多路径旅行商优化

多路径旅行商优化问题（Multi-depot Vehicle Routing Problem, MDVRP）是旅行商问题（TSP）的一个变种，它考虑了多个仓库（depot）和多个配送车辆之间的路线规划问题。下面是一个解决该问题的代码示例：

import numpy as np
import random

# 定义问题参数
num_depots = 3  # 仓库数量
num_customers = 10  # 客户数量
num_vehicles = 5  # 车辆数量
depot_capacity = 100  # 仓库容量
customer_demands = [random.randint(1, 10) for _ in range(num_customers)]  # 客户需求

# 生成随机距离矩阵
distance_matrix = np.random.randint(1, 10, size=(num_depots + num_customers, num_depots + num_customers))
np.fill_diagonal(distance_matrix, 0)

# 初始化解
solution = [[] for _ in range(num_vehicles)]

# 循环分配客户到车辆路径
for customer in range(num_customers):
    # 计算每个车辆到该客户的距离
    distances = []
    for vehicle in range(num_vehicles):
        if solution[vehicle]:
            last_customer = solution[vehicle][-1]
            distance = distance_matrix[last_customer, customer + num_depots]
        else:
            distance = distance_matrix[vehicle, customer + num_depots]
        distances.append(distance)
    
    # 找到距离最短的车辆
    min_distance = min(distances)
    min_distance_vehicle = distances.index(min_distance)
    
    # 检查车辆容量是否足够
    if sum([customer_demands[customer] for customer in solution[min_distance_vehicle]]) + customer_demands[customer] <= depot_capacity:
        solution[min_distance_vehicle].append(customer + num_depots)

# 输出解
for vehicle, route in enumerate(solution):
    depot = vehicle % num_depots
    print(f"Vehicle {vehicle + 1}, Depot {depot + 1}: {route}")

该代码使用numpy库生成随机的距离矩阵，并采用贪婪策略将客户分配到车辆路径中，同时考虑了车辆容量限制。最后输出了每个车辆的路径。请注意，该代码示例并未考虑多个仓库之间的距离，仅仅考虑了仓库与客户之间的距离。如果需要考虑多个仓库之间的距离，可以相应地修改距离矩阵的生成方式。