禁忌搜索算法求解CVRP问题Python代码复现，每行代码标注中文注释和画图

以下是禁忌搜索算法求解CVRP问题Python代码的复现：

import random
import copy
import matplotlib.pyplot as plt

# 定义车辆容量
capacity = 50

# 定义城市坐标
cities = {
    0: (50, 50),
    1: (30, 40),
    2: (10, 30),
    3: (40, 70),
    4: (70, 30),
    5: (20, 20),
    6: (80, 60),
    7: (30, 60),
    8: (50, 10),
    9: (90, 30)
}

# 定义初始解
init_solution = [[0], [1, 2, 3, 4, 5], [6, 7], [8, 9]]

# 计算两个城市之间的距离
def distance(city1, city2):
    x1, y1 = cities[city1]
    x2, y2 = cities[city2]
    return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5

# 计算解的总距离
def total_distance(solution):
    total = 0
    for route in solution:
        for i in range(len(route) - 1):
            total += distance(route[i], route[i+1])
    return total

# 交换两个城市的位置
def swap(solution, i, j):
    new_solution = copy.deepcopy(solution)
    for route in new_solution:
        if i in route and j in route:
            index_i = route.index(i)
            index_j = route.index(j)
            route[index_i], route[index_j] = route[index_j], route[index_i]
            break
    return new_solution

# 随机选择两个城市进行交换
def random_swap(solution):
    new_solution = copy.deepcopy(solution)
    while True:
        route1 = random.choice(new_solution)
        route2 = random.choice(new_solution)
        if len(route1) == 1 or len(route2) == 1:
            continue
        i = random.choice(route1[1:-1])
        j = random.choice(route2[1:-1])
        if sum([capacity - cities[i][1] for i in route1]) + cities[j][1] > capacity \
            or sum([capacity - cities[i][1] for i in route2]) + cities[i][1] > capacity:
            continue
        return swap(new_solution, i, j)

# 计算移动的距离
def move_distance(solution, i, j):
    new_solution = swap(solution, i, j)
    return total_distance(new_solution) - total_distance(solution)

# 禁忌搜索算法
def tabu_search(init_solution, max_iter, tabu_tenure):
    # 初始化当前解和最优解
    current_solution = init_solution
    best_solution = init_solution
    # 初始化禁忌列表
    tabu_list = []
    # 迭代max_iter次
    for i in range(max_iter):
        # 选择邻域中移动距离最小的解
        min_distance = float('inf')
        for i in range(len(current_solution)):
            for j in range(i+1, len(current_solution)):
                if (i, j) in tabu_list:
                    continue
                distance = move_distance(current_solution, i, j)
                if distance < min_distance:
                    min_distance = distance
                    move_i, move_j = i, j
        # 更新当前解和最优解
        current_solution = swap(current_solution, move_i, move_j)
        if total_distance(current_solution) < total_distance(best_solution):
            best_solution = current_solution
        # 更新禁忌列表
        tabu_list.append((move_i, move_j))
        if len(tabu_list) > tabu_tenure:
            tabu_list.pop(0)
    return best_solution

# 打印最优解和最优解的距离
best_solution = tabu_search(init_solution, 100, 10)
print('最优解：', best_solution)
print('最优解的距离：', total_distance(best_solution))

# 画出最优解的路径图
for route in best_solution:
    x = []
    y = []
    for city in route:
        x.append(cities[city][0])
        y.append(cities[city][1])
    plt.plot(x, y, 'o-')
plt.show()

代码中首先定义了车辆容量和城市坐标。然后定义了计算两个城市之间距离的函数、计算解的总距离的函数、交换两个城市位置的函数、随机选择两个城市进行交换的函数、计算移动的距离的函数以及禁忌搜索算法的函数。在主函数中，首先调用禁忌搜索算法函数求解最优解，并打印最优解和最优解的距离。最后，使用Matplotlib库画出最优解的路径图。