模拟退火解决旅行商问题 可视化

以下是一种用Python实现的模拟退火算法解决旅行商问题的可视化方法：

首先，我们需要一个随机生成城市坐标的函数。这里我们随机生成了10个城市，坐标在一个100x100的矩形区域内。

import random

def generate_cities(n, width, height):
    cities = []
    for i in range(n):
        x = random.uniform(0, width)
        y = random.uniform(0, height)
        cities.append((x, y))
    return cities

cities = generate_cities(10, 100, 100)
print(cities)

输出：

[(27.799366440294174, 64.05489175940608), (25.19058739809022, 34.21238518302706), (41.712236274551926, 91.4144840134254), (25.797187315206313, 23.686978996546863), (77.10640273218437, 51.29280511933505), (5.144348270969409, 54.21307845345768), (90.0703655662937, 94.38789421843861), (46.4501186236276, 39.72275888549114), (72.64792449422894, 49.78815751253559), (12.85715953693026, 45.95523751105682)]

接下来，我们需要一个计算任意两个城市之间距离的函数。

import math

def distance(city1, city2):
    x1, y1 = city1
    x2, y2 = city2
    return math.sqrt((x1-x2)**2 + (y1-y2)**2)

然后，我们定义一个计算路径长度的函数，用于评估一条路径的优劣性。

def path_length(path):
    total_distance = 0
    for i in range(len(path)-1):
        total_distance += distance(path[i], path[i+1])
    total_distance += distance(path[-1], path[0])
    return total_distance

下一步，我们需要一个生成随机路径的函数。

def random_path(cities):
    path = cities[:]
    random.shuffle(path)
    return path

然后，我们需要一个模拟退火函数。这个函数接受一个初始路径、一个温度、一个降温率和一个停止温度作为参数，并返回找到的最优路径。

def simulated_annealing(cities, initial_temperature=1000, cooling_rate=0.99, stop_temperature=1e-8):
    current_path = random_path(cities)
    current_length = path_length(current_path)
    best_path = current_path[:]
    best_length = current_length

    temperature = initial_temperature
    while temperature > stop_temperature:
        new_path = current_path[:]
        i = random.randint(0, len(cities)-1)
        j = random.randint(0, len(cities)-1)
        new_path[i], new_path[j] = new_path[j], new_path[i]
        new_length = path_length(new_path)

        delta = new_length - current_length
        if delta < 0 or math.exp(-delta/temperature) > random.uniform(0, 1):
            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

最后，我们可以使用Matplotlib库将结果可视化。

import matplotlib.pyplot as plt

def plot_path(cities, path):
    x = [city[0] for city in cities]
    y = [city[1] for city in cities]
    plt.plot(x, y, 'o')

    path.append(path[0])
    x = [cities[i][0] for i in path]
    y = [cities[i][1] for i in path]
    plt.plot(x, y, 'r-', linewidth=2)

    plt.show()

best_path = simulated_annealing(cities)
plot_path(cities, best_path)

这段代码将生成以下可视化结果：