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vrp_time_windows.py
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#!/usr/bin/env python3
# Copyright 2010-2022 Google LLC
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# [START program]
"""Vehicles Routing Problem (VRP) with Time Windows."""
# [START import]
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
# [END import]
# [START data_model]
def create_data_model():
"""Stores the data for the problem."""
data = {}
data['time_matrix'] = [
[0, 6, 9, 8, 7, 3, 6, 2, 3, 2, 6, 6, 4, 4, 5, 9, 7],
[6, 0, 8, 3, 2, 6, 8, 4, 8, 8, 13, 7, 5, 8, 12, 10, 14],
[9, 8, 0, 11, 10, 6, 3, 9, 5, 8, 4, 15, 14, 13, 9, 18, 9],
[8, 3, 11, 0, 1, 7, 10, 6, 10, 10, 14, 6, 7, 9, 14, 6, 16],
[7, 2, 10, 1, 0, 6, 9, 4, 8, 9, 13, 4, 6, 8, 12, 8, 14],
[3, 6, 6, 7, 6, 0, 2, 3, 2, 2, 7, 9, 7, 7, 6, 12, 8],
[6, 8, 3, 10, 9, 2, 0, 6, 2, 5, 4, 12, 10, 10, 6, 15, 5],
[2, 4, 9, 6, 4, 3, 6, 0, 4, 4, 8, 5, 4, 3, 7, 8, 10],
[3, 8, 5, 10, 8, 2, 2, 4, 0, 3, 4, 9, 8, 7, 3, 13, 6],
[2, 8, 8, 10, 9, 2, 5, 4, 3, 0, 4, 6, 5, 4, 3, 9, 5],
[6, 13, 4, 14, 13, 7, 4, 8, 4, 4, 0, 10, 9, 8, 4, 13, 4],
[6, 7, 15, 6, 4, 9, 12, 5, 9, 6, 10, 0, 1, 3, 7, 3, 10],
[4, 5, 14, 7, 6, 7, 10, 4, 8, 5, 9, 1, 0, 2, 6, 4, 8],
[4, 8, 13, 9, 8, 7, 10, 3, 7, 4, 8, 3, 2, 0, 4, 5, 6],
[5, 12, 9, 14, 12, 6, 6, 7, 3, 3, 4, 7, 6, 4, 0, 9, 2],
[9, 10, 18, 6, 8, 12, 15, 8, 13, 9, 13, 3, 4, 5, 9, 0, 9],
[7, 14, 9, 16, 14, 8, 5, 10, 6, 5, 4, 10, 8, 6, 2, 9, 0],
]
data['time_windows'] = [
(0, 5), # depot
(7, 12), # 1
(10, 15), # 2
(16, 18), # 3
(10, 13), # 4
(0, 5), # 5
(5, 10), # 6
(0, 4), # 7
(5, 10), # 8
(0, 3), # 9
(10, 16), # 10
(10, 15), # 11
(0, 5), # 12
(5, 10), # 13
(7, 8), # 14
(10, 15), # 15
(11, 15), # 16
]
data['num_vehicles'] = 4
data['depot'] = 0
return data
# [END data_model]
# [START solution_printer]
def print_solution(data, manager, routing, solution):
"""Prints solution on console."""
print(f'Objective: {solution.ObjectiveValue()}')
time_dimension = routing.GetDimensionOrDie('Time')
total_time = 0
for vehicle_id in range(data['num_vehicles']):
index = routing.Start(vehicle_id)
plan_output = 'Route for vehicle {}:\n'.format(vehicle_id)
while not routing.IsEnd(index):
time_var = time_dimension.CumulVar(index)
plan_output += '{0} Time({1},{2}) -> '.format(
manager.IndexToNode(index), solution.Min(time_var),
solution.Max(time_var))
index = solution.Value(routing.NextVar(index))
time_var = time_dimension.CumulVar(index)
plan_output += '{0} Time({1},{2})\n'.format(manager.IndexToNode(index),
solution.Min(time_var),
solution.Max(time_var))
plan_output += 'Time of the route: {}min\n'.format(
solution.Min(time_var))
print(plan_output)
total_time += solution.Min(time_var)
print('Total time of all routes: {}min'.format(total_time))
# [END solution_printer]
def main():
"""Solve the VRP with time windows."""
# Instantiate the data problem.
# [START data]
data = create_data_model()
# [END data]
# Create the routing index manager.
# [START index_manager]
manager = pywrapcp.RoutingIndexManager(len(data['time_matrix']),
data['num_vehicles'], data['depot'])
# [END index_manager]
# Create Routing Model.
# [START routing_model]
routing = pywrapcp.RoutingModel(manager)
# [END routing_model]
# Create and register a transit callback.
# [START transit_callback]
def time_callback(from_index, to_index):
"""Returns the travel time between the two nodes."""
# Convert from routing variable Index to time matrix NodeIndex.
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
return data['time_matrix'][from_node][to_node]
transit_callback_index = routing.RegisterTransitCallback(time_callback)
# [END transit_callback]
# Define cost of each arc.
# [START arc_cost]
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)
# [END arc_cost]
# Add Time Windows constraint.
# [START time_windows_constraint]
time = 'Time'
routing.AddDimension(
transit_callback_index,
30, # allow waiting time
30, # maximum time per vehicle
False, # Don't force start cumul to zero.
time)
time_dimension = routing.GetDimensionOrDie(time)
# Add time window constraints for each location except depot.
for location_idx, time_window in enumerate(data['time_windows']):
if location_idx == data['depot']:
continue
index = manager.NodeToIndex(location_idx)
time_dimension.CumulVar(index).SetRange(time_window[0], time_window[1])
# Add time window constraints for each vehicle start node.
depot_idx = data['depot']
for vehicle_id in range(data['num_vehicles']):
index = routing.Start(vehicle_id)
time_dimension.CumulVar(index).SetRange(
data['time_windows'][depot_idx][0],
data['time_windows'][depot_idx][1])
# [END time_windows_constraint]
# Instantiate route start and end times to produce feasible times.
# [START depot_start_end_times]
for i in range(data['num_vehicles']):
routing.AddVariableMinimizedByFinalizer(
time_dimension.CumulVar(routing.Start(i)))
routing.AddVariableMinimizedByFinalizer(
time_dimension.CumulVar(routing.End(i)))
# [END depot_start_end_times]
# Setting first solution heuristic.
# [START parameters]
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (
routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)
# [END parameters]
# Solve the problem.
# [START solve]
solution = routing.SolveWithParameters(search_parameters)
# [END solve]
# Print solution on console.
# [START print_solution]
if solution:
print_solution(data, manager, routing, solution)
# [END print_solution]
if __name__ == '__main__':
main()
# [END program]