311 lines
11 KiB
Python
Executable File
311 lines
11 KiB
Python
Executable File
#!/usr/bin/env python3
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# Copyright 2010-2022 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# [START program]
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"""Vehicles Routing Problem (VRP).
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Each route as an associated objective cost equal to the max node value along the
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road multiply by a constant factor (4200)
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"""
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# [START import]
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from ortools.constraint_solver import routing_enums_pb2
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from ortools.constraint_solver import pywrapcp
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# [END import]
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# [START data_model]
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def create_data_model():
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"""Stores the data for the problem."""
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data = {}
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data['distance_matrix'] = [
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[
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0, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354,
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468, 776, 662
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],
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[
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548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674,
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1016, 868, 1210
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],
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[
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776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164,
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1130, 788, 1552, 754
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],
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[
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696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822,
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1164, 560, 1358
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],
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[
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582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708,
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1050, 674, 1244
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],
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[
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274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628,
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514, 1050, 708
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],
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[
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502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856,
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514, 1278, 480
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],
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[
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194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320,
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662, 742, 856
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],
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[
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308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662,
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320, 1084, 514
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],
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[
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194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388,
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274, 810, 468
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],
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[
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536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764,
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730, 388, 1152, 354
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],
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[
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502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114,
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308, 650, 274, 844
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],
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[
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388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194,
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536, 388, 730
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],
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[
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354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0,
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342, 422, 536
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],
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[
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468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536,
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342, 0, 764, 194
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],
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[
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776, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274,
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388, 422, 764, 0, 798
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],
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[
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662, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730,
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536, 194, 798, 0
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],
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]
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data['value'] = [
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0, # depot
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42, # 1
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42, # 2
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8, # 3
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8, # 4
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8, # 5
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8, # 6
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8, # 7
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8, # 8
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8, # 9
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8, # 10
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8, # 11
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8, # 12
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8, # 13
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8, # 14
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42, # 15
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42, # 16
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]
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assert len(data['distance_matrix']) == len(data['value'])
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data['num_vehicles'] = 4
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data['depot'] = 0
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return data
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# [END data_model]
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# [START solution_printer]
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def print_solution(data, manager, routing, solution):
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"""Prints solution on console."""
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print(f'Objective: {solution.ObjectiveValue()}')
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max_route_distance = 0
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dim_one = routing.GetDimensionOrDie('One')
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dim_two = routing.GetDimensionOrDie('Two')
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for vehicle_id in range(data['num_vehicles']):
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index = routing.Start(vehicle_id)
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plan_output = 'Route for vehicle {}:\n'.format(vehicle_id)
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route_distance = 0
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while not routing.IsEnd(index):
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one_var = dim_one.CumulVar(index)
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one_slack_var = dim_one.SlackVar(index)
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two_var = dim_two.CumulVar(index)
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two_slack_var = dim_two.SlackVar(index)
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plan_output += ' N:{0} one:({1},{2}) two:({3},{4}) -> '.format(
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manager.IndexToNode(index), solution.Value(one_var),
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solution.Value(one_slack_var), solution.Value(two_var),
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solution.Value(two_slack_var))
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previous_index = index
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index = solution.Value(routing.NextVar(index))
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route_distance += routing.GetArcCostForVehicle(
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previous_index, index, vehicle_id)
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one_var = dim_one.CumulVar(index)
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two_var = dim_two.CumulVar(index)
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plan_output += 'N:{0} one:{1} two:{2}\n'.format(
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manager.IndexToNode(index), solution.Value(one_var),
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solution.Value(two_var))
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plan_output += 'Distance of the route: {}m\n'.format(route_distance)
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print(plan_output)
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max_route_distance = max(route_distance, max_route_distance)
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print('Maximum of the route distances: {}m'.format(max_route_distance))
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# [END solution_printer]
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def main():
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"""Solve the CVRP problem."""
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# Instantiate the data problem.
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# [START data]
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data = create_data_model()
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# [END data]
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# Create the routing index manager.
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# [START index_manager]
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manager = pywrapcp.RoutingIndexManager(len(data['distance_matrix']),
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data['num_vehicles'], data['depot'])
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# [END index_manager]
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# Create Routing Model.
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# [START routing_model]
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routing = pywrapcp.RoutingModel(manager)
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# [END routing_model]
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# Create and register a transit callback.
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# [START transit_callback]
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def distance_callback(from_index, to_index):
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"""Returns the distance between the two nodes."""
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# Convert from routing variable Index to distance matrix NodeIndex.
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from_node = manager.IndexToNode(from_index)
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to_node = manager.IndexToNode(to_index)
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return data['distance_matrix'][from_node][to_node]
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transit_callback_index = routing.RegisterTransitCallback(distance_callback)
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# [END transit_callback]
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# Define cost of each arc.
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# [START arc_cost]
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routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)
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# [END arc_cost]
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# Add Distance constraint.
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# [START distance_constraint]
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dimension_name = 'Distance'
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routing.AddDimension(
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transit_callback_index,
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0, # no slack
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3_000, # vehicle maximum travel distance
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True, # start cumul to zero
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dimension_name)
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distance_dimension = routing.GetDimensionOrDie(dimension_name)
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distance_dimension.SetGlobalSpanCostCoefficient(10)
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# [END distance_constraint]
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# Max Node value Constraint.
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# Dimension One will be used to compute the max node value up to the node in
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# the route and store the result in the SlackVar of the node.
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routing.AddConstantDimensionWithSlack(
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0, # transit 0
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42 * 16, # capacity: be able to store PEAK*ROUTE_LENGTH in worst case
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42, # slack_max: to be able to store peak in slack
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True, # Fix StartCumulToZero not really matter here
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'One')
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dim_one = routing.GetDimensionOrDie('One')
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# Dimension Two will be used to store the max node value in the route end node
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# CumulVar so we can use it as an objective cost.
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routing.AddConstantDimensionWithSlack(
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0, # transit 0
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42 * 16, # capacity: be able to have PEAK value in CumulVar(End)
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42, # slack_max: to be able to store peak in slack
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True, # Fix StartCumulToZero YES here
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'Two')
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dim_two = routing.GetDimensionOrDie('Two')
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# force depot Slack to be value since we don't have any predecessor...
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for v in range(manager.GetNumberOfVehicles()):
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start = routing.Start(v)
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dim_one.SlackVar(start).SetValue(data['value'][0])
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routing.AddToAssignment(dim_one.SlackVar(start))
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dim_two.SlackVar(start).SetValue(data['value'][0])
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routing.AddToAssignment(dim_two.SlackVar(start))
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# Step by step relation
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# Slack(N) = max( Slack(N-1) , value(N) )
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solver = routing.solver()
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for node in range(1, 17):
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index = manager.NodeToIndex(node)
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routing.AddToAssignment(dim_one.SlackVar(index))
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routing.AddToAssignment(dim_two.SlackVar(index))
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test = []
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for v in range(manager.GetNumberOfVehicles()):
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previous_index = routing.Start(v)
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cond = routing.NextVar(previous_index) == index
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value = solver.Max(dim_one.SlackVar(previous_index),
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data['value'][node])
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test.append((cond * value).Var())
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for previous in range(1, 17):
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previous_index = manager.NodeToIndex(previous)
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cond = routing.NextVar(previous_index) == index
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value = solver.Max(dim_one.SlackVar(previous_index),
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data['value'][node])
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test.append((cond * value).Var())
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solver.Add(solver.Sum(test) == dim_one.SlackVar(index))
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# relation between dimensions, copy last node Slack from dim ONE to dim TWO
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for node in range(1, 17):
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index = manager.NodeToIndex(node)
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values = []
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for v in range(manager.GetNumberOfVehicles()):
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next_index = routing.End(v)
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cond = routing.NextVar(index) == next_index
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value = dim_one.SlackVar(index)
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values.append((cond * value).Var())
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solver.Add(solver.Sum(values) == dim_two.SlackVar(index))
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# Should force all others dim_two slack var to zero...
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for v in range(manager.GetNumberOfVehicles()):
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end = routing.End(v)
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dim_two.SetCumulVarSoftUpperBound(end, 0, 4200)
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# Setting first solution heuristic.
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# [START parameters]
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search_parameters = pywrapcp.DefaultRoutingSearchParameters()
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search_parameters.first_solution_strategy = (
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routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)
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search_parameters.local_search_metaheuristic = (
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routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
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# search_parameters.log_search = True
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search_parameters.time_limit.FromSeconds(5)
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# [END parameters]
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# Solve the problem.
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# [START solve]
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solution = routing.SolveWithParameters(search_parameters)
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# [END solve]
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# Print solution on console.
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# [START print_solution]
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if solution:
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print_solution(data, manager, routing, solution)
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else:
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print('No solution found !')
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# [END print_solution]
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if __name__ == '__main__':
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main()
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# [END program]
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