如何在 Google OR-Tools 中为每个节点添加时间维度

如何解决如何在 Google OR-Tools 中为每个节点添加时间维度

我正在使用 OR-Tools 解决多站点多车辆车辆路径问题，到目前为止，我已经成功建立了一个模型，其中一辆车从每个站点离开，并且它们在它们之间的最大时间允许内访问每个节点然后通过虚拟节点 0 退出。 然而，由于这是一个现实世界的问题，在每个节点，车辆都需要停下设定的时间来执行一项服务，每个节点都有一个设定的等待时间，例如在下表中：

节点	持续时间
4	9
38	8
...	...
8545	17

我不确定如何将这些添加到每个节点，尽管到目前为止节点之间的弧长表示每个节点之间的行驶时间（假设所有车辆都以相同的速度行驶）。所以我的问题是如何将这些等待时间添加到模型中，同时仍然最大限度地减少每辆车的行驶时间并将它们保持在 25200 秒的最大阈值以下（对应于 7 小时轮班）。我在下面包含了我的工作代码：

from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

距离矩阵是从一个像这样布局的 csv 中输入的：

空白	4	38	71	90	94	...	8545
4	0	1280	1762	1406	1589	...	1017
38	1280	0	681	202	385	...	1433
71	1762	681	0	503	0	...	0
90	1406	202	503	0	0	...	1559
94	1589	385	0	0	0	...	1742
..	..	...	...	...	...	0	...
8545	1017	1433	0	1559	1742	...	0

Caredist_Matrix = np.loadtxt(open("Caredistances-FULL.csv","rb"),dtype=int,delimiter=",",skiprows=1)
Caredist_Matrix

模型主体如下：

def create_data_model():
    """Stores the data for the problem."""
    data = {}
    data['distance_matrix'] = Caredist_Matrix
    data['num_vehicles'] = 6
    data['starts'] = [3,7,14,104,185,220]
    data['ends'] = [0,0]
    return data

def print_solution(data,manager,routing,solution):
    """Prints solution on console."""
    max_route_distance = 0
    for vehicle_id in range(data['num_vehicles']):
        index = routing.Start(vehicle_id)
        plan_output = 'Route for vehicle {}:\n'.format(vehicle_id)
        route_distance = 0
        while not routing.IsEnd(index):
            plan_output += ' {} -> '.format(manager.IndexToNode(index))
            prevIoUs_index = index
            index = solution.Value(routing.Nextvar(index))
            route_distance += routing.GetArcCostForVehicle(
                prevIoUs_index,index,vehicle_id)
        plan_output += '{}\n'.format(manager.IndexToNode(index))
        plan_output += 'distance of the route: {}m\n'.format(route_distance)
        print(plan_output)
        max_route_distance = max(route_distance,max_route_distance)
    print('Maximum of the route distances: {}m'.format(max_route_distance))

    """Entry point of the program."""
    # Instantiate the data problem.
    data = create_data_model()

    # Create the routing index manager.
    manager = pywrapcp.RoutingIndexManager(len(data['distance_matrix']),data['num_vehicles'],data['starts'],data['ends'])

    # Create Routing Model.
    routing = pywrapcp.RoutingModel(manager)


    # Create and register a transit callback.
    def distance_callback(from_index,to_index):
        """Returns the distance between the two nodes."""
        # Convert from routing variable Index to distance matrix NodeIndex.
        from_node = manager.IndexToNode(from_index)
        to_node = manager.IndexToNode(to_index)
        return data['distance_matrix'][from_node][to_node]

    transit_callback_index = routing.RegisterTransitCallback(distance_callback)

    # Define cost of each arc.
    routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)

    # Add distance constraint.
    dimension_name = 'distance'
    routing.AddDimension(
        transit_callback_index,# no slack
        25200,# vehicle maximum travel distance
        True,# start cumul to zero
        dimension_name)
    distance_dimension = routing.GetDimensionorDie(dimension_name)
    distance_dimension.SetGlobalSpanCostCoefficient(100)

    # Setting first solution heuristic.
    search_parameters = pywrapcp.DefaultRoutingSearchParameters()
    search_parameters.first_solution_strategy = (
        routing_enums_pb2.FirstSolutionStrategy.PATH_CHEApest_ARC)

    # Solve the problem.
    solution = routing.solveWithParameters(search_parameters)

    # Print solution on console.
    if solution:
        print_solution(data,solution)

if __name__ == '__main__':
    main()