Le sezioni seguenti spiegano come eseguire alcune attività comuni correlate alla risoluzione problemi di percorso del veicolo.
Limiti per le ricerche
La risoluzione dei problemi relativi ai percorsi dei veicoli in molte località può richiedere molto tempo. Per problemi di questo tipo, è una buona idea impostare un limite di ricerca, che termini dopo un determinato periodo di tempo o un numero di soluzioni restituite.
Limiti di tempo
I seguenti esempi mostrano come impostare un limite di tempo di 30 secondi per una ricerca.
Python
search_parameters = pywrapcp.DefaultRoutingSearchParameters() search_parameters.time_limit.seconds = 30
C++
RoutingSearchParameters searchParameters = DefaultRoutingSearchParameters(); searchParameters.mutable_time_limit()->set_seconds(30);
Java
Aggiungi questa "importazione" all'inizio del programma:import com.google.protobuf.Duration;
RoutingSearchParameters searchParameters =
main.defaultRoutingSearchParameters()
.toBuilder()
.setTimeLimit(Duration.newBuilder().setSeconds(30).build())
.build();C#
Aggiungi la seguente riga all'inizio del programma:using Google.Protobuf.WellKnownTypes; // Duration
RoutingSearchParameters searchParameters = operations_research_constraint_solver.DefaultRoutingSearchParameters(); searchParameters.TimeLimit = new Duration { Seconds = 10 };
Consulta Modificare la strategia di ricerca per un esempio che imposta un limite di tempo.
Limiti delle soluzioni
Gli esempi riportati di seguito mostrano come impostare un limite di 100 soluzioni per una ricerca.
Python
search_parameters = pywrapcp.DefaultRoutingSearchParameters() search_parameters.solution_limit = 100
C++
RoutingSearchParameters searchParameters = DefaultRoutingSearchParameters(); searchParameters.set_solution_limit(100);
Java
RoutingSearchParameters searchParameters =
main.defaultRoutingSearchParameters()
.toBuilder()
.setSolutionLimit(100)
.build();C#
RoutingSearchParameters searchParameters = operations_research_constraint_solver.DefaultRoutingSearchParameters(); searchParameters.SolutionLimit(100);
Impostazione delle route iniziali per una ricerca
Per alcuni problemi, potresti voler specificare un insieme di route iniziali per un VRP, invece di lasciare che sia il risolutore a trovare una soluzione iniziale, ad esempio se hai già trovato una buona soluzione a un problema e vuoi utilizzarla come punto di partenza per risolvere un problema modificato.
Per creare le route iniziali:
- Definisci un array contenente le route iniziali.
- Crea la soluzione iniziale utilizzando il metodo
ReadAssignmentFromRoutes.
Il seguente codice definisce le route iniziali nei dati.
Python
data["initial_routes"] = [ # fmt: off [8, 16, 14, 13, 12, 11], [3, 4, 9, 10], [15, 1], [7, 5, 2, 6], # fmt: on ]
C++
const std::vector<std::vector<int64_t>> initial_routes{ {8, 16, 14, 13, 12, 11}, {3, 4, 9, 10}, {15, 1}, {7, 5, 2, 6}, };
Java
public final long[][] initialRoutes = {
{8, 16, 14, 13, 12, 11},
{3, 4, 9, 10},
{15, 1},
{7, 5, 2, 6},
};C#
public long[][] InitialRoutes = {
new long[] { 8, 16, 14, 13, 12, 11 },
new long[] { 3, 4, 9, 10 },
new long[] { 15, 1 },
new long[] { 7, 5, 2, 6 },
};Il codice seguente crea la soluzione iniziale dalle route esegue una ricerca partendo dalla soluzione iniziale.
Il programma visualizza sia la soluzione iniziale sia la soluzione trovata dalla ricerca.
Python
initial_solution = routing.ReadAssignmentFromRoutes(data["initial_routes"], True) print("Initial solution:") print_solution(data, manager, routing, initial_solution)
C++
const Assignment* initial_solution = routing.ReadAssignmentFromRoutes(data.initial_routes, true); // Print initial solution on console. LOG(INFO) << "Initial solution: "; PrintSolution(data, manager, routing, *initial_solution);
Java
Assignment initialSolution = routing.readAssignmentFromRoutes(data.initialRoutes, true); logger.info("Initial solution:"); printSolution(data, routing, manager, initialSolution);
C#
Assignment initialSolution = routing.ReadAssignmentFromRoutes(data.InitialRoutes, true); // Print initial solution on console. Console.WriteLine("Initial solution:"); PrintSolution(data, routing, manager, initialSolution);
Quando aggiungi questo codice alla precedente programma VRP ed eseguire il programma, visualizza il seguente output:
Initial solution: Route for vehicle 0: 0 -> 8 -> 16 -> 14 -> 13 -> 12 -> 11 -> 0 Distance of the route: 2168m Route for vehicle 1: 0 -> 3 -> 4 -> 9 -> 10 -> 0 Distance of the route: 2464m Route for vehicle 2: 0 -> 15 -> 1 -> 0 Distance of the route: 2192m Route for vehicle 3: 0 -> 7 -> 5 -> 2 -> 6 -> 0 Distance of the route: 1780m Maximum of the route distances: 2464m Solution after search: Route for vehicle 0: 0 -> 9 -> 10 -> 16 -> 14 -> 0 Distance of the route: 1552m Route for vehicle 1: 0 -> 12 -> 11 -> 15 -> 13 -> 0 Distance of the route: 1552 Route for vehicle 2: 0 -> 3 -> 4 -> 1 -> 7 -> 0 Distance of the route: 1552 Route for vehicle 3: 0 -> 5 -> 2 -> 6 -> 8 -> 0 Distance of the route: 1552 Maximum of the route distances: 1552
Ecco i programmi completi che impostano i percorsi iniziali.
Python
"""Vehicles Routing Problem (VRP).""" 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"] = [ # 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["initial_routes"] = [ # fmt: off [8, 16, 14, 13, 12, 11], [3, 4, 9, 10], [15, 1], [7, 5, 2, 6], # fmt: on ] data["num_vehicles"] = 4 data["depot"] = 0 return data def print_solution(data, manager, routing, solution): """Prints solution on console.""" print(f"Objective: {solution.ObjectiveValue()}") max_route_distance = 0 for vehicle_id in range(data["num_vehicles"]): index = routing.Start(vehicle_id) plan_output = f"Route for vehicle {vehicle_id}:\n" route_distance = 0 while not routing.IsEnd(index): plan_output += f" {manager.IndexToNode(index)} -> " previous_index = index index = solution.Value(routing.NextVar(index)) route_distance += routing.GetArcCostForVehicle( previous_index, index, vehicle_id ) plan_output += f"{manager.IndexToNode(index)}\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") def main(): """Solve the CVRP problem.""" # Instantiate the data problem. 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) # Create and register a 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) # Define cost of each arc. routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index) # Add Distance constraint. dimension_name = "Distance" routing.AddDimension( transit_callback_index, 0, # no slack 3000, # vehicle maximum travel distance True, # start cumul to zero dimension_name, ) distance_dimension = routing.GetDimensionOrDie(dimension_name) distance_dimension.SetGlobalSpanCostCoefficient(100) # Close model with the custom search 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.time_limit.FromSeconds(5) # When an initial solution is given for search, the model will be closed with # the default search parameters unless it is explicitly closed with the custom # search parameters. routing.CloseModelWithParameters(search_parameters) # Get initial solution from routes after closing the model. initial_solution = routing.ReadAssignmentFromRoutes(data["initial_routes"], True) print("Initial solution:") print_solution(data, manager, routing, initial_solution) # Solve the problem. solution = routing.SolveFromAssignmentWithParameters( initial_solution, search_parameters ) # Print solution on console. if solution: print("Solution after search:") print_solution(data, manager, routing, solution) if __name__ == "__main__": main()
C++
#include <algorithm> #include <cstdint> #include <cstdlib> #include <sstream> #include <vector> #include "google/protobuf/duration.pb.h" #include "ortools/base/logging.h" #include "ortools/constraint_solver/constraint_solver.h" #include "ortools/constraint_solver/routing.h" #include "ortools/constraint_solver/routing_enums.pb.h" #include "ortools/constraint_solver/routing_index_manager.h" #include "ortools/constraint_solver/routing_parameters.h" namespace operations_research { struct DataModel { const std::vector<std::vector<int64_t>> distance_matrix{ {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}, }; const std::vector<std::vector<int64_t>> initial_routes{ {8, 16, 14, 13, 12, 11}, {3, 4, 9, 10}, {15, 1}, {7, 5, 2, 6}, }; const int num_vehicles = 4; const RoutingIndexManager::NodeIndex depot{0}; }; //! @brief Print the solution. //! @param[in] data Data of the problem. //! @param[in] manager Index manager used. //! @param[in] routing Routing solver used. //! @param[in] solution Solution found by the solver. void PrintSolution(const DataModel& data, const RoutingIndexManager& manager, const RoutingModel& routing, const Assignment& solution) { LOG(INFO) << "Objective: " << solution.ObjectiveValue(); int64_t max_route_distance{0}; for (int vehicle_id = 0; vehicle_id < data.num_vehicles; ++vehicle_id) { int64_t index = routing.Start(vehicle_id); LOG(INFO) << "Route for Vehicle " << vehicle_id << ":"; int64_t route_distance{0}; std::stringstream route; while (!routing.IsEnd(index)) { route << manager.IndexToNode(index).value() << " -> "; const int64_t previous_index = index; index = solution.Value(routing.NextVar(index)); route_distance += routing.GetArcCostForVehicle(previous_index, index, int64_t{vehicle_id}); } LOG(INFO) << route.str() << manager.IndexToNode(index).value(); LOG(INFO) << "Distance of the route: " << route_distance << "m"; max_route_distance = std::max(route_distance, max_route_distance); } LOG(INFO) << "Maximum of the route distances: " << max_route_distance << "m"; LOG(INFO) << ""; LOG(INFO) << "Problem solved in " << routing.solver()->wall_time() << "ms"; } void VrpInitialRoutes() { // Instantiate the data problem. DataModel data; // Create Routing Index Manager RoutingIndexManager manager(data.distance_matrix.size(), data.num_vehicles, data.depot); // Create Routing Model. RoutingModel routing(manager); // Create and register a transit callback. const int transit_callback_index = routing.RegisterTransitCallback( [&data, &manager](const int64_t from_index, const int64_t to_index) -> int64_t { // Convert from routing variable Index to distance matrix NodeIndex. const int from_node = manager.IndexToNode(from_index).value(); const int to_node = manager.IndexToNode(to_index).value(); return data.distance_matrix[from_node][to_node]; }); // Define cost of each arc. routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index); // Add Distance constraint. routing.AddDimension(transit_callback_index, 0, 3000, true, // start cumul to zero "Distance"); routing.GetMutableDimension("Distance")->SetGlobalSpanCostCoefficient(100); // Close model with the custom search parameters RoutingSearchParameters searchParameters = DefaultRoutingSearchParameters(); searchParameters.set_first_solution_strategy( FirstSolutionStrategy::PATH_CHEAPEST_ARC); searchParameters.set_local_search_metaheuristic( LocalSearchMetaheuristic::GUIDED_LOCAL_SEARCH); searchParameters.mutable_time_limit()->set_seconds(5); // When an initial solution is given for search, the model will be closed with // the default search parameters unless it is explicitly closed with the // custom search parameters. routing.CloseModelWithParameters(searchParameters); // Get initial solution from routes after closing the model. const Assignment* initial_solution = routing.ReadAssignmentFromRoutes(data.initial_routes, true); // Print initial solution on console. LOG(INFO) << "Initial solution: "; PrintSolution(data, manager, routing, *initial_solution); // Solve from initial solution. const Assignment* solution = routing.SolveFromAssignmentWithParameters( initial_solution, searchParameters); // Print solution on console. LOG(INFO) << ""; LOG(INFO) << "Solution from search: "; PrintSolution(data, manager, routing, *solution); } } // namespace operations_research int main(int /*argc*/, char* /*argv*/[]) { operations_research::VrpInitialRoutes(); return EXIT_SUCCESS; }
Java
package com.google.ortools.constraintsolver.samples; import com.google.ortools.Loader; import com.google.ortools.constraintsolver.Assignment; import com.google.ortools.constraintsolver.RoutingDimension; import com.google.ortools.constraintsolver.RoutingIndexManager; import com.google.ortools.constraintsolver.RoutingModel; import com.google.ortools.constraintsolver.RoutingSearchParameters; import com.google.ortools.constraintsolver.main; import java.util.logging.Logger; /** Minimal VRP. */ public class VrpInitialRoutes { private static final Logger logger = Logger.getLogger(VrpInitialRoutes.class.getName()); static class DataModel { public final long[][] distanceMatrix = { {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}, }; public final long[][] initialRoutes = { {8, 16, 14, 13, 12, 11}, {3, 4, 9, 10}, {15, 1}, {7, 5, 2, 6}, }; public final int vehicleNumber = 4; public final int depot = 0; } /// @brief Print the solution. static void printSolution( DataModel data, RoutingModel routing, RoutingIndexManager manager, Assignment solution) { // Solution cost. logger.info("Objective : " + solution.objectiveValue()); // Inspect solution. long maxRouteDistance = 0; for (int i = 0; i < data.vehicleNumber; ++i) { long index = routing.start(i); logger.info("Route for Vehicle " + i + ":"); long routeDistance = 0; String route = ""; while (!routing.isEnd(index)) { route += manager.indexToNode(index) + " -> "; long previousIndex = index; index = solution.value(routing.nextVar(index)); routeDistance += routing.getArcCostForVehicle(previousIndex, index, i); } logger.info(route + manager.indexToNode(index)); logger.info("Distance of the route: " + routeDistance + "m"); maxRouteDistance = Math.max(routeDistance, maxRouteDistance); } logger.info("Maximum of the route distances: " + maxRouteDistance + "m"); } public static void main(String[] args) throws Exception { Loader.loadNativeLibraries(); // Instantiate the data problem. final DataModel data = new DataModel(); // Create Routing Index Manager RoutingIndexManager manager = new RoutingIndexManager(data.distanceMatrix.length, data.vehicleNumber, data.depot); // Create Routing Model. RoutingModel routing = new RoutingModel(manager); // Create and register a transit callback. final int transitCallbackIndex = routing.registerTransitCallback((long fromIndex, long toIndex) -> { // Convert from routing variable Index to user NodeIndex. int fromNode = manager.indexToNode(fromIndex); int toNode = manager.indexToNode(toIndex); return data.distanceMatrix[fromNode][toNode]; }); // Define cost of each arc. routing.setArcCostEvaluatorOfAllVehicles(transitCallbackIndex); // Add Distance constraint. routing.addDimension(transitCallbackIndex, 0, 3000, true, // start cumul to zero "Distance"); RoutingDimension distanceDimension = routing.getMutableDimension("Distance"); distanceDimension.setGlobalSpanCostCoefficient(100); Assignment initialSolution = routing.readAssignmentFromRoutes(data.initialRoutes, true); logger.info("Initial solution:"); printSolution(data, routing, manager, initialSolution); // Setting first solution heuristic. RoutingSearchParameters searchParameters = main.defaultRoutingSearchParameters(); // Solve the problem. Assignment solution = routing.solveFromAssignmentWithParameters( initialSolution, searchParameters); // Print solution on console. logger.info("Solution after search:"); printSolution(data, routing, manager, solution); } }
C#
// Copyright 2010-2024 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. using System; using System.Collections.Generic; using Google.OrTools.ConstraintSolver; /// <summary> /// VRP with initial routes. /// </summary> public class InitialRoutes { class DataModel { public long[,] DistanceMatrix = { { 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 }, }; public long[][] InitialRoutes = { new long[] { 8, 16, 14, 13, 12, 11 }, new long[] { 3, 4, 9, 10 }, new long[] { 15, 1 }, new long[] { 7, 5, 2, 6 }, }; public int VehicleNumber = 4; public int Depot = 0; }; /// <summary> /// Print the solution. /// </summary> static void PrintSolution(in DataModel data, in RoutingModel routing, in RoutingIndexManager manager, in Assignment solution) { Console.WriteLine($"Objective {solution.ObjectiveValue()}:"); // Inspect solution. long maxRouteDistance = 0; for (int i = 0; i < data.VehicleNumber; ++i) { Console.WriteLine("Route for Vehicle {0}:", i); long routeDistance = 0; var index = routing.Start(i); while (routing.IsEnd(index) == false) { Console.Write("{0} -> ", manager.IndexToNode((int)index)); var previousIndex = index; index = solution.Value(routing.NextVar(index)); routeDistance += routing.GetArcCostForVehicle(previousIndex, index, 0); } Console.WriteLine("{0}", manager.IndexToNode((int)index)); Console.WriteLine("Distance of the route: {0}", routeDistance); maxRouteDistance = Math.Max(routeDistance, maxRouteDistance); } Console.WriteLine("Maximum distance of the routes: {0}", maxRouteDistance); } public static void Main(String[] args) { // Instantiate the data problem. DataModel data = new DataModel(); // Create Routing Index Manager RoutingIndexManager manager = new RoutingIndexManager(data.DistanceMatrix.GetLength(0), data.VehicleNumber, data.Depot); // Create Routing Model. RoutingModel routing = new RoutingModel(manager); // Create and register a transit callback. int transitCallbackIndex = routing.RegisterTransitCallback((long fromIndex, long toIndex) => { // Convert from routing variable Index to // distance matrix NodeIndex. var fromNode = manager.IndexToNode(fromIndex); var toNode = manager.IndexToNode(toIndex); return data.DistanceMatrix[fromNode, toNode]; }); // Define cost of each arc. routing.SetArcCostEvaluatorOfAllVehicles(transitCallbackIndex); // Add Distance constraint. routing.AddDimension(transitCallbackIndex, 0, 3000, true, // start cumul to zero "Distance"); RoutingDimension distanceDimension = routing.GetMutableDimension("Distance"); distanceDimension.SetGlobalSpanCostCoefficient(100); // Get initial solution from routes. Assignment initialSolution = routing.ReadAssignmentFromRoutes(data.InitialRoutes, true); // Print initial solution on console. Console.WriteLine("Initial solution:"); PrintSolution(data, routing, manager, initialSolution); // Setting first solution heuristic. RoutingSearchParameters searchParameters = operations_research_constraint_solver.DefaultRoutingSearchParameters(); // Solve the problem. Assignment solution = routing.SolveFromAssignmentWithParameters( initialSolution, searchParameters); // Print solution on console. Console.WriteLine("Solution after search:"); PrintSolution(data, routing, manager, solution); } }
Impostazione delle posizioni di partenza e di arrivo dei percorsi
Finora, abbiamo ipotizzato che tutti i veicoli inizino e finiscano in un'unica posizione, al deposito. Puoi anche impostare località di partenza e di arrivo potenzialmente diverse per ogni veicolo in risolvere il problema. Per farlo, passa due vettori, contenenti gli indici di inizio e fine più località, come input RoutingModel nella funzione principale. Ecco come creare i vettori di inizio e fine in sezione dati del programma:
Python
data["starts"] = [1, 2, 15, 16] data["ends"] = [0, 0, 0, 0]
C++
const std::vector<RoutingIndexManager::NodeIndex> starts{ RoutingIndexManager::NodeIndex{1}, RoutingIndexManager::NodeIndex{2}, RoutingIndexManager::NodeIndex{15}, RoutingIndexManager::NodeIndex{16}, }; const std::vector<RoutingIndexManager::NodeIndex> ends{ RoutingIndexManager::NodeIndex{0}, RoutingIndexManager::NodeIndex{0}, RoutingIndexManager::NodeIndex{0}, RoutingIndexManager::NodeIndex{0}, };
Java
public final int[] starts = {1, 2, 15, 16};
public final int[] ends = {0, 0, 0, 0};C#
public int[] Starts = { 1, 2, 15, 16 };
public int[] Ends = { 0, 0, 0, 0 };Ecco i programmi completi che impostano le località di partenza e di arrivo in questo modo.
Python
"""Simple Vehicles Routing Problem.""" 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"] = [ # 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["num_vehicles"] = 4 data["starts"] = [1, 2, 15, 16] data["ends"] = [0, 0, 0, 0] return data def print_solution(data, manager, routing, solution): """Prints solution on console.""" print(f"Objective: {solution.ObjectiveValue()}") max_route_distance = 0 for vehicle_id in range(data["num_vehicles"]): index = routing.Start(vehicle_id) plan_output = f"Route for vehicle {vehicle_id}:\n" route_distance = 0 while not routing.IsEnd(index): plan_output += f" {manager.IndexToNode(index)} -> " previous_index = index index = solution.Value(routing.NextVar(index)) route_distance += routing.GetArcCostForVehicle( previous_index, index, vehicle_id ) plan_output += f"{manager.IndexToNode(index)}\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") def main(): """Entry point of the program.""" # Instantiate the data problem. data = create_data_model() # Create the routing index manager. manager = pywrapcp.RoutingIndexManager( len(data["distance_matrix"]), data["num_vehicles"], data["starts"], data["ends"] ) # Create Routing Model. routing = pywrapcp.RoutingModel(manager) # Create and register a 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) # Define cost of each arc. routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index) # Add Distance constraint. dimension_name = "Distance" routing.AddDimension( transit_callback_index, 0, # no slack 2000, # vehicle maximum travel distance True, # start cumul to zero dimension_name, ) distance_dimension = routing.GetDimensionOrDie(dimension_name) distance_dimension.SetGlobalSpanCostCoefficient(100) # Setting first solution heuristic. search_parameters = pywrapcp.DefaultRoutingSearchParameters() search_parameters.first_solution_strategy = ( routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC ) # Solve the problem. solution = routing.SolveWithParameters(search_parameters) # Print solution on console. if solution: print_solution(data, manager, routing, solution) if __name__ == "__main__": main()
C++
#include <algorithm> #include <cstdint> #include <sstream> #include <vector> #include "ortools/constraint_solver/routing.h" #include "ortools/constraint_solver/routing_enums.pb.h" #include "ortools/constraint_solver/routing_index_manager.h" #include "ortools/constraint_solver/routing_parameters.h" namespace operations_research { struct DataModel { const std::vector<std::vector<int64_t>> distance_matrix{ {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}, }; const int num_vehicles = 4; const std::vector<RoutingIndexManager::NodeIndex> starts{ RoutingIndexManager::NodeIndex{1}, RoutingIndexManager::NodeIndex{2}, RoutingIndexManager::NodeIndex{15}, RoutingIndexManager::NodeIndex{16}, }; const std::vector<RoutingIndexManager::NodeIndex> ends{ RoutingIndexManager::NodeIndex{0}, RoutingIndexManager::NodeIndex{0}, RoutingIndexManager::NodeIndex{0}, RoutingIndexManager::NodeIndex{0}, }; }; //! @brief Print the solution. //! @param[in] data Data of the problem. //! @param[in] manager Index manager used. //! @param[in] routing Routing solver used. //! @param[in] solution Solution found by the solver. void PrintSolution(const DataModel& data, const RoutingIndexManager& manager, const RoutingModel& routing, const Assignment& solution) { int64_t max_route_distance{0}; for (int vehicle_id = 0; vehicle_id < data.num_vehicles; ++vehicle_id) { int64_t index = routing.Start(vehicle_id); LOG(INFO) << "Route for Vehicle " << vehicle_id << ":"; int64_t route_distance{0}; std::stringstream route; while (!routing.IsEnd(index)) { route << manager.IndexToNode(index).value() << " -> "; const int64_t previous_index = index; index = solution.Value(routing.NextVar(index)); route_distance += routing.GetArcCostForVehicle(previous_index, index, int64_t{vehicle_id}); } LOG(INFO) << route.str() << manager.IndexToNode(index).value(); LOG(INFO) << "Distance of the route: " << route_distance << "m"; max_route_distance = std::max(route_distance, max_route_distance); } LOG(INFO) << "Maximum of the route distances: " << max_route_distance << "m"; LOG(INFO) << ""; LOG(INFO) << "Problem solved in " << routing.solver()->wall_time() << "ms"; } void VrpStartsEnds() { // Instantiate the data problem. DataModel data; // Create Routing Index Manager RoutingIndexManager manager(data.distance_matrix.size(), data.num_vehicles, data.starts, data.ends); // Create Routing Model. RoutingModel routing(manager); // Create and register a transit callback. const int transit_callback_index = routing.RegisterTransitCallback( [&data, &manager](const int64_t from_index, const int64_t to_index) -> int64_t { // Convert from routing variable Index to distance matrix NodeIndex. const int from_node = manager.IndexToNode(from_index).value(); const int to_node = manager.IndexToNode(to_index).value(); return data.distance_matrix[from_node][to_node]; }); // Define cost of each arc. routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index); // Add Distance constraint. routing.AddDimension(transit_callback_index, 0, 2000, /*fix_start_cumul_to_zero=*/true, "Distance"); routing.GetMutableDimension("Distance")->SetGlobalSpanCostCoefficient(100); // Setting first solution heuristic. RoutingSearchParameters searchParameters = DefaultRoutingSearchParameters(); searchParameters.set_first_solution_strategy( FirstSolutionStrategy::PATH_CHEAPEST_ARC); // Solve the problem. const Assignment* solution = routing.SolveWithParameters(searchParameters); // Print solution on console. PrintSolution(data, manager, routing, *solution); } } // namespace operations_research int main(int /*argc*/, char* /*argv*/[]) { operations_research::VrpStartsEnds(); return EXIT_SUCCESS; }
Java
package com.google.ortools.constraintsolver.samples; import com.google.ortools.Loader; import com.google.ortools.constraintsolver.Assignment; import com.google.ortools.constraintsolver.FirstSolutionStrategy; import com.google.ortools.constraintsolver.RoutingDimension; import com.google.ortools.constraintsolver.RoutingIndexManager; import com.google.ortools.constraintsolver.RoutingModel; import com.google.ortools.constraintsolver.RoutingSearchParameters; import com.google.ortools.constraintsolver.main; import java.util.logging.Logger; /** Minimal VRP.*/ public class VrpStartsEnds { private static final Logger logger = Logger.getLogger(VrpStartsEnds.class.getName()); static class DataModel { public final long[][] distanceMatrix = { {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}, }; public final int vehicleNumber = 4; public final int[] starts = {1, 2, 15, 16}; public final int[] ends = {0, 0, 0, 0}; } /// @brief Print the solution. static void printSolution( DataModel data, RoutingModel routing, RoutingIndexManager manager, Assignment solution) { // Solution cost. logger.info("Objective : " + solution.objectiveValue()); // Inspect solution. long maxRouteDistance = 0; for (int i = 0; i < data.vehicleNumber; ++i) { long index = routing.start(i); logger.info("Route for Vehicle " + i + ":"); long routeDistance = 0; String route = ""; while (!routing.isEnd(index)) { route += manager.indexToNode(index) + " -> "; long previousIndex = index; index = solution.value(routing.nextVar(index)); routeDistance += routing.getArcCostForVehicle(previousIndex, index, i); } logger.info(route + manager.indexToNode(index)); logger.info("Distance of the route: " + routeDistance + "m"); maxRouteDistance = Math.max(routeDistance, maxRouteDistance); } logger.info("Maximum of the route distances: " + maxRouteDistance + "m"); } public static void main(String[] args) throws Exception { Loader.loadNativeLibraries(); // Instantiate the data problem. final DataModel data = new DataModel(); // Create Routing Index Manager RoutingIndexManager manager = new RoutingIndexManager( data.distanceMatrix.length, data.vehicleNumber, data.starts, data.ends); // Create Routing Model. RoutingModel routing = new RoutingModel(manager); // Create and register a transit callback. final int transitCallbackIndex = routing.registerTransitCallback((long fromIndex, long toIndex) -> { // Convert from routing variable Index to user NodeIndex. int fromNode = manager.indexToNode(fromIndex); int toNode = manager.indexToNode(toIndex); return data.distanceMatrix[fromNode][toNode]; }); // Define cost of each arc. routing.setArcCostEvaluatorOfAllVehicles(transitCallbackIndex); // Add Distance constraint. routing.addDimension(transitCallbackIndex, 0, 2000, true, // start cumul to zero "Distance"); RoutingDimension distanceDimension = routing.getMutableDimension("Distance"); distanceDimension.setGlobalSpanCostCoefficient(100); // Setting first solution heuristic. RoutingSearchParameters searchParameters = main.defaultRoutingSearchParameters() .toBuilder() .setFirstSolutionStrategy(FirstSolutionStrategy.Value.PATH_CHEAPEST_ARC) .build(); // Solve the problem. Assignment solution = routing.solveWithParameters(searchParameters); // Print solution on console. printSolution(data, routing, manager, solution); } }
C#
using System; using System.Collections.Generic; using Google.OrTools.ConstraintSolver; /// <summary> /// Minimal TSP using distance matrix. /// </summary> public class VrpStartsEnds { class DataModel { public long[,] DistanceMatrix = { { 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 } }; public int VehicleNumber = 4; public int[] Starts = { 1, 2, 15, 16 }; public int[] Ends = { 0, 0, 0, 0 }; }; /// <summary> /// Print the solution. /// </summary> static void PrintSolution(in DataModel data, in RoutingModel routing, in RoutingIndexManager manager, in Assignment solution) { Console.WriteLine($"Objective {solution.ObjectiveValue()}:"); // Inspect solution. long maxRouteDistance = 0; for (int i = 0; i < data.VehicleNumber; ++i) { Console.WriteLine("Route for Vehicle {0}:", i); long routeDistance = 0; var index = routing.Start(i); while (routing.IsEnd(index) == false) { Console.Write("{0} -> ", manager.IndexToNode((int)index)); var previousIndex = index; index = solution.Value(routing.NextVar(index)); routeDistance += routing.GetArcCostForVehicle(previousIndex, index, 0); } Console.WriteLine("{0}", manager.IndexToNode((int)index)); Console.WriteLine("Distance of the route: {0}m", routeDistance); maxRouteDistance = Math.Max(routeDistance, maxRouteDistance); } Console.WriteLine("Maximum distance of the routes: {0}m", maxRouteDistance); } public static void Main(String[] args) { // Instantiate the data problem. DataModel data = new DataModel(); // Create Routing Index Manager RoutingIndexManager manager = new RoutingIndexManager(data.DistanceMatrix.GetLength(0), data.VehicleNumber, data.Starts, data.Ends); // Create Routing Model. RoutingModel routing = new RoutingModel(manager); // Create and register a transit callback. int transitCallbackIndex = routing.RegisterTransitCallback((long fromIndex, long toIndex) => { // Convert from routing variable Index to // distance matrix NodeIndex. var fromNode = manager.IndexToNode(fromIndex); var toNode = manager.IndexToNode(toIndex); return data.DistanceMatrix[fromNode, toNode]; }); // Define cost of each arc. routing.SetArcCostEvaluatorOfAllVehicles(transitCallbackIndex); // Add Distance constraint. routing.AddDimension(transitCallbackIndex, 0, 2000, true, // start cumul to zero "Distance"); RoutingDimension distanceDimension = routing.GetMutableDimension("Distance"); distanceDimension.SetGlobalSpanCostCoefficient(100); // Setting first solution heuristic. RoutingSearchParameters searchParameters = operations_research_constraint_solver.DefaultRoutingSearchParameters(); searchParameters.FirstSolutionStrategy = FirstSolutionStrategy.Types.Value.PathCheapestArc; // Solve the problem. Assignment solution = routing.SolveWithParameters(searchParameters); // Print solution on console. PrintSolution(data, routing, manager, solution); } }
Quando esegui il programma, ottieni il seguente output, in cui le route iniziano e terminano nelle posizioni specificate:
Route for vehicle 0: 1 -> 4 -> 3 -> 7 -> 0 Distance of the route: 1004m Route for vehicle 1: 2 -> 6 -> 8 -> 5 -> 0 Distance of the route: 936m Route for vehicle 2: 15 -> 11 -> 12 -> 13 -> 0 Distance of the route: 936m Route for vehicle 3: 16 -> 14 -> 10 -> 9 -> 0 Distance of the route: 1118m Total distance of all routes: 3994m
La distanza totale è più corta rispetto all'esempio precedente perché i veicoli non devono iniziare o terminare nel deposito.
Possibilità di utilizzare posizioni di partenza e di arrivo arbitrarie
In altre versioni del problema di percorso dei veicoli, i veicoli possono avviarsi e terminano in posizioni arbitrarie. Per impostare il problema in questo modo, è sufficiente modificare la matrice delle distanze in modo che la distanza dal deposito a qualsiasi altra posizione sia pari a 0, impostando la prima riga e colonna della matrice in modo che abbia tutti gli zeri. In questo modo il deposito viene trasformato in una posizione fittizia che non ha alcun effetto sui percorsi ottimali.
Ecco un esempio in cui la matrice delle distanze L'esempio VRP è stato modificato per rendere la distanza dal deposito a tutti gli altri nodi è pari a 0.
data['distance_matrix'] = [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674, 1016, 868, 1210 ], [ 0, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164, 1130, 788, 1552, 754 ], [ 0, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822, 1164, 560, 1358 ], [ 0, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708, 1050, 674, 1244 ], [ 0, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628, 514, 1050, 708 ], [ 0, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856, 514, 1278, 480 ], [ 0, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320, 662, 742, 856 ], [ 0, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662, 0, 1084, 514 ], [ 0, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388, 0, 810, 468 ], [ 0, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764, 730, 388, 1152, 354 ], [ 0, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114, 308, 650, 274, 844 ], [ 0, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194, 536, 388, 730 ], [ 0, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0, 342, 422, 536 ], [ 0, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536, 342, 0, 764, 194 ], [ 0, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274, 388, 422, 764, 0, 798 ], [ 0, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730, 536, 194, 798, 0 ], ]
Quando esegui il programma VRP con la matrice delle distanze modificata (e la stampante della soluzione per omettere il deposito) , il programma visualizza i seguenti percorsi:
Route for vehicle 0: 5 -> 8 -> 6 -> 2 Distance of the route: 662m Route for vehicle 1: 7 -> 1 -> 4 -> 3 Distance of the route: 662m Route for vehicle 2: 16 -> 14 -> 13 -> 15 Distance of the route: 958m Route for vehicle 3: 10 -> 9 -> 12 -> 11 Distance of the route: 878m Maximum of the route distances: 958m