Aşağıdaki bölümlerde araç yönlendirme sorunlarının çözümüyle ilgili sık yapılan bazı işlemlerin nasıl yapılacağı açıklanmaktadır.
Arama sınırları
Birçok konumla ilgili araç yönlendirme sorunlarının çözülmesi uzun sürebilir. Bu tür sorunlar için belirli bir süre veya döndürülen çözüm sayısı sonra aramayı sonlandıran arama sınırı koymak iyi bir fikirdir.
Süre sınırları
Aşağıdaki örneklerde, bir arama için 30 saniyelik süre sınırının nasıl ayarlanacağı gösterilmektedir.
Python
search_parameters = pywrapcp.DefaultRoutingSearchParameters() search_parameters.time_limit.seconds = 30
C++
RoutingSearchParameters searchParameters = DefaultRoutingSearchParameters(); searchParameters.mutable_time_limit()->set_seconds(30);
Java
Programın başına şu "import" ifadesini ekleyin:import com.google.protobuf.Duration;Ardından arama parametrelerini şu şekilde ayarlayın:
RoutingSearchParameters searchParameters =
main.defaultRoutingSearchParameters()
.toBuilder()
.setTimeLimit(Duration.newBuilder().setSeconds(30).build())
.build();
C#
Programın başına aşağıdaki satırı ekleyin:using Google.Protobuf.WellKnownTypes; // DurationArdından arama parametrelerini şu şekilde ayarlayın:
RoutingSearchParameters searchParameters =
operations_research_constraint_solver.DefaultRoutingSearchParameters();
searchParameters.TimeLimit = new Duration { Seconds = 10 };
Zaman sınırı belirleyen bir örnek için Arama stratejisini değiştirme konusuna bakın.
Çözüm sınırları
Aşağıdaki örneklerde, bir arama için 100'lük bir çözüm sınırının nasıl belirleneceği gösterilmektedir.
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);
Bir arama için ilk rotaları belirleme
Bazı sorunlara yönelik olarak, çözümleyicinin başlangıç çözümü bulmasına izin vermek yerine VRP için bir başlangıç rotası grubu belirtmek isteyebilirsiniz (örneğin, bir problem için iyi bir çözüm bulduysanız ve bunu, değiştirilen bir sorunu çözmek için başlangıç noktası olarak kullanmak istiyorsanız).
İlk rotaları oluşturmak için aşağıdaki adımları uygulayın:
- İlk rotaları içeren bir dizi tanımlayın.
ReadAssignmentFromRoutesyöntemini kullanarak ilk çözümü oluşturun.
Aşağıdaki kod, verilerdeki ilk rotaları tanımlar.
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 },
};
Aşağıdaki kod, rotalardan ilk çözümü oluşturur ve ardından ilk çözümden başlayarak bir arama gerçekleştirir.
Bu program hem ilk çözümü hem de arama tarafından bulunan çözümü gösterir.
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);
Bu kodu önceki VRP programına ekleyip çalıştırdığınızda aşağıdaki çıkışı gösterir:
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
İlk rotaları oluşturan programların tamamını aşağıda bulabilirsiniz.
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) {
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.solveWithParameters(searchParameters);
// Print solution on console.
logger.info("Solution after search:");
printSolution(data, routing, manager, solution);
}
}
C#
// Copyright 2010-2022 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
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.SolveWithParameters(searchParameters);
// Print solution on console.
Console.WriteLine("Solution after search:");
PrintSolution(data, routing, manager, solution);
}
}
Rotalar için başlangıç ve bitiş konumlarını ayarlama
Şu ana kadar tüm araçların tek bir konumdan, yani depodan başladığını ve sona erdiğini varsayarız. Ayrıca, sorunlu her araç için muhtemelen farklı başlangıç ve bitiş konumları belirleyebilirsiniz. Bunu yapmak için başlangıç ve bitiş konumlarının dizinlerini içeren iki vektörü, ana işlevdeki YönlendirmeModeli yöntemine giriş olarak sağlayın. Programın veri bölümünde başlangıç ve bitiş vektörlerini nasıl oluşturacağınız aşağıda açıklanmıştır:
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 };
Başlangıç ve bitiş konumlarını bu şekilde ayarlayan tüm programlar aşağıda verilmiştir.
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);
}
}
Programı çalıştırdığınızda, rotaların başladığı ve belirtilen konumlarda sona erdiği aşağıdaki çıkışı alırsınız:
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
Araçların depoda başlaması veya bitmesi gerekmediği için toplam mesafe önceki örnekten daha kısadır.
İsteğe bağlı başlangıç ve bitiş konumlarına izin verme
Araç yönlendirme sorununun diğer sürümlerinde araçların rastgele konumlarda başlayıp bitmesine izin verilir. Soruyu bu şekilde oluşturmak için mesafe matrisini, matrisin ilk satırı ile sütununu sıfır olacak şekilde ayarlayarak depodan başka bir konuma olan mesafeyi 0 olarak ayarlamanız yeterlidir. Bu işlem, depoyu en iyi rotaları etkilemeyen sahte bir konuma dönüştürür.
Aşağıda, VRP örneğinden mesafe matrisinin, depodan diğer tüm düğümlere 0 mesafe olacak şekilde değiştirildiği bir örnek verilmiştir.
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
],
]
Değiştirilmiş mesafe matrisiyle VRP programını çalıştırdığınızda (ve depoyu hariç tutmak için çözüm yazıcısını değiştirdiğinizde) program aşağıdaki rotaları görüntüler:
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