275 lines
10 KiB
Python
Executable File
275 lines
10 KiB
Python
Executable File
#!/usr/bin/env python3
|
|
# Copyright 2010-2025 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).
|
|
|
|
Each route as an associated objective cost equal to the max node value along the
|
|
road multiply by a constant factor (4200)
|
|
"""
|
|
|
|
# [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["distance_matrix"] = [
|
|
# fmt: off
|
|
[0, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354, 468, 776, 662],
|
|
[548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674, 1016, 868, 1210],
|
|
[776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164, 1130, 788, 1552, 754],
|
|
[696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822, 1164, 560, 1358],
|
|
[582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708, 1050, 674, 1244],
|
|
[274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628, 514, 1050, 708],
|
|
[502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856, 514, 1278, 480],
|
|
[194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320, 662, 742, 856],
|
|
[308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662, 320, 1084, 514],
|
|
[194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388, 274, 810, 468],
|
|
[536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764, 730, 388, 1152, 354],
|
|
[502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114, 308, 650, 274, 844],
|
|
[388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194, 536, 388, 730],
|
|
[354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0, 342, 422, 536],
|
|
[468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536, 342, 0, 764, 194],
|
|
[776, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274, 388, 422, 764, 0, 798],
|
|
[662, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730, 536, 194, 798, 0],
|
|
# fmt: on
|
|
]
|
|
data["value"] = [
|
|
0, # depot
|
|
42, # 1
|
|
42, # 2
|
|
8, # 3
|
|
8, # 4
|
|
8, # 5
|
|
8, # 6
|
|
8, # 7
|
|
8, # 8
|
|
8, # 9
|
|
8, # 10
|
|
8, # 11
|
|
8, # 12
|
|
8, # 13
|
|
8, # 14
|
|
42, # 15
|
|
42, # 16
|
|
]
|
|
assert len(data["distance_matrix"]) == len(data["value"])
|
|
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()}")
|
|
max_route_distance = 0
|
|
dim_one = routing.GetDimensionOrDie("One")
|
|
dim_two = routing.GetDimensionOrDie("Two")
|
|
|
|
for vehicle_id in range(data["num_vehicles"]):
|
|
if not routing.IsVehicleUsed(solution, vehicle_id):
|
|
continue
|
|
index = routing.Start(vehicle_id)
|
|
plan_output = f"Route for vehicle {vehicle_id}:\n"
|
|
route_distance = 0
|
|
while not routing.IsEnd(index):
|
|
one_var = dim_one.CumulVar(index)
|
|
one_slack_var = dim_one.SlackVar(index)
|
|
two_var = dim_two.CumulVar(index)
|
|
two_slack_var = dim_two.SlackVar(index)
|
|
plan_output += (
|
|
f" N:{manager.IndexToNode(index)}"
|
|
f" one:({solution.Value(one_var)}, {solution.Value(one_slack_var)})"
|
|
f" two:({solution.Value(two_var)}, {solution.Value(two_slack_var)})"
|
|
" -> "
|
|
)
|
|
previous_index = index
|
|
index = solution.Value(routing.NextVar(index))
|
|
route_distance += routing.GetArcCostForVehicle(
|
|
previous_index, index, vehicle_id
|
|
)
|
|
one_var = dim_one.CumulVar(index)
|
|
two_var = dim_two.CumulVar(index)
|
|
plan_output += (
|
|
f"N:{manager.IndexToNode(index)}"
|
|
f" one:{solution.Value(one_var)}"
|
|
f" two:{solution.Value(two_var)}\n"
|
|
)
|
|
plan_output += f"Distance of the route: {route_distance}m\n"
|
|
print(plan_output)
|
|
max_route_distance = max(route_distance, max_route_distance)
|
|
print(f"Maximum of the route distances: {max_route_distance}m")
|
|
|
|
# [END solution_printer]
|
|
|
|
|
|
def main():
|
|
"""Solve the CVRP problem."""
|
|
# 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["distance_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 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)
|
|
# [END transit_callback]
|
|
|
|
# Define cost of each arc.
|
|
# [START arc_cost]
|
|
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)
|
|
# [END arc_cost]
|
|
|
|
# Add Distance constraint.
|
|
# [START distance_constraint]
|
|
dimension_name = "Distance"
|
|
routing.AddDimension(
|
|
transit_callback_index,
|
|
0, # no slack
|
|
3_000, # vehicle maximum travel distance
|
|
True, # start cumul to zero
|
|
dimension_name,
|
|
)
|
|
distance_dimension = routing.GetDimensionOrDie(dimension_name)
|
|
distance_dimension.SetGlobalSpanCostCoefficient(10)
|
|
# [END distance_constraint]
|
|
|
|
# Max Node value Constraint.
|
|
# Dimension One will be used to compute the max node value up to the node in
|
|
# the route and store the result in the SlackVar of the node.
|
|
routing.AddConstantDimensionWithSlack(
|
|
0, # transit 0
|
|
42 * 16, # capacity: be able to store PEAK*ROUTE_LENGTH in worst case
|
|
42, # slack_max: to be able to store peak in slack
|
|
True, # Fix StartCumulToZero not really matter here
|
|
"One",
|
|
)
|
|
dim_one = routing.GetDimensionOrDie("One")
|
|
|
|
# Dimension Two will be used to store the max node value in the route end node
|
|
# CumulVar so we can use it as an objective cost.
|
|
routing.AddConstantDimensionWithSlack(
|
|
0, # transit 0
|
|
42 * 16, # capacity: be able to have PEAK value in CumulVar(End)
|
|
42, # slack_max: to be able to store peak in slack
|
|
True, # Fix StartCumulToZero YES here
|
|
"Two",
|
|
)
|
|
dim_two = routing.GetDimensionOrDie("Two")
|
|
|
|
# force depot Slack to be value since we don't have any predecessor...
|
|
for v in range(manager.GetNumberOfVehicles()):
|
|
start = routing.Start(v)
|
|
dim_one.SlackVar(start).SetValue(data["value"][0])
|
|
routing.AddToAssignment(dim_one.SlackVar(start))
|
|
|
|
dim_two.SlackVar(start).SetValue(data["value"][0])
|
|
routing.AddToAssignment(dim_two.SlackVar(start))
|
|
|
|
# Step by step relation
|
|
# Slack(N) = max( Slack(N-1) , value(N) )
|
|
solver = routing.solver()
|
|
for node in range(1, 17):
|
|
index = manager.NodeToIndex(node)
|
|
routing.AddToAssignment(dim_one.SlackVar(index))
|
|
routing.AddToAssignment(dim_two.SlackVar(index))
|
|
test = []
|
|
for v in range(manager.GetNumberOfVehicles()):
|
|
previous_index = routing.Start(v)
|
|
cond = routing.NextVar(previous_index) == index
|
|
value = solver.Max(dim_one.SlackVar(previous_index), data["value"][node])
|
|
test.append((cond * value).Var())
|
|
for previous in range(1, 17):
|
|
previous_index = manager.NodeToIndex(previous)
|
|
cond = routing.NextVar(previous_index) == index
|
|
value = solver.Max(dim_one.SlackVar(previous_index), data["value"][node])
|
|
test.append((cond * value).Var())
|
|
solver.Add(solver.Sum(test) == dim_one.SlackVar(index))
|
|
|
|
# relation between dimensions, copy last node Slack from dim ONE to dim TWO
|
|
for node in range(1, 17):
|
|
index = manager.NodeToIndex(node)
|
|
values = []
|
|
for v in range(manager.GetNumberOfVehicles()):
|
|
next_index = routing.End(v)
|
|
cond = routing.NextVar(index) == next_index
|
|
value = dim_one.SlackVar(index)
|
|
values.append((cond * value).Var())
|
|
solver.Add(solver.Sum(values) == dim_two.SlackVar(index))
|
|
|
|
# Should force all others dim_two slack var to zero...
|
|
for v in range(manager.GetNumberOfVehicles()):
|
|
end = routing.End(v)
|
|
dim_two.SetCumulVarSoftUpperBound(end, 0, 4200)
|
|
|
|
# Setting first solution heuristic.
|
|
# [START parameters]
|
|
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.log_search = True
|
|
search_parameters.time_limit.FromSeconds(5)
|
|
# [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)
|
|
else:
|
|
print("No solution found !")
|
|
# [END print_solution]
|
|
|
|
|
|
if __name__ == "__main__":
|
|
main()
|
|
# [END program]
|