In questa sezione spieghiamo come gestire i problemi di calcolo itinerario che non sono soluzione di archiviazione a causa di vincoli. Ad esempio, se ricevi un VRP con vincoli di capacità in cui la domanda totale in tutte le sedi supera la capacità totale del servizio non c'è soluzione. In questi casi, i veicoli devono impedire le visite in alcune località. Il problema è come decidere quali visite abbandonare.
Per risolvere il problema, introdurremo nuovi costi, chiamati sanzioni in tutte le località. Ogni volta che viene rifiutata una visita a un luogo, viene applicata viene sommata alla distanza totale percorsa. Il risolutore trova quindi un percorso riduce al minimo la distanza totale più la somma delle penalità per tutti luoghi.
Considera ad esempio il semplice VRP con vincoli di capacità forniti dal sottostante, in cui i numeri accanto alle tre posizioni (ad eccezione del depot) sono richieste.
Supponiamo che ci sia un solo veicolo con 50 posti. Non può visitare tutti e tre
località A, B e C, perché la domanda totale è pari a 60. Per risolvere il problema,
assegni una grave penalità, ad esempio 100, a ciascuna località. Dopo il giorno
rilevando che il problema non è fattibile, il risolutore inserisce la posizione B e
restituisce il seguente percorso: Depot -> A -> C -> Depot
Si tratta del percorso più breve per visitare due delle tre località (la distanza è 55).
Dimensioni delle penalità
Nell'esempio precedente, abbiamo scelto penalità maggiori della somma di tutte distanze tra le sedi (escluso il deposito). Di conseguenza, dopo aver perso una posizione per rendere il problema fattibile, il risolutore non tralascia località aggiuntive, in quanto la penale per farlo supererebbe ogni ulteriore di riduzione della distanza da percorrere.
Supponendo di voler effettuare il maggior numero possibile di pubblicazioni, si ottiene in modo soddisfacente al problema.
Se non devi effettuare il maggior numero possibile di consegne, potresti voler assegnare penalità minori, nel qual caso il risolutore può inserire più località rispetto perché il problema sia fattibile. Ad esempio, puoi eseguire questa operazione se sono previsti costi aggiuntivi, oltre al costo di base del viaggio, per visitare determinati luoghi.
Esempio
Successivamente, presentiamo un esempio più ampio di un VRP che può essere risolto utilizzando le penalità. L'esempio è simile all'esempio precedente Esempio di CVRP, ma questa volta abbiamo aumentato delle richieste, costringendo alcuni veicoli a diminuire le visite.
Di seguito è riportato un grafico delle località e delle nuove richieste.
Risoluzione dell'esempio con OR-Tools
Le sezioni seguenti spiegano come risolvere l'esempio con OR-Tools.
crea i dati
I dati per questo esempio includono quelli della sessione Esempio di VRP e aggiunge le seguenti richieste e capacità:
Python
data["demands"] = [0, 1, 1, 3, 6, 3, 6, 8, 8, 1, 2, 1, 2, 6, 6, 8, 8] data["vehicle_capacities"] = [15, 15, 15, 15]
C++
const std::vector<int64_t> demands{ 0, 1, 1, 3, 6, 3, 6, 8, 8, 1, 2, 1, 2, 6, 6, 8, 8, }; const std::vector<int64_t> vehicle_capacities{15, 15, 15, 15};
Java
public final long[] demands = {0, 1, 1, 3, 6, 3, 6, 8, 8, 1, 2, 1, 2, 6, 6, 8, 8};
public final long[] vehicleCapacities = {15, 15, 15, 15};C#
public long[] Demands = { 0, 1, 1, 3, 6, 3, 6, 8, 8, 1, 2, 1, 2, 6, 6, 8, 8 };
public long[] VehicleCapacities = { 15, 15, 15, 15 };Aggiungi vincoli e penalità di capacità
Il codice seguente aggiunge il callback della domanda e i vincoli di capacità e aggiunge
le penalità usando
AddDisjunction
.
Python
def demand_callback(from_index): """Returns the demand of the node.""" # Convert from routing variable Index to demands NodeIndex. from_node = manager.IndexToNode(from_index) return data["demands"][from_node] demand_callback_index = routing.RegisterUnaryTransitCallback(demand_callback) routing.AddDimensionWithVehicleCapacity( demand_callback_index, 0, # null capacity slack data["vehicle_capacities"], # vehicle maximum capacities True, # start cumul to zero "Capacity", ) # Allow to drop nodes. penalty = 1000 for node in range(1, len(data["distance_matrix"])): routing.AddDisjunction([manager.NodeToIndex(node)], penalty)
C++
const int demand_callback_index = routing.RegisterUnaryTransitCallback( [&data, &manager](const int64_t from_index) -> int64_t { // Convert from routing variable Index to demand NodeIndex. const int from_node = manager.IndexToNode(from_index).value(); return data.demands[from_node]; }); routing.AddDimensionWithVehicleCapacity( demand_callback_index, // transit callback index int64_t{0}, // null capacity slack data.vehicle_capacities, // vehicle maximum capacities true, // start cumul to zero "Capacity"); // Allow to drop nodes. int64_t penalty{1000}; for (int i = 1; i < data.distance_matrix.size(); ++i) { routing.AddDisjunction( {manager.NodeToIndex(RoutingIndexManager::NodeIndex(i))}, penalty); }
Java
final int demandCallbackIndex = routing.registerUnaryTransitCallback((long fromIndex) -> { // Convert from routing variable Index to user NodeIndex. int fromNode = manager.indexToNode(fromIndex); return data.demands[fromNode]; }); routing.addDimensionWithVehicleCapacity(demandCallbackIndex, 0, // null capacity slack data.vehicleCapacities, // vehicle maximum capacities true, // start cumul to zero "Capacity"); // Allow to drop nodes. long penalty = 1000; for (int i = 1; i < data.distanceMatrix.length; ++i) { routing.addDisjunction(new long[] {manager.nodeToIndex(i)}, penalty); }
C#
int demandCallbackIndex = routing.RegisterUnaryTransitCallback((long fromIndex) => { // Convert from routing variable Index to // demand NodeIndex. var fromNode = manager.IndexToNode(fromIndex); return data.Demands[fromNode]; }); routing.AddDimensionWithVehicleCapacity(demandCallbackIndex, 0, // null capacity slack data.VehicleCapacities, // vehicle maximum capacities true, // start cumul to zero "Capacity"); // Allow to drop nodes. long penalty = 1000; for (int i = 1; i < data.DistanceMatrix.GetLength(0); ++i) { routing.AddDisjunction(new long[] { manager.NodeToIndex(i) }, penalty); }
In questo contesto, una disgiunzione è semplicemente una variabile che il risolutore utilizza per decide se includere una determinata località nella soluzione. In questo esempio, aggiunge la stessa penalità a ogni località, ma in generale puoi aggiungere penalità diverse a seconda della località.
Aggiungi la stampante della soluzione
La stampante della soluzione, mostrata di seguito, è simile a quella nella Esempio di CVRP, ma mostra anche di questi luoghi.
Python
def print_solution(data, manager, routing, assignment): """Prints assignment on console.""" print(f"Objective: {assignment.ObjectiveValue()}") # Display dropped nodes. dropped_nodes = "Dropped nodes:" for node in range(routing.Size()): if routing.IsStart(node) or routing.IsEnd(node): continue if assignment.Value(routing.NextVar(node)) == node: dropped_nodes += f" {manager.IndexToNode(node)}" print(dropped_nodes) # Display routes total_distance = 0 total_load = 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 route_load = 0 while not routing.IsEnd(index): node_index = manager.IndexToNode(index) route_load += data["demands"][node_index] plan_output += f" {node_index} Load({route_load}) -> " previous_index = index index = assignment.Value(routing.NextVar(index)) route_distance += routing.GetArcCostForVehicle( previous_index, index, vehicle_id ) plan_output += f" {manager.IndexToNode(index)} Load({route_load})\n" plan_output += f"Distance of the route: {route_distance}m\n" plan_output += f"Load of the route: {route_load}\n" print(plan_output) total_distance += route_distance total_load += route_load print(f"Total Distance of all routes: {total_distance}m") print(f"Total Load of all routes: {total_load}")
C++
//! @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) { // Display dropped nodes. std::ostringstream dropped_nodes; for (int64_t node = 0; node < routing.Size(); ++node) { if (routing.IsStart(node) || routing.IsEnd(node)) continue; if (solution.Value(routing.NextVar(node)) == node) { dropped_nodes << " " << manager.IndexToNode(node).value(); } } LOG(INFO) << "Dropped nodes:" << dropped_nodes.str(); // Display routes int64_t total_distance{0}; int64_t total_load{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}; int64_t route_load{0}; std::ostringstream route; while (!routing.IsEnd(index)) { const int node_index = manager.IndexToNode(index).value(); route_load += data.demands[node_index]; route << node_index << " Load(" << route_load << ") -> "; 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"; LOG(INFO) << "Load of the route: " << route_load; total_distance += route_distance; total_load += route_load; } LOG(INFO) << "Total distance of all routes: " << total_distance << "m"; LOG(INFO) << "Total load of all routes: " << total_load; LOG(INFO) << ""; LOG(INFO) << "Advanced usage:"; LOG(INFO) << "Problem solved in " << routing.solver()->wall_time() << "ms"; }
Java
/// @brief Print the solution. static void printSolution( DataModel data, RoutingModel routing, RoutingIndexManager manager, Assignment solution) { // Solution cost. logger.info("Objective: " + solution.objectiveValue()); // Inspect solution. // Display dropped nodes. String droppedNodes = "Dropped nodes:"; for (int node = 0; node < routing.size(); ++node) { if (routing.isStart(node) || routing.isEnd(node)) { continue; } if (solution.value(routing.nextVar(node)) == node) { droppedNodes += " " + manager.indexToNode(node); } } logger.info(droppedNodes); // Display routes long totalDistance = 0; long totalLoad = 0; for (int i = 0; i < data.vehicleNumber; ++i) { long index = routing.start(i); logger.info("Route for Vehicle " + i + ":"); long routeDistance = 0; long routeLoad = 0; String route = ""; while (!routing.isEnd(index)) { long nodeIndex = manager.indexToNode(index); routeLoad += data.demands[(int) nodeIndex]; route += nodeIndex + " Load(" + routeLoad + ") -> "; long previousIndex = index; index = solution.value(routing.nextVar(index)); routeDistance += routing.getArcCostForVehicle(previousIndex, index, i); } route += manager.indexToNode(routing.end(i)); logger.info(route); logger.info("Distance of the route: " + routeDistance + "m"); totalDistance += routeDistance; totalLoad += routeLoad; } logger.info("Total Distance of all routes: " + totalDistance + "m"); logger.info("Total Load of all routes: " + totalLoad); }
C#
/// <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. // Display dropped nodes. string droppedNodes = "Dropped nodes:"; for (int index = 0; index < routing.Size(); ++index) { if (routing.IsStart(index) || routing.IsEnd(index)) { continue; } if (solution.Value(routing.NextVar(index)) == index) { droppedNodes += " " + manager.IndexToNode(index); } } Console.WriteLine("{0}", droppedNodes); // Inspect solution. long totalDistance = 0; long totalLoad = 0; for (int i = 0; i < data.VehicleNumber; ++i) { Console.WriteLine("Route for Vehicle {0}:", i); long routeDistance = 0; long routeLoad = 0; var index = routing.Start(i); while (routing.IsEnd(index) == false) { long nodeIndex = manager.IndexToNode(index); routeLoad += data.Demands[nodeIndex]; Console.Write("{0} Load({1}) -> ", nodeIndex, routeLoad); 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); totalDistance += routeDistance; totalLoad += routeLoad; } Console.WriteLine("Total Distance of all routes: {0}m", totalDistance); Console.WriteLine("Total Load of all routes: {0}m", totalLoad); }
Esecuzione del programma
Quando esegui il programma, viene restituito il seguente output. Tieni presente che il risolutore inserisce le località 6 e 15.
Objective: 7936 Dropped nodes: 6 15 Route for vehicle 0: 0 Load(0) -> 9 Load(1) -> 14 Load(7) -> 16 Load(15) -> 0 Load(15) Distance of the route: 1324m Load of the route: 15 Route for vehicle 1: 0 Load(0) -> 12 Load(2) -> 11 Load(3) -> 4 Load(9) -> 3 Load(12) -> 1 Load(13) -> 0 Load(13) Distance of the route: 1872m Load of the route: 13 Route for vehicle 2: 0 Load(0) -> 7 Load(8) -> 13 Load(14) -> 0 Load(14) Distance of the route: 868m Load of the route: 14 Route for vehicle 3: 0 Load(0) -> 8 Load(8) -> 10 Load(10) -> 2 Load(11) -> 5 Load(14) -> 0 Load(14) Distance of the route: 1872m Load of the route: 14 Total Distance of all routes: 5936m Total Load of all routes: 56
Ecco il diagramma dei percorsi.
Completa i programmi
Ecco i programmi completi.
Python
"""Capacited Vehicles Routing Problem (CVRP).""" 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["demands"] = [0, 1, 1, 3, 6, 3, 6, 8, 8, 1, 2, 1, 2, 6, 6, 8, 8] data["vehicle_capacities"] = [15, 15, 15, 15] data["num_vehicles"] = 4 data["depot"] = 0 return data def print_solution(data, manager, routing, assignment): """Prints assignment on console.""" print(f"Objective: {assignment.ObjectiveValue()}") # Display dropped nodes. dropped_nodes = "Dropped nodes:" for node in range(routing.Size()): if routing.IsStart(node) or routing.IsEnd(node): continue if assignment.Value(routing.NextVar(node)) == node: dropped_nodes += f" {manager.IndexToNode(node)}" print(dropped_nodes) # Display routes total_distance = 0 total_load = 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 route_load = 0 while not routing.IsEnd(index): node_index = manager.IndexToNode(index) route_load += data["demands"][node_index] plan_output += f" {node_index} Load({route_load}) -> " previous_index = index index = assignment.Value(routing.NextVar(index)) route_distance += routing.GetArcCostForVehicle( previous_index, index, vehicle_id ) plan_output += f" {manager.IndexToNode(index)} Load({route_load})\n" plan_output += f"Distance of the route: {route_distance}m\n" plan_output += f"Load of the route: {route_load}\n" print(plan_output) total_distance += route_distance total_load += route_load print(f"Total Distance of all routes: {total_distance}m") print(f"Total Load of all routes: {total_load}") 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 Capacity constraint. def demand_callback(from_index): """Returns the demand of the node.""" # Convert from routing variable Index to demands NodeIndex. from_node = manager.IndexToNode(from_index) return data["demands"][from_node] demand_callback_index = routing.RegisterUnaryTransitCallback(demand_callback) routing.AddDimensionWithVehicleCapacity( demand_callback_index, 0, # null capacity slack data["vehicle_capacities"], # vehicle maximum capacities True, # start cumul to zero "Capacity", ) # Allow to drop nodes. penalty = 1000 for node in range(1, len(data["distance_matrix"])): routing.AddDisjunction([manager.NodeToIndex(node)], penalty) # Setting first solution heuristic. 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(1) # Solve the problem. assignment = routing.SolveWithParameters(search_parameters) # Print solution on console. if assignment: print_solution(data, manager, routing, assignment) if __name__ == "__main__": main()
C++
#include <cstdint> #include <sstream> #include <vector> #include "google/protobuf/duration.pb.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<int64_t> demands{ 0, 1, 1, 3, 6, 3, 6, 8, 8, 1, 2, 1, 2, 6, 6, 8, 8, }; const std::vector<int64_t> vehicle_capacities{15, 15, 15, 15}; 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) { // Display dropped nodes. std::ostringstream dropped_nodes; for (int64_t node = 0; node < routing.Size(); ++node) { if (routing.IsStart(node) || routing.IsEnd(node)) continue; if (solution.Value(routing.NextVar(node)) == node) { dropped_nodes << " " << manager.IndexToNode(node).value(); } } LOG(INFO) << "Dropped nodes:" << dropped_nodes.str(); // Display routes int64_t total_distance{0}; int64_t total_load{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}; int64_t route_load{0}; std::ostringstream route; while (!routing.IsEnd(index)) { const int node_index = manager.IndexToNode(index).value(); route_load += data.demands[node_index]; route << node_index << " Load(" << route_load << ") -> "; 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"; LOG(INFO) << "Load of the route: " << route_load; total_distance += route_distance; total_load += route_load; } LOG(INFO) << "Total distance of all routes: " << total_distance << "m"; LOG(INFO) << "Total load of all routes: " << total_load; LOG(INFO) << ""; LOG(INFO) << "Advanced usage:"; LOG(INFO) << "Problem solved in " << routing.solver()->wall_time() << "ms"; } void VrpDropNodes() { // 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 Capacity constraint. const int demand_callback_index = routing.RegisterUnaryTransitCallback( [&data, &manager](const int64_t from_index) -> int64_t { // Convert from routing variable Index to demand NodeIndex. const int from_node = manager.IndexToNode(from_index).value(); return data.demands[from_node]; }); routing.AddDimensionWithVehicleCapacity( demand_callback_index, // transit callback index int64_t{0}, // null capacity slack data.vehicle_capacities, // vehicle maximum capacities true, // start cumul to zero "Capacity"); // Allow to drop nodes. int64_t penalty{1000}; for (int i = 1; i < data.distance_matrix.size(); ++i) { routing.AddDisjunction( {manager.NodeToIndex(RoutingIndexManager::NodeIndex(i))}, penalty); } // Setting first solution heuristic. RoutingSearchParameters search_parameters = DefaultRoutingSearchParameters(); search_parameters.set_first_solution_strategy( FirstSolutionStrategy::PATH_CHEAPEST_ARC); search_parameters.set_local_search_metaheuristic( LocalSearchMetaheuristic::GUIDED_LOCAL_SEARCH); search_parameters.mutable_time_limit()->set_seconds(1); // Solve the problem. const Assignment* solution = routing.SolveWithParameters(search_parameters); // Print solution on console. PrintSolution(data, manager, routing, *solution); } } // namespace operations_research int main(int /*argc*/, char* /*argv*/[]) { operations_research::VrpDropNodes(); 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.LocalSearchMetaheuristic; 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 com.google.protobuf.Duration; import java.util.logging.Logger; /** Minimal VRP.*/ public class VrpDropNodes { private static final Logger logger = Logger.getLogger(VrpDropNodes.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[] demands = {0, 1, 1, 3, 6, 3, 6, 8, 8, 1, 2, 1, 2, 6, 6, 8, 8}; public final long[] vehicleCapacities = {15, 15, 15, 15}; 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. // Display dropped nodes. String droppedNodes = "Dropped nodes:"; for (int node = 0; node < routing.size(); ++node) { if (routing.isStart(node) || routing.isEnd(node)) { continue; } if (solution.value(routing.nextVar(node)) == node) { droppedNodes += " " + manager.indexToNode(node); } } logger.info(droppedNodes); // Display routes long totalDistance = 0; long totalLoad = 0; for (int i = 0; i < data.vehicleNumber; ++i) { long index = routing.start(i); logger.info("Route for Vehicle " + i + ":"); long routeDistance = 0; long routeLoad = 0; String route = ""; while (!routing.isEnd(index)) { long nodeIndex = manager.indexToNode(index); routeLoad += data.demands[(int) nodeIndex]; route += nodeIndex + " Load(" + routeLoad + ") -> "; long previousIndex = index; index = solution.value(routing.nextVar(index)); routeDistance += routing.getArcCostForVehicle(previousIndex, index, i); } route += manager.indexToNode(routing.end(i)); logger.info(route); logger.info("Distance of the route: " + routeDistance + "m"); totalDistance += routeDistance; totalLoad += routeLoad; } logger.info("Total Distance of all routes: " + totalDistance + "m"); logger.info("Total Load of all routes: " + totalLoad); } 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 Capacity constraint. final int demandCallbackIndex = routing.registerUnaryTransitCallback((long fromIndex) -> { // Convert from routing variable Index to user NodeIndex. int fromNode = manager.indexToNode(fromIndex); return data.demands[fromNode]; }); routing.addDimensionWithVehicleCapacity(demandCallbackIndex, 0, // null capacity slack data.vehicleCapacities, // vehicle maximum capacities true, // start cumul to zero "Capacity"); // Allow to drop nodes. long penalty = 1000; for (int i = 1; i < data.distanceMatrix.length; ++i) { routing.addDisjunction(new long[] {manager.nodeToIndex(i)}, penalty); } // Setting first solution heuristic. RoutingSearchParameters searchParameters = main.defaultRoutingSearchParameters() .toBuilder() .setFirstSolutionStrategy(FirstSolutionStrategy.Value.PATH_CHEAPEST_ARC) .setLocalSearchMetaheuristic(LocalSearchMetaheuristic.Value.GUIDED_LOCAL_SEARCH) .setTimeLimit(Duration.newBuilder().setSeconds(1).build()) .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; using Google.Protobuf.WellKnownTypes; // Duration /// <summary> /// Minimal Vrp with drop nodes. /// </summary> public class VrpDropNodes { 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[] Demands = { 0, 1, 1, 3, 6, 3, 6, 8, 8, 1, 2, 1, 2, 6, 6, 8, 8 }; public long[] VehicleCapacities = { 15, 15, 15, 15 }; 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. // Display dropped nodes. string droppedNodes = "Dropped nodes:"; for (int index = 0; index < routing.Size(); ++index) { if (routing.IsStart(index) || routing.IsEnd(index)) { continue; } if (solution.Value(routing.NextVar(index)) == index) { droppedNodes += " " + manager.IndexToNode(index); } } Console.WriteLine("{0}", droppedNodes); // Inspect solution. long totalDistance = 0; long totalLoad = 0; for (int i = 0; i < data.VehicleNumber; ++i) { Console.WriteLine("Route for Vehicle {0}:", i); long routeDistance = 0; long routeLoad = 0; var index = routing.Start(i); while (routing.IsEnd(index) == false) { long nodeIndex = manager.IndexToNode(index); routeLoad += data.Demands[nodeIndex]; Console.Write("{0} Load({1}) -> ", nodeIndex, routeLoad); 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); totalDistance += routeDistance; totalLoad += routeLoad; } Console.WriteLine("Total Distance of all routes: {0}m", totalDistance); Console.WriteLine("Total Load of all routes: {0}m", totalLoad); } 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 Capacity constraint. int demandCallbackIndex = routing.RegisterUnaryTransitCallback((long fromIndex) => { // Convert from routing variable Index to // demand NodeIndex. var fromNode = manager.IndexToNode(fromIndex); return data.Demands[fromNode]; }); routing.AddDimensionWithVehicleCapacity(demandCallbackIndex, 0, // null capacity slack data.VehicleCapacities, // vehicle maximum capacities true, // start cumul to zero "Capacity"); // Allow to drop nodes. long penalty = 1000; for (int i = 1; i < data.DistanceMatrix.GetLength(0); ++i) { routing.AddDisjunction(new long[] { manager.NodeToIndex(i) }, penalty); } // Setting first solution heuristic. RoutingSearchParameters searchParameters = operations_research_constraint_solver.DefaultRoutingSearchParameters(); searchParameters.FirstSolutionStrategy = FirstSolutionStrategy.Types.Value.PathCheapestArc; searchParameters.LocalSearchMetaheuristic = LocalSearchMetaheuristic.Types.Value.GuidedLocalSearch; searchParameters.TimeLimit = new Duration { Seconds = 1 }; // Solve the problem. Assignment solution = routing.SolveWithParameters(searchParameters); // Print solution on console. PrintSolution(data, routing, manager, solution); } }