Google OR-Tools：具有多种货物类型和容量的 CVRP

Posted 2023-02-16

【中文标题】Google OR-Tools：具有多种货物类型和容量的 CVRP

【英文标题】：Google OR-Tools: CVRP with multiple cargo types and capacities

【发布时间】：2021-02-03 11:56:51

【问题描述】：

我正在尝试解决具有多种货物类型和容量的 CVRP。假设我有四辆车和两种货物（橙子和苹果）。每辆车都有不同的苹果和橙子容量，每个节点都有不同的需求。两辆车只能运苹果，两辆车只能运橙子。所以我定义了以下数据：

    data['demands_oranges'] = [0, 1, 1, 2, 4, 2, 4, 1, 8, 1, 2, 1, 2, 4, 4, 8, 8]
    data['demands_apples'] = [0, 1, 1, 2, 4, 2, 4, 1, 8, 1, 2, 1, 2, 4, 4, 8, 8]
    data['vehicle_capacities_oranges'] = [0, 0, 40, 40]
    data['vehicle_capacities_apples'] = [40, 40, 0, 0]

另外，我为每个容量定义了两个维度：

    # Add Capacity constraint.
    def demand_callback_apples(from_index):
        """Returns the demand of the node."""
        # Convert from routing variable Index to demands NodeIndex.
        from_node = manager.IndexToNode(from_index)
        return data['demands_apples'][from_node]

    demand_callback_index_apples = routing.RegisterUnaryTransitCallback(
        demand_callback_apples)
    routing.AddDimensionWithVehicleCapacity(
        demand_callback_index_apples,
        0,  # null capacity slack
        data['vehicle_capacities_apples'],  # vehicle maximum capacities
        True,  # start cumul to zero
        'Capacity_apples')

    def demand_callback_oranges(from_index):
        """Returns the demand of the node."""
        # Convert from routing variable Index to demands NodeIndex.
        from_node = manager.IndexToNode(from_index)
        return data['demands_oranges'][from_node]

    demand_callback_index_oranges = routing.RegisterUnaryTransitCallback(
        demand_callback_oranges)
    routing.AddDimensionWithVehicleCapacity(
        demand_callback_index_oranges,
        0,  # null capacity slack
        data['vehicle_capacities_oranges'],  # vehicle maximum capacities
        True,  # start cumul to zero
        'Capacity_oranges')

问题是，没有针对此输入数据返回任何解决方案。尽管事实上车辆容量甚至没有被超过。 当我使用时，该模型出于某种原因工作：

data['vehicle_capacities_oranges'] = [0, 0, 40, 40]
data['vehicle_capacities_apples'] = [0, 0, 40, 40]

但这不是我需要的。这是什么原因？

代码：

    """Capacited Vehicles Routing Problem (CVRP)."""

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


def create_data_model():
    """Stores the data for the problem."""
    data = 
    data['distance_matrix'] = [
        [
            0, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354,
            468, 776, 662
        ],
        [
            548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674,
            1016, 868, 1210
        ],
        [
            776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164,
            1130, 788, 1552, 754
        ],
        [
            696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822,
            1164, 560, 1358
        ],
        [
            582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708,
            1050, 674, 1244
        ],
        [
            274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628,
            514, 1050, 708
        ],
        [
            502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856,
            514, 1278, 480
        ],
        [
            194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320,
            662, 742, 856
        ],
        [
            308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662,
            320, 1084, 514
        ],
        [
            194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388,
            274, 810, 468
        ],
        [
            536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764,
            730, 388, 1152, 354
        ],
        [
            502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114,
            308, 650, 274, 844
        ],
        [
            388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194,
            536, 388, 730
        ],
        [
            354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0,
            342, 422, 536
        ],
        [
            468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536,
            342, 0, 764, 194
        ],
        [
            776, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274,
            388, 422, 764, 0, 798
        ],
        [
            662, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730,
            536, 194, 798, 0
        ],
    ]
    data['demands_oranges'] = [0, 1, 1, 2, 4, 2, 4, 1, 8, 1, 2, 1, 2, 4, 4, 8, 8]
    data['demands_apples'] = [0, 1, 1, 2, 4, 2, 4, 1, 8, 1, 2, 1, 2, 4, 4, 8, 8]

    data['vehicle_capacities_oranges'] = [0, 0, 40, 40]
    data['vehicle_capacities_apples'] = [0, 0, 40, 40]

    data['price_per_km'] = [1, 1, 1, 1]
    data["price_per_stop"] = [1, 1, 1, 1]
    data['num_vehicles'] = 4
    data['depot'] = 0

    return data


def print_solution(data, manager, routing, solution):
    """Prints solution on console."""
    for capacity_ID in ['demands_oranges','demands_apples']:
        print("____Capacity______".format(capacity_ID))
        total_distance = 0
        total_load = 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
            route_load = 0
            while not routing.IsEnd(index):
                node_index = manager.IndexToNode(index)
                route_load += data[str(capacity_ID)][node_index]
                plan_output += ' 0 Load(1) -> '.format(node_index, route_load)
                previous_index = index
                index = solution.Value(routing.NextVar(index))
                route_distance += routing.GetArcCostForVehicle(
                    previous_index, index, vehicle_id)
            plan_output += ' 0 Load(1)\n'.format(manager.IndexToNode(index),
                                                     route_load)
            plan_output += 'Distance of the route: m\n'.format(route_distance)
            plan_output += 'Load of the route: \n'.format(route_load)
            print(plan_output)
            total_distance += route_distance
            total_load += route_load
        print('Total distance of all routes: m'.format(total_distance))
        print('Total load of all routes: '.format(total_load))



def main():
    """Solve the CVRP problem."""
    # Instantiate the data problem.
    data = create_data_model()

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

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

    ### Kosten  festlegen ###
    def create_cost_callback(dist_matrix, km_costs, stop_costs):
        # Create a callback to calculate distances between cities.

        def distance_callback(from_index, to_index):
            from_node = manager.IndexToNode(from_index)
            to_node = manager.IndexToNode(to_index)
            return int(dist_matrix[from_node][to_node]) * (km_costs) + (stop_costs)

        return distance_callback

    for i in range(data['num_vehicles']):
        cost_callback = create_cost_callback(data['distance_matrix'], data["price_per_km"][i],
                                             data["price_per_stop"][i])  # Callbackfunktion erstellen
        cost_callback_index = routing.RegisterTransitCallback(cost_callback)  # registrieren
        routing.SetArcCostEvaluatorOfVehicle(cost_callback_index, i)  # Vehicle zuordnen


    # Add Capacity constraint.
    def demand_callback_apples(from_index):
        """Returns the demand of the node."""
        # Convert from routing variable Index to demands NodeIndex.
        from_node = manager.IndexToNode(from_index)
        return data['demands_apples'][from_node]

    demand_callback_index_apples = routing.RegisterUnaryTransitCallback(
        demand_callback_apples)
    routing.AddDimensionWithVehicleCapacity(
        demand_callback_index_apples,
        0,  # null capacity slack
        data['vehicle_capacities_apples'],  # vehicle maximum capacities
        True,  # start cumul to zero
        'Capacity_apples')

    def demand_callback_oranges(from_index):
        """Returns the demand of the node."""
        # Convert from routing variable Index to demands NodeIndex.
        from_node = manager.IndexToNode(from_index)
        return data['demands_oranges'][from_node]

    demand_callback_index_oranges = routing.RegisterUnaryTransitCallback(
        demand_callback_oranges)
    routing.AddDimensionWithVehicleCapacity(
        demand_callback_index_oranges,
        0,  # null capacity slack
        data['vehicle_capacities_oranges'],  # vehicle maximum capacities
        True,  # start cumul to zero
        'Capacity_oranges')


    # Setting first solution heuristic.
    search_parameters = pywrapcp.DefaultRoutingSearchParameters()
    search_parameters.first_solution_strategy = (
        routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)
    search_parameters.local_search_metaheuristic = (
        routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
    search_parameters.time_limit.FromSeconds(10)

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

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

if __name__ == '__main__':
    main()

【参考方案1】：

所有位置只能访问一次

因此，如果您有apples 和 oranges，则应该复制该位置，这样一辆车将访问一个位置，而另一辆车将访问一个位置...

注意：当您更改容量以使车辆可以同时携带两种类型时，它就可以工作