordinates)
    matrix = [[0] * n for i in range(n)]
    for i in range(n):
        for j in range(n):
            if i != j:
                x1, y1 = city_coordinates[i]
                x2, y2 = city_coordinates[j]
                matrix[i][j] = math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)
    return matrix

# 邻域结构：交换两个城市的位置
def swap_cities(path):
    n = len(path)
    i, j = random.sample(range(n), 2)
    new_path = path[:]
    new_path[i], new_path[j] = new_path[j], new_path[i]
    return new_path

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

# 优化后的退火算法
def simulated_annealing(distance, max_iterations=50000, start_temperature=10000, cooling_rate=0.99):
    n = len(distance)
    current_path = random.sample(range(n), n)
    current_length = path_length(current_path, distance)
    best_path = current_path[:]
    best_length = current_length
    temperature = start_temperature

    for i in range(max_iterations):
        new_path = swap_cities(current_path)
        new_length = path_length(new_path, distance)
        delta = new_length - current_length
        if delta < 0 or random.random() < math.exp(-delta/temperature):
            current_path = new_path[:]
            current_length = new_length
        if current_length < best_length:
            best_path = current_path[:]
            best_length = current_length
        temperature *= cooling_rate

    return best_path, best_length

# 绘制最优路径
def plot_path(city_coordinates, path):
    x = [city_coordinates[path[i]][0] for i in range(len(path))]
    y = [city_coordinates[path[i]][1] for i in range(len(path))]
    x.append(city_coordinates[path[0]][0])
    y.append(city_coordinates[path[0]][1])
    plt.plot(x, y, marker='o')
    plt.show()

# 读取tsp文件并求解最优路径
filename = 'att48.tsp'
city_coordinates = read_tsp_file(filename)
distance = distance_matrix(city_coordinates)
best_path, best_length = simulated_annealing(distance)

# 输出最优路径和最短距离
print('最优路径:', best_path)
print('最短距离:', best_length)

# 绘制最优路径
plot_path(city_coordinates, best_path)

在代码中，我们读取了att48.tsp文件并将其转换为城市坐标，然后使用定义的距离矩阵和优化后的退火算法求解最优路径，最后绘制最优路径的图像。代码运行后，会输出最优路径和最短距离，并绘制最优路径的图像。