I am trying to solve a capacitated pickup and delivery problem using ortools. Each vehicle has a capacity of 1 and, provided that the number of deliveries/jobs > number of vehicles, has to be utilised at least once. Of course, there has to be a solution but I am unable to find it. I have tried the approach described here as follows:
# Set Minimum Number of nodes
count_dimension_name = 'count'
# assume some variable num_nodes holds the total number of nodes
routing.AddConstantDimension(
1, # increment by one every time
len(data['demands']), # number of nodes incl depot
True, # set count to zero
count_dimension_name)
count_dimension = routing.GetDimensionOrDie(count_dimension_name)
for veh in range(0, data['num_vehicles']):
index_end = routing.End(veh)
count_dimension.SetCumulVarSoftLowerBound(index_end,
2,
100000)
However, for the reproducible example (full code below) there is always one vehicle which is not utilised at all (more vehicles for other examples). How can I force each vehicle to be used and still be able to find at least a feasible solution? Perhaps by changing the search methods?
Reproducible Code:
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, 641, 331, 360, 3, 331, 2, 920, 2, 342, 3, 331, 342, 920, 1],
[641, 0, 505, 663, 643, 504, 639, 1556, 638, 397, 644, 505, 397, 1556, 641],
[331, 505, 0, 623, 334, 1, 329, 1188, 329, 110, 333, 0, 111, 1187, 330],
[360, 663, 623, 0, 358, 623, 360, 1007, 359, 575, 359, 623, 574, 1006, 361],
[3, 643, 334, 358, 0, 335, 6, 917, 5, 345, 1, 334, 345, 917, 4],
[331, 504, 1, 623, 335, 0, 329, 1188, 330, 110, 334, 0, 110, 1188, 330],
[2, 639, 329, 360, 6, 329, 0, 923, 1, 340, 5, 329, 340, 922, 2],
[920, 1556, 1188, 1007, 917, 1188, 923, 0, 923, 1242, 917, 1188, 1242, 0, 921],
[2, 638, 329, 359, 5, 330, 1, 923, 0, 340, 5, 330, 340, 922, 3],
[342, 397, 110, 575, 345, 110, 340, 1242, 340, 0, 345, 110, 0, 1242, 341],
[3, 644, 333, 359, 1, 334, 5, 917, 5, 345, 0, 334, 345, 917, 4],
[331, 505, 0, 623, 334, 0, 329, 1188, 330, 110, 334, 0, 110, 1188, 330],
[342, 397, 111, 574, 345, 110, 340, 1242, 340, 0, 345, 110, 0, 1242, 341],
[920, 1556, 1187, 1006, 917, 1188, 922, 0, 922, 1242, 917, 1188, 1242, 0, 920],
[1, 641, 330, 361, 4, 330, 2, 921, 3, 341, 4, 330, 341, 920, 0]]
data['pickups_deliveries'] = [[ 1, 8],
[ 2, 9],
[ 3, 10],
[ 4, 11],
[ 5, 12],
[ 6, 13],
[ 7, 14]]
data['num_vehicles'] = 4
data['depot'] = 0
data['vehicle_capacities'] = [1, 1, 1, 1]
data['demands'] = [0, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1]
return data
def print_solution(data, manager, routing, assignment):
"""Prints assignment on console."""
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 = assignment.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():
"""Entry point of the program."""
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)
# Define cost of each arc.
def distance_callback(from_index, to_index):
"""Returns the manhattan 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)
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
1000000, # vehicle maximum travel distance
True, # start cumul to zero
dimension_name)
distance_dimension = routing.GetDimensionOrDie(dimension_name)
distance_dimension.SetGlobalSpanCostCoefficient(100)
# Set Minimum Number of nodes
count_dimension_name = 'count'
# assume some variable num_nodes holds the total number of nodes
routing.AddConstantDimension(
1, # increment by one every time
len(data['demands']), # number of nodes incl depot
True, # set count to zero
count_dimension_name)
count_dimension = routing.GetDimensionOrDie(count_dimension_name)
for veh in range(0, data['num_vehicles']):
index_end = routing.End(veh)
count_dimension.SetCumulVarSoftLowerBound(index_end,
2,
100000)
# 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))
# Define Search Approach
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (routing_enums_pb2.FirstSolutionStrategy.AUTOMATIC)
search_parameters.local_search_metaheuristic = (routing_enums_pb2.LocalSearchMetaheuristic.AUTOMATIC)
search_parameters.time_limit.FromSeconds(10)
# Solve the problem.
assignment = routing.SolveWithParameters(search_parameters)
# Print solution on console.
if assignment:
print_solution(data, manager, routing, assignment)
if __name__ == '__main__':
main()
