Problem understanding Pickups & delivery array using OR-TOOLS

Question

So, I've been trying to understand what is the problem with the following experiment, but wasn't able to find the issue.. So, below is the code I am using (note that there is a duplicate node, as that node is both a pick and a delivery node):

"""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, 220, 460, 460, 700, 280, 610],
        [220,   0, 570, 570, 670, 500, 500],
        [460, 570,   0,   0, 350, 550, 450],
        [460, 570,   0,   0, 350, 550, 450],
        [700, 670, 350, 350,   0, 850, 250],
        [280, 500, 550, 550, 850,   0, 830],
        [610, 500, 450, 450, 250, 830,   0]
    ]
    data['pickups_deliveries'] = [
        [1, 2], #1,2 
        [3, 6], #3,4
        [4, 5], #5,6
    ]
    data['demands'] = [
        0,  # departs empty
        1,  # load in 1
        -1, # unload in 2
        1,  # load in 3 (duplicate of 2)
        1,  # load in 4
        -1, # unload in 5 
        -1] # unload in 5
    data['vehicle_capacities'] = [1]
    data['num_vehicles'] = 1
    data['depot'] = 0
    return data


def print_solution(data, manager, routing, solution):
    """Prints solution on console."""
    print(f'Objective: {solution.ObjectiveValue()}')
    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['demands'][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)


    # 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 Capacity constraint.
    def demand_callback(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'][from_node]

    demand_callback_index = routing.RegisterUnaryTransitCallback(demand_callback)
    
    routing.AddDimensionWithVehicleCapacity(
        demand_callback_index,
        0,  # null capacity slack
        data['vehicle_capacities'],  # vehicle maximum capacities
        True,  # start cumul to zero
        'Capacity')
    
    # Add Distance constraint.
    dimension_name = 'Distance'
    routing.AddDimension(
        transit_callback_index,
        0,  # no slack
        3000,  # vehicle maximum travel distance
        True,  # start cumul to zero
        dimension_name)
    distance_dimension = routing.GetDimensionOrDie(dimension_name)
    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))


    # 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(1)

    # Solve the problem.
    solution = routing.SolveWithParameters(search_parameters)
    # Print solution on console.
    if solution:
        print_solution(data, manager, routing, solution)


if __name__ == '__main__':
    main()

When run, the algorithm returns:

Objective: 264620
Route for vehicle 0:
 0 Load(0) ->  1 Load(1) ->  2 Load(0) ->  3 Load(1) ->  6 Load(0) ->  4 Load(1) ->  5 Load(0) ->  0 Load(0)
Distance of the route: 2620m
Load of the route: 0

Total distance of all routes: 2620m
Total load of all routes: 0

which is fine. Now, If I only change the order of the pickups_deliveries from nodes 4->5 to 5->4 (just reversing they roles), say from this

data['pickups_deliveries'] = [
        [1, 2], #1,2 
        [3, 6], #3,4
        [4, 5], #5,6
    ]

to this

data['pickups_deliveries'] = [
        [1, 2], #1,2 
        [3, 6], #3,4
        [5, 4], #5,6
    ]

and change the demands accordingly from this:

data['demands'] = [
        0,  # departs empty
        1,  # load in 1
        -1, # unload in 2
        1,  # load in 3 (duplicate of 2)
        1,  # load in 4
        -1, # unload in 5 
        -1] # unload in 6

to this:

data['demands'] = [
        0,  # departs empty
        1,  # load in 1
        -1, # unload in 2
        1,  # load in 3 (duplicate of 2)
        -1, # unload in 4
        1,  # load in 5 
        -1] # unload in 6

the algorithm is unable to find a solution. When the only thing that has been changed is the order of the last segment. What am I doing wrong here? Any help would be very much appreciated! Thanks in advance!

PD: A posible solution would be:

1. Depart at (0),
2. load in 1 ---> unload in 2,
3. load in 3(same node as 2) ---> unload in 6
4. load in 5---> unload in 4

Answer 1

If you look at the original solution we can see

Distance of the route: 2620m

And we have

 routing.AddDimension(
        transit_callback_index,
        0,  # no slack
        3000,  # vehicle maximum travel distance

So I'm pretty sure increasing the limit could help here, so let's increase it to 3500

and you'll get:

./plop.py
Objective: 346430
Route for vehicle 0:
 0 Load(0) ->  5 Load(1) ->  4 Load(0) ->  1 Load(1) ->  2 Load(0) ->  3 Load(1) ->  6 Load(0) ->  0 Load(0)
Distance of the route: 3430m
Load of the route: 0

Total distance of all routes: 3430m
Total load of all routes: 0

notice the:

Distance of the route: 3430m

ps: next time, please keep import statement
pps: your snippet didn't work since you've added some float in the distance matrix, please use only int matrix or in your callback round it using return int(data[...][][])