234 lines
8.0 KiB
Python
Executable File
234 lines
8.0 KiB
Python
Executable File
#!/usr/bin/env python3
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# Copyright 2010-2025 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) with Resource Constraints."""
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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["time_matrix"] = [
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[0, 6, 9, 8, 7, 3, 6, 2, 3, 2, 6, 6, 4, 4, 5, 9, 7],
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[6, 0, 8, 3, 2, 6, 8, 4, 8, 8, 13, 7, 5, 8, 12, 10, 14],
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[9, 8, 0, 11, 10, 6, 3, 9, 5, 8, 4, 15, 14, 13, 9, 18, 9],
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[8, 3, 11, 0, 1, 7, 10, 6, 10, 10, 14, 6, 7, 9, 14, 6, 16],
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[7, 2, 10, 1, 0, 6, 9, 4, 8, 9, 13, 4, 6, 8, 12, 8, 14],
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[3, 6, 6, 7, 6, 0, 2, 3, 2, 2, 7, 9, 7, 7, 6, 12, 8],
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[6, 8, 3, 10, 9, 2, 0, 6, 2, 5, 4, 12, 10, 10, 6, 15, 5],
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[2, 4, 9, 6, 4, 3, 6, 0, 4, 4, 8, 5, 4, 3, 7, 8, 10],
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[3, 8, 5, 10, 8, 2, 2, 4, 0, 3, 4, 9, 8, 7, 3, 13, 6],
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[2, 8, 8, 10, 9, 2, 5, 4, 3, 0, 4, 6, 5, 4, 3, 9, 5],
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[6, 13, 4, 14, 13, 7, 4, 8, 4, 4, 0, 10, 9, 8, 4, 13, 4],
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[6, 7, 15, 6, 4, 9, 12, 5, 9, 6, 10, 0, 1, 3, 7, 3, 10],
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[4, 5, 14, 7, 6, 7, 10, 4, 8, 5, 9, 1, 0, 2, 6, 4, 8],
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[4, 8, 13, 9, 8, 7, 10, 3, 7, 4, 8, 3, 2, 0, 4, 5, 6],
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[5, 12, 9, 14, 12, 6, 6, 7, 3, 3, 4, 7, 6, 4, 0, 9, 2],
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[9, 10, 18, 6, 8, 12, 15, 8, 13, 9, 13, 3, 4, 5, 9, 0, 9],
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[7, 14, 9, 16, 14, 8, 5, 10, 6, 5, 4, 10, 8, 6, 2, 9, 0],
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]
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data["time_windows"] = [
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(0, 5), # depot
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(7, 12), # 1
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(10, 15), # 2
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(5, 14), # 3
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(5, 13), # 4
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(0, 5), # 5
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(5, 10), # 6
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(0, 10), # 7
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(5, 10), # 8
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(0, 5), # 9
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(10, 16), # 10
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(10, 15), # 11
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(0, 5), # 12
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(5, 10), # 13
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(7, 12), # 14
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(10, 15), # 15
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(5, 15), # 16
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]
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data["num_vehicles"] = 4
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# [START resources_data]
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data["vehicle_load_time"] = 5
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data["vehicle_unload_time"] = 5
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data["depot_capacity"] = 2
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# [END resources_data]
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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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time_dimension = routing.GetDimensionOrDie("Time")
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total_time = 0
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for vehicle_id in range(data["num_vehicles"]):
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if not routing.IsVehicleUsed(solution, vehicle_id):
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continue
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index = routing.Start(vehicle_id)
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plan_output = f"Route for vehicle {vehicle_id}:\n"
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while not routing.IsEnd(index):
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time_var = time_dimension.CumulVar(index)
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plan_output += (
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f"{manager.IndexToNode(index)}"
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f" Time({solution.Min(time_var)}, {solution.Max(time_var)})"
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" -> "
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)
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index = solution.Value(routing.NextVar(index))
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time_var = time_dimension.CumulVar(index)
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plan_output += (
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f"{manager.IndexToNode(index)}"
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f" Time({solution.Min(time_var)},{solution.Max(time_var)})\n"
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)
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plan_output += f"Time of the route: {solution.Min(time_var)}min\n"
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print(plan_output)
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total_time += solution.Min(time_var)
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print(f"Total time of all routes: {total_time}min")
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# [END solution_printer]
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def main():
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"""Solve the VRP with time windows."""
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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(
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len(data["time_matrix"]), data["num_vehicles"], data["depot"]
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)
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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 time_callback(from_index, to_index):
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"""Returns the travel time between the two nodes."""
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# Convert from routing variable Index to time 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["time_matrix"][from_node][to_node]
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transit_callback_index = routing.RegisterTransitCallback(time_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 Time Windows constraint.
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# [START time_windows_constraint]
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time = "Time"
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routing.AddDimension(
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transit_callback_index,
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60, # allow waiting time
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60, # maximum time per vehicle
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False, # Don't force start cumul to zero.
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time,
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)
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time_dimension = routing.GetDimensionOrDie(time)
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# Add time window constraints for each location except depot.
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for location_idx, time_window in enumerate(data["time_windows"]):
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if location_idx == 0:
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continue
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index = manager.NodeToIndex(location_idx)
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time_dimension.CumulVar(index).SetRange(time_window[0], time_window[1])
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# Add time window constraints for each vehicle start node.
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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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time_dimension.CumulVar(index).SetRange(
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data["time_windows"][0][0], data["time_windows"][0][1]
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)
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# [END time_windows_constraint]
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# Add resource constraints at the depot.
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# [START depot_load_time]
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solver = routing.solver()
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intervals = []
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for i in range(data["num_vehicles"]):
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# Add time windows at start of routes
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intervals.append(
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solver.FixedDurationIntervalVar(
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time_dimension.CumulVar(routing.Start(i)),
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data["vehicle_load_time"],
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"depot_interval",
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)
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)
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# Add time windows at end of routes.
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intervals.append(
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solver.FixedDurationIntervalVar(
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time_dimension.CumulVar(routing.End(i)),
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data["vehicle_unload_time"],
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"depot_interval",
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)
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)
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# [END depot_load_time]
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# [START depot_capacity]
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depot_usage = [1 for _ in range(len(intervals))]
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solver.Add(
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solver.Cumulative(intervals, depot_usage, data["depot_capacity"], "depot")
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)
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# [END depot_capacity]
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# Instantiate route start and end times to produce feasible times.
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# [START depot_start_end_times]
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for i in range(data["num_vehicles"]):
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routing.AddVariableMinimizedByFinalizer(
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time_dimension.CumulVar(routing.Start(i))
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)
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routing.AddVariableMinimizedByFinalizer(time_dimension.CumulVar(routing.End(i)))
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# [END depot_start_end_times]
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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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)
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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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# [END print_solution]
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else:
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print("No solution found !")
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if __name__ == "__main__":
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main()
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# [END program]
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