OR-Tools CVRP_reload with Pickup-Delivery

Question

我使用 or-tools 來解決諸如從 EC 倉庫提貨等問題。

我想做的與 cvrp_reload 示例非常相似。 https://github.com/google/or-tools/blob/stable/ortools/constraint_solver/samples/cvrp_reload.py與示例不同的是，不是將負載帶回倉庫，而是放置拾取的負載在特定的交貨點。

我在查看指南中的 Pickup & Delivery 示例時更改了 cvrp_reload 的來源。 （假設 Node.1 到 5 是交付點）

1. 將取貨點列表添加到數據中

    data['pickups_deliveries'] = [
        [6, 1], [7, 1],
        [8, 1], [9, 1],
        [10, 2], [11, 2],
        [12, 2], [13, 3],
        [14, 3], [15, 3],
        [16, 4], [17, 4],
        [18, 4], [19, 5],
        [20, 5], [21, 5]        
    ]

2. 數據中需求和time_windows的簡化

    data['demands'] = \
          [0, # depot
           -_capacity, # unload depot_first
           -_capacity, # unload depot_second
           -_capacity, # unload depot_third
           -_capacity, # unload depot_fourth
           -_capacity, # unload depot_fifth
           4, 4, # 1, 2   changed from original
           4, 4, # 3, 4   changed from original
           4, 4, # 5, 6   changed from original
           4, 4, # 7, 8   changed from original
           4, 4, # 9,10   changed from original
           4, 4, # 11,12   changed from original
           4, 4, # 13, 14   changed from original
           4, 4] # 15, 16   changed from original
    data['time_windows'] = \
          [(0, 0), # depot
           (0, 1500), # unload depot_first. changed from original
           (0, 1500), # unload depot_second. changed from original
           (0, 1500), # unload depot_third. changed from original
           (0, 1500), # unload depot_fourth. changed from original
           (0, 1500), # unload depot_fifth. changed from original
           (0, 750), (0, 750), # 1, 2   changed from original
           (0, 750), (0, 750), # 3, 4   changed from original
           (0, 750), (0, 750), # 5, 6   changed from original
           (0, 750), (0, 750), # 7, 8   changed from original
           (0, 750), (0, 750), # 9, 10   changed from original
           (750, 1500), (750, 1500), # 11, 12   changed from original
           (750, 1500), (750, 1500), # 13, 14   changed from original
           (750, 1500), (750, 1500)] # 15, 16   changed from original

3. 在 add_distance_dimension function 中定義運輸請求

    for request in data['pickups_deliveries']:
        pickup_index = manager.NodeToIndex(request[0])
        delivery_index = manager.NodeToIndex(request[1])
        routing.AddPickupAndDelivery(pickup_index, delivery_index)
        routing.solver().Add(
            routing.VehicleVar(pickup_index) == routing.VehicleVar(
                delivery_index))
        routing.solver().Add(
            distance_dimension.CumulVar(pickup_index) <=
            distance_dimension.CumulVar(delivery_index))

運行此代碼將刪除所有節點。 但是，將 P&D 列表限制在少數幾個提供了解決方案。

data['pickups_deliveries'] = [
    [6, 1], [7, 1],
    [8, 1], [9, 1],
    [10, 2], [11, 2],
    # [12, 2], [13, 3],
    # [14, 3], [15, 3],
    # [16, 4], [17, 4],
    # [18, 4], [19, 5],
    # [20, 5], [21, 5]        
]

請給我一個提示，我的方法是錯誤的。

這是整個代碼。 感謝您閱讀我的問題。

from functools import partial

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


###########################
# Problem Data Definition #
###########################
def create_data_model():
    """Stores the data for the problem"""
    data = {}
    _capacity = 15
    # Locations in block unit
    _locations = [
        (4, 4),  # depot
        (4, 4),  # unload depot_first
        (4, 4),  # unload depot_second
        (4, 4),  # unload depot_third
        (4, 4),  # unload depot_fourth
        (4, 4),  # unload depot_fifth
        (2, 0),
        (8, 0),  # locations to visit
        (0, 1),
        (1, 1),
        (5, 2),
        (7, 2),
        (3, 3),
        (6, 3),
        (5, 5),
        (8, 5),
        (1, 6),
        (2, 6),
        (3, 7),
        (6, 7),
        (0, 8),
        (7, 8)
    ]
    # Compute locations in meters using the block dimension defined as follow
    # Manhattan average block: 750ft x 264ft -> 228m x 80m
    # here we use: 114m x 80m city block
    data['locations'] = [(l[0] * 114, l[1] * 80) for l in _locations]
    data['num_locations'] = len(data['locations'])
    data['demands'] = \
          [0, # depot
           -_capacity, # unload depot_first
           -_capacity, # unload depot_second
           -_capacity, # unload depot_third
           -_capacity, # unload depot_fourth
           -_capacity, # unload depot_fifth
           4, 4, # 1, 2   changed from original
           4, 4, # 3, 4   changed from original
           4, 4, # 5, 6   changed from original
           4, 4, # 7, 8   changed from original
           4, 4, # 9,10   changed from original
           4, 4, # 11,12   changed from original
           4, 4, # 13, 14   changed from original
           4, 4] # 15, 16   changed from original
    data['time_per_demand_unit'] = 5  # 5 minutes/unit
    data['time_windows'] = \
          [(0, 0), # depot
           (0, 1500), # unload depot_first. changed from original
           (0, 1500), # unload depot_second. changed from original
           (0, 1500), # unload depot_third. changed from original
           (0, 1500), # unload depot_fourth. changed from original
           (0, 1500), # unload depot_fifth. changed from original
           (0, 750), (0, 750), # 1, 2   changed from original
           (0, 750), (0, 750), # 3, 4   changed from original
           (0, 750), (0, 750), # 5, 6   changed from original
           (0, 750), (0, 750), # 7, 8   changed from original
           (0, 750), (0, 750), # 9, 10   changed from original
           (750, 1500), (750, 1500), # 11, 12   changed from original
           (750, 1500), (750, 1500), # 13, 14   changed from original
           (750, 1500), (750, 1500)] # 15, 16   changed from original
    #added p&d list.##############################
    data['pickups_deliveries'] = [
        [6, 1], [7, 1],
        [8, 1], [9, 1],
        [10, 2], [11, 2],
        [12, 2], [13, 3],
        [14, 3], [15, 3],
        [16, 4], [17, 4],
        [18, 4], [19, 5],
        [20, 5], [21, 5]        
    ]
    ##############################################
    data['num_vehicles'] = 3
    data['vehicle_capacity'] = _capacity
    data['vehicle_max_distance'] = 10_000
    data['vehicle_max_time'] = 1_500
    data[
        'vehicle_speed'] = 5 * 60 / 3.6  # Travel speed: 5km/h to convert in m/min
    data['depot'] = 0
    return data


#######################
# Problem Constraints #
#######################
def manhattan_distance(position_1, position_2):
    """Computes the Manhattan distance between two points"""
    return (abs(position_1[0] - position_2[0]) +
            abs(position_1[1] - position_2[1]))


def create_distance_evaluator(data):
    """Creates callback to return distance between points."""
    _distances = {}
    # precompute distance between location to have distance callback in O(1)
    for from_node in range(data['num_locations']):
        _distances[from_node] = {}
        for to_node in range(data['num_locations']):
            if from_node == to_node:
                _distances[from_node][to_node] = 0
            # Forbid start/end/reload node to be consecutive.
            elif from_node in range(6) and to_node in range(6):
                _distances[from_node][to_node] = data['vehicle_max_distance']
            else:
                _distances[from_node][to_node] = (manhattan_distance(
                    data['locations'][from_node], data['locations'][to_node]))

    def distance_evaluator(manager, from_node, to_node):
        """Returns the manhattan distance between the two nodes"""
        return _distances[manager.IndexToNode(from_node)][manager.IndexToNode(
            to_node)]

    return distance_evaluator


def add_distance_dimension(routing, manager, data, distance_evaluator_index):
    """Add Global Span constraint"""
    distance = 'Distance'
    routing.AddDimension(
        distance_evaluator_index,
        0,  # null slack
        data['vehicle_max_distance'],  # maximum distance per vehicle
        True,  # start cumul to zero
        distance)
    distance_dimension = routing.GetDimensionOrDie(distance)
    # Try to minimize the max distance among vehicles.
    # /!\ It doesn't mean the standard deviation is minimized
    distance_dimension.SetGlobalSpanCostCoefficient(100)

    # Define Transportation Requests. #######################################
    for request in data['pickups_deliveries']:
        pickup_index = manager.NodeToIndex(request[0])
        delivery_index = manager.NodeToIndex(request[1])
        routing.AddPickupAndDelivery(pickup_index, delivery_index)
        routing.solver().Add(
            routing.VehicleVar(pickup_index) == routing.VehicleVar(
                delivery_index))
        routing.solver().Add(
            distance_dimension.CumulVar(pickup_index) <=
            distance_dimension.CumulVar(delivery_index))
    ##########################################################################

def create_demand_evaluator(data):
    """Creates callback to get demands at each location."""
    _demands = data['demands']

    def demand_evaluator(manager, from_node):
        """Returns the demand of the current node"""
        return _demands[manager.IndexToNode(from_node)]

    return demand_evaluator


def add_capacity_constraints(routing, manager, data, demand_evaluator_index):
    """Adds capacity constraint"""
    vehicle_capacity = data['vehicle_capacity']
    capacity = 'Capacity'
    routing.AddDimension(
        demand_evaluator_index,
        vehicle_capacity,
        vehicle_capacity,
        True,  # start cumul to zero
        capacity)

    # Add Slack for reseting to zero unload depot nodes.
    # e.g. vehicle with load 10/15 arrives at node 1 (depot unload)
    # so we have CumulVar = 10(current load) + -15(unload) + 5(slack) = 0.
    capacity_dimension = routing.GetDimensionOrDie(capacity)
    # Allow to drop reloading nodes with zero cost.
    for node in [1, 2, 3, 4, 5]:
        node_index = manager.NodeToIndex(node)
        routing.AddDisjunction([node_index], 0)

    # Allow to drop regular node with a cost.
    for node in range(6, len(data['demands'])):
        node_index = manager.NodeToIndex(node)
        capacity_dimension.SlackVar(node_index).SetValue(0)
        routing.AddDisjunction([node_index], 100_000)


def create_time_evaluator(data):
    """Creates callback to get total times between locations."""

    def service_time(data, node):
        """Gets the service time for the specified location."""
        return abs(data['demands'][node]) * data['time_per_demand_unit']

    def travel_time(data, from_node, to_node):
        """Gets the travel times between two locations."""
        if from_node == to_node:
            travel_time = 0
        else:
            travel_time = manhattan_distance(
                    data['locations'][from_node], data['locations'][to_node]) / data['vehicle_speed']
        return travel_time

    _total_time = {}
    # precompute total time to have time callback in O(1)
    for from_node in range(data['num_locations']):
        _total_time[from_node] = {}
        for to_node in range(data['num_locations']):
            if from_node == to_node:
                _total_time[from_node][to_node] = 0
            else:
                _total_time[from_node][to_node] = int(
                    service_time(data, from_node) + travel_time(
                        data, from_node, to_node))

    def time_evaluator(manager, from_node, to_node):
        """Returns the total time between the two nodes"""
        return _total_time[manager.IndexToNode(from_node)][manager.IndexToNode(
            to_node)]

    return time_evaluator


def add_time_window_constraints(routing, manager, data, time_evaluator):
    """Add Time windows constraint"""
    time = 'Time'
    max_time = data['vehicle_max_time']
    routing.AddDimension(
        time_evaluator,
        max_time,  # allow waiting time
        max_time,  # maximum time per vehicle
        False,  # don't force start cumul to zero since we are giving TW to start nodes
        time)
    time_dimension = routing.GetDimensionOrDie(time)
    # Add time window constraints for each location except depot
    # and 'copy' the slack var in the solution object (aka Assignment) to print it
    for location_idx, time_window in enumerate(data['time_windows']):
        if location_idx == 0:
            continue
        index = manager.NodeToIndex(location_idx)
        time_dimension.CumulVar(index).SetRange(time_window[0], time_window[1])
        routing.AddToAssignment(time_dimension.SlackVar(index))
    # Add time window constraints for each vehicle start node
    # and 'copy' the slack var in the solution object (aka Assignment) to print it
    for vehicle_id in range(data['num_vehicles']):
        index = routing.Start(vehicle_id)
        time_dimension.CumulVar(index).SetRange(data['time_windows'][0][0],
                                                data['time_windows'][0][1])
        routing.AddToAssignment(time_dimension.SlackVar(index))
        # Warning: Slack var is not defined for vehicle's end node
        #routing.AddToAssignment(time_dimension.SlackVar(self.routing.End(vehicle_id)))


###########
# Printer #
###########
def print_solution(data, manager, routing, assignment):  # pylint:disable=too-many-locals
    """Prints assignment on console"""
    print(f'Objective: {assignment.ObjectiveValue()}')
    total_distance = 0
    total_load = 0
    total_time = 0
    capacity_dimension = routing.GetDimensionOrDie('Capacity')
    time_dimension = routing.GetDimensionOrDie('Time')
    dropped = []
    for order in range(6, routing.nodes()):
        index = manager.NodeToIndex(order)
        if assignment.Value(routing.NextVar(index)) == index:
            dropped.append(order)
    print(f'dropped orders: {dropped}')
    for reload in range(1, 6):
        index = manager.NodeToIndex(reload)
        if assignment.Value(routing.NextVar(index)) == index:
            dropped.append(reload)
    print(f'dropped reload stations: {dropped}')

    for vehicle_id in range(data['num_vehicles']):
        index = routing.Start(vehicle_id)
        plan_output = f'Route for vehicle {vehicle_id}:\n'
        distance = 0
        while not routing.IsEnd(index):
            load_var = capacity_dimension.CumulVar(index)
            time_var = time_dimension.CumulVar(index)
            plan_output += ' {0} Load({1}) Time({2},{3}) ->'.format(
                manager.IndexToNode(index),
                assignment.Value(load_var),
                assignment.Min(time_var), assignment.Max(time_var))
            previous_index = index
            index = assignment.Value(routing.NextVar(index))
            distance += routing.GetArcCostForVehicle(previous_index, index,
                                                     vehicle_id)
        load_var = capacity_dimension.CumulVar(index)
        time_var = time_dimension.CumulVar(index)
        plan_output += ' {0} Load({1}) Time({2},{3})\n'.format(
            manager.IndexToNode(index),
            assignment.Value(load_var),
            assignment.Min(time_var), assignment.Max(time_var))
        plan_output += f'Distance of the route: {distance}m\n'
        plan_output += f'Load of the route: {assignment.Value(load_var)}\n'
        plan_output += f'Time of the route: {assignment.Value(time_var)}min\n'
        print(plan_output)
        total_distance += distance
        total_load += assignment.Value(load_var)
        total_time += assignment.Value(time_var)
    print('Total Distance of all routes: {}m'.format(total_distance))
    print('Total Load of all routes: {}'.format(total_load))
    print('Total Time of all routes: {}min'.format(total_time))


########
# Main #
########
def main():
    """Entry point of the program"""
    # Instantiate the data problem.
    data = create_data_model()

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

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

    # Define weight of each edge
    distance_evaluator_index = routing.RegisterTransitCallback(
        partial(create_distance_evaluator(data), manager))
    routing.SetArcCostEvaluatorOfAllVehicles(distance_evaluator_index)

    # Add Distance constraint to minimize the longuest route
    add_distance_dimension(routing, manager, data, distance_evaluator_index)

    # Add Capacity constraint
    demand_evaluator_index = routing.RegisterUnaryTransitCallback(
        partial(create_demand_evaluator(data), manager))
    add_capacity_constraints(routing, manager, data, demand_evaluator_index)

    # Add Time Window constraint
    time_evaluator_index = routing.RegisterTransitCallback(
        partial(create_time_evaluator(data), manager))
    add_time_window_constraints(routing, manager, data, time_evaluator_index)

    # Setting first solution heuristic (cheapest addition).
    search_parameters = pywrapcp.DefaultRoutingSearchParameters()
    search_parameters.first_solution_strategy = (
        routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)  # pylint: disable=no-member
    search_parameters.local_search_metaheuristic = (
        routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
    search_parameters.time_limit.FromSeconds(3)

    # Solve the problem.
    solution = routing.SolveWithParameters(search_parameters)
    if solution:
        print_solution(data, manager, routing, solution)
    else:
        print("No solution found !")


if __name__ == '__main__':
    main()

Answer 1

我從 Mizux 獲得了建議意見並修復了代碼。

我有一對取貨點和送貨點以及 map 相同的送貨點到相同的坐標。 感謝 Mizux 的建議。

from functools import partial

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


###########################
# Problem Data Definition #
###########################
def create_data_model():
    """Stores the data for the problem"""
    data = {}
    _capacity = 15
    # Locations in block unit
    _locations = [
        (4, 4),  # depot
        (7, 3), (5, 5), #1,2   pickup_loc, delivery_loc
        (6, 6), (5, 5), #3,4   pickup_loc, delivery_loc
        (3, 4), (5, 5), #5,6   pickup_loc, delivery_loc
        (3, 5), (3, 3), #7,8   pickup_loc, delivery_loc
        (2, 7), (3, 3), #9,10   pickup_loc, delivery_loc
        (6, 3), (3, 3), #11,12   pickup_loc, delivery_loc
        (8, 5), (7, 7), #13,14   pickup_loc, delivery_loc
        (2, 6), (7, 7), #15,16   pickup_loc, delivery_loc
        (6, 7), (7, 7), #17,18   pickup_loc, delivery_loc
        (7, 8), (8, 8), #19,20   pickup_loc, delivery_loc
        (5, 7), (8, 8), #20,21   pickup_loc, delivery_loc
    ]
    # Compute locations in meters using the block dimension defined as follow
    # Manhattan average block: 750ft x 264ft -> 228m x 80m
    # here we use: 114m x 80m city block
    data['locations'] = [(l[0] * 114, l[1] * 80) for l in _locations]
    data['num_locations'] = len(data['locations'])
    data['demands'] = \
          [0, # depot           
           4, -4, # 1, 2   load, unload
           4, -4, # 3, 4   load, unload
           4, -4, # 5, 6   load, unload
           4, -4, # 7, 8   load, unload
           4, -4, # 9, 10   load, unload
           4, -4, # 11, 12   load, unload
           4, -4, # 13, 14   load, unload
           4, -4, # 15, 16   load, unload
           4, -4, # 17, 18   load, unload
           4, -4, # 19, 20   load, unload
           4, -4] # 21, 22   load, unload          
    data['time_per_demand_unit'] = 5  # 5 minutes/unit
    data['time_windows'] = \
          [(0, 0), # depot           
           (0, 1500), (0, 750), # 1, 2   specify delivery time
           (0, 1500), (0, 750), # 3, 4   specify delivery time
           (0, 1500), (0, 750), # 5, 6   specify delivery time
           (0, 1500), (0, 750), # 7, 8   specify delivery time
           (0, 1500), (0, 750), # 9, 10   specify delivery time
           (0, 1500), (0, 750), # 11, 12   specify delivery time
           (0, 1500), (750, 1500), # 13, 14   specify delivery time
           (0, 1500), (750, 1500), # 15, 16   specify delivery time
           (0, 1500), (750, 1500), # 17, 18   specify delivery time
           (0, 1500), (750, 1500), # 19, 20   specify delivery time
           (0, 1500), (750, 1500)] # 21, 22   specify delivery time
    #added p&d list.##############################
    data['pickups_deliveries'] = [
        [1, 2], [3, 4],
        [5, 6], [7, 8],
        [9, 10], [11, 12],
        [13, 14], [15, 16],
        [17, 18], [19, 20],
        [21, 22]
    ]
    ##############################################
    data['num_vehicles'] = 3    
    data['vehicle_capacity'] = _capacity
    data['vehicle_max_distance'] = 10_000
    data['vehicle_max_time'] = 1_500
    data[
        'vehicle_speed'] = 5 * 60 / 3.6  # Travel speed: 5km/h to convert in m/min
    data['depot'] = 0
    return data


#######################
# Problem Constraints #
#######################
def manhattan_distance(position_1, position_2):
    """Computes the Manhattan distance between two points"""
    return (abs(position_1[0] - position_2[0]) +
            abs(position_1[1] - position_2[1]))


def create_distance_evaluator(data):
    """Creates callback to return distance between points."""
    _distances = {}
    # precompute distance between location to have distance callback in O(1)
    for from_node in range(data['num_locations']):
        _distances[from_node] = {}
        for to_node in range(data['num_locations']):
            if from_node == to_node:
                _distances[from_node][to_node] = 0
            # commented out for unused duplicate depot######################
            # elif from_node in range(6) and to_node in range(6):
            #     _distances[from_node][to_node] = data['vehicle_max_distance']
            else:
                _distances[from_node][to_node] = (manhattan_distance(
                    data['locations'][from_node], data['locations'][to_node]))

    def distance_evaluator(manager, from_node, to_node):
        """Returns the manhattan distance between the two nodes"""
        return _distances[manager.IndexToNode(from_node)][manager.IndexToNode(
            to_node)]

    return distance_evaluator


def add_distance_dimension(routing, manager, data, distance_evaluator_index):
    """Add Global Span constraint"""
    distance = 'Distance'
    routing.AddDimension(
        distance_evaluator_index,
        0,  # null slack
        data['vehicle_max_distance'],  # maximum distance per vehicle
        True,  # start cumul to zero
        distance)
    distance_dimension = routing.GetDimensionOrDie(distance)
    # Try to minimize the max distance among vehicles.
    # /!\ It doesn't mean the standard deviation is minimized
    distance_dimension.SetGlobalSpanCostCoefficient(100)

    # Define Transportation Requests. #######################################
    for request in data['pickups_deliveries']:
        pickup_index = manager.NodeToIndex(request[0])
        delivery_index = manager.NodeToIndex(request[1])
        routing.AddPickupAndDelivery(pickup_index, delivery_index)
        routing.solver().Add(
            routing.VehicleVar(pickup_index) == routing.VehicleVar(
                delivery_index))
        routing.solver().Add(
            distance_dimension.CumulVar(pickup_index) <=
            distance_dimension.CumulVar(delivery_index))
    ##########################################################################

def create_demand_evaluator(data):
    """Creates callback to get demands at each location."""
    _demands = data['demands']

    def demand_evaluator(manager, from_node):
        """Returns the demand of the current node"""
        return _demands[manager.IndexToNode(from_node)]

    return demand_evaluator


def add_capacity_constraints(routing, manager, data, demand_evaluator_index):
    """Adds capacity constraint"""
    vehicle_capacity = data['vehicle_capacity']
    capacity = 'Capacity'
    routing.AddDimension(
        demand_evaluator_index,
        vehicle_capacity,
        vehicle_capacity,
        True,  # start cumul to zero
        capacity)

    # Add Slack for reseting to zero unload depot nodes.
    # e.g. vehicle with load 10/15 arrives at node 1 (depot unload)
    # so we have CumulVar = 10(current load) + -15(unload) + 5(slack) = 0.
    capacity_dimension = routing.GetDimensionOrDie(capacity)
    # Allow to drop reloading nodes with zero cost.
    # for node in [1, 2, 3, 4, 5]:
    #     node_index = manager.NodeToIndex(node)
    #     routing.AddDisjunction([node_index], 0)

    # Allow to drop regular node with a cost. (Pickup & Delivery node)
    for node in range(1, len(data['demands'])):
        node_index = manager.NodeToIndex(node)
        capacity_dimension.SlackVar(node_index).SetValue(0)
        routing.AddDisjunction([node_index], 100_000)


def create_time_evaluator(data):
    """Creates callback to get total times between locations."""

    def service_time(data, node):
        """Gets the service time for the specified location."""
        return abs(data['demands'][node]) * data['time_per_demand_unit']

    def travel_time(data, from_node, to_node):
        """Gets the travel times between two locations."""
        if from_node == to_node:
            travel_time = 0
        else:
            travel_time = manhattan_distance(
                    data['locations'][from_node], data['locations'][to_node]) / data['vehicle_speed']
        return travel_time

    _total_time = {}
    # precompute total time to have time callback in O(1)
    for from_node in range(data['num_locations']):
        _total_time[from_node] = {}
        for to_node in range(data['num_locations']):
            if from_node == to_node:
                _total_time[from_node][to_node] = 0
            else:
                _total_time[from_node][to_node] = int(
                    service_time(data, from_node) + travel_time(
                        data, from_node, to_node))

    def time_evaluator(manager, from_node, to_node):
        """Returns the total time between the two nodes"""
        return _total_time[manager.IndexToNode(from_node)][manager.IndexToNode(
            to_node)]

    return time_evaluator


def add_time_window_constraints(routing, manager, data, time_evaluator):
    """Add Time windows constraint"""
    time = 'Time'
    max_time = data['vehicle_max_time']
    routing.AddDimension(
        time_evaluator,
        max_time,  # allow waiting time
        max_time,  # maximum time per vehicle
        False,  # don't force start cumul to zero since we are giving TW to start nodes
        time)
    time_dimension = routing.GetDimensionOrDie(time)
    # Add time window constraints for each location except depot
    # and 'copy' the slack var in the solution object (aka Assignment) to print it
    for location_idx, time_window in enumerate(data['time_windows']):
        if location_idx == 0:
            continue
        index = manager.NodeToIndex(location_idx)
        time_dimension.CumulVar(index).SetRange(time_window[0], time_window[1])
        routing.AddToAssignment(time_dimension.SlackVar(index))
    # Add time window constraints for each vehicle start node
    # and 'copy' the slack var in the solution object (aka Assignment) to print it
    for vehicle_id in range(data['num_vehicles']):
        index = routing.Start(vehicle_id)
        time_dimension.CumulVar(index).SetRange(data['time_windows'][0][0],
                                                data['time_windows'][0][1])
        routing.AddToAssignment(time_dimension.SlackVar(index))
        # Warning: Slack var is not defined for vehicle's end node
        #routing.AddToAssignment(time_dimension.SlackVar(self.routing.End(vehicle_id)))


###########
# Printer #
###########
def print_solution(data, manager, routing, assignment):  # pylint:disable=too-many-locals
    """Prints assignment on console"""
    print(f'Objective: {assignment.ObjectiveValue()}')
    total_distance = 0
    total_load = 0
    total_time = 0
    capacity_dimension = routing.GetDimensionOrDie('Capacity')
    time_dimension = routing.GetDimensionOrDie('Time')
    dropped = []
    for order in range(6, routing.nodes()):
        index = manager.NodeToIndex(order)
        if assignment.Value(routing.NextVar(index)) == index:
            dropped.append(order)
    print(f'dropped orders: {dropped}')
    for reload in range(1, 6):
        index = manager.NodeToIndex(reload)
        if assignment.Value(routing.NextVar(index)) == index:
            dropped.append(reload)
    print(f'dropped reload stations: {dropped}')

    for vehicle_id in range(data['num_vehicles']):
        index = routing.Start(vehicle_id)
        plan_output = f'Route for vehicle {vehicle_id}:\n'
        distance = 0
        while not routing.IsEnd(index):
            load_var = capacity_dimension.CumulVar(index)
            time_var = time_dimension.CumulVar(index)
            plan_output += ' {0} Load({1}) Time({2},{3}) ->'.format(
                manager.IndexToNode(index),
                assignment.Value(load_var),
                assignment.Min(time_var), assignment.Max(time_var))
            previous_index = index
            index = assignment.Value(routing.NextVar(index))
            distance += routing.GetArcCostForVehicle(previous_index, index,
                                                     vehicle_id)
        load_var = capacity_dimension.CumulVar(index)
        time_var = time_dimension.CumulVar(index)
        plan_output += ' {0} Load({1}) Time({2},{3})\n'.format(
            manager.IndexToNode(index),
            assignment.Value(load_var),
            assignment.Min(time_var), assignment.Max(time_var))
        plan_output += f'Distance of the route: {distance}m\n'
        plan_output += f'Load of the route: {assignment.Value(load_var)}\n'
        plan_output += f'Time of the route: {assignment.Value(time_var)}min\n'
        print(plan_output)
        total_distance += distance
        total_load += assignment.Value(load_var)
        total_time += assignment.Value(time_var)
    print('Total Distance of all routes: {}m'.format(total_distance))
    print('Total Load of all routes: {}'.format(total_load))
    print('Total Time of all routes: {}min'.format(total_time))


########
# Main #
########
def main():
    """Entry point of the program"""
    # Instantiate the data problem.
    data = create_data_model()

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

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

    # Define weight of each edge
    distance_evaluator_index = routing.RegisterTransitCallback(
        partial(create_distance_evaluator(data), manager))
    routing.SetArcCostEvaluatorOfAllVehicles(distance_evaluator_index)

    # Add Distance constraint to minimize the longuest route
    add_distance_dimension(routing, manager, data, distance_evaluator_index)

    # Add Capacity constraint
    demand_evaluator_index = routing.RegisterUnaryTransitCallback(
        partial(create_demand_evaluator(data), manager))
    add_capacity_constraints(routing, manager, data, demand_evaluator_index)

    # Add Time Window constraint
    time_evaluator_index = routing.RegisterTransitCallback(
        partial(create_time_evaluator(data), manager))
    add_time_window_constraints(routing, manager, data, time_evaluator_index)

    # Setting first solution heuristic (cheapest addition).
    search_parameters = pywrapcp.DefaultRoutingSearchParameters()
    search_parameters.first_solution_strategy = (
        routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)  # pylint: disable=no-member
    search_parameters.local_search_metaheuristic = (
        routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
    search_parameters.time_limit.FromSeconds(3)

    # Solve the problem.
    solution = routing.SolveWithParameters(search_parameters)
    if solution:
        print_solution(data, manager, routing, solution)
    else:
        print("No solution found !")


if __name__ == '__main__':
    main()