توضح الأقسام التالية كيفية تنفيذ بعض المهام الشائعة ذات الصلة بحل مشكلات توجيه المركبات.
حدود البحث
قد يستغرق حل مشاكل توجيه المركبات في العديد من المواقع الجغرافية وقتًا طويلاً. وفي ما يتعلق بهذه المشكلات، من الأفضل تعيين حد للبحث، وهو ما يؤدي إلى إنهاء البحث بعد مدة زمنية محددة أو عدد من الحلول المعروضة.
الحدود الزمنية
توضح الأمثلة أدناه كيفية تعيين حد زمني يبلغ 30 ثانية لإجراء بحث.
لغة Python
search_parameters = pywrapcp.DefaultRoutingSearchParameters() search_parameters.time_limit.seconds = 30
C++
RoutingSearchParameters searchParameters = DefaultRoutingSearchParameters(); searchParameters.mutable_time_limit()->set_seconds(30);
لغة Java
أضِف `import` التالي في بداية البرنامج:import com.google.protobuf.Duration;ثم اضبط معلمات البحث على النحو التالي:
RoutingSearchParameters searchParameters =
main.defaultRoutingSearchParameters()
.toBuilder()
.setTimeLimit(Duration.newBuilder().setSeconds(30).build())
.build();
C#
أضف السطر التالي في بداية البرنامج:using Google.Protobuf.WellKnownTypes; // Durationبعد ذلك، اضبط معلمات البحث على النحو التالي:
RoutingSearchParameters searchParameters =
operations_research_constraint_solver.DefaultRoutingSearchParameters();
searchParameters.TimeLimit = new Duration { Seconds = 10 };
راجع تغيير إستراتيجية البحث للاطلاع على مثال يحدد حدًا زمنيًا.
حدود الحلول
توضح الأمثلة الواردة أدناه كيفية تعيين حد حل 100 لعملية بحث.
لغة Python
search_parameters = pywrapcp.DefaultRoutingSearchParameters() search_parameters.solution_limit = 100
C++
RoutingSearchParameters searchParameters = DefaultRoutingSearchParameters(); searchParameters.set_solution_limit(100);
لغة Java
RoutingSearchParameters searchParameters =
main.defaultRoutingSearchParameters()
.toBuilder()
.setSolutionLimit(100)
.build();
C#
RoutingSearchParameters searchParameters = operations_research_constraint_solver.DefaultRoutingSearchParameters(); searchParameters.SolutionLimit(100);
تعيين مسارات أولية لعملية بحث
بالنسبة إلى بعض المشاكل، قد تحتاج إلى تحديد مجموعة من المسارات الأولية لـ VRP، بدلاً من السماح للحل بالعثور على حل أولي - على سبيل المثال، إذا كنت قد عثرت على حل جيد لإحدى المشكلات، وتريد استخدامه كنقطة بداية لحل مشكلة معدلة.
لإنشاء المسارات الأولية، اتبع الخطوات التالية:
- حدد مصفوفة تحتوي على المسارات الأولية.
- أنشئ الحل الأولي باستخدام الطريقة
ReadAssignmentFromRoutes.
تحدد الشفرة التالية المسارات الأولية في البيانات.
لغة 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},
};
لغة 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 },
};
تعمل الشفرة التالية على إنشاء الحل الأولي من المسارات، ثم تجري عملية بحث تبدأ من الحل المبدئي.
يعرض البرنامج كلاً من الحل الأولي، والحل الذي تم العثور عليه من خلال البحث.
لغة 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);
لغة 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);
وعند إضافة هذا الرمز إلى برنامج VRP السابق وتشغيل البرنامج، سيعرض النتيجة التالية:
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
في ما يلي البرامج الكاملة التي تعيّن المسارات الأولية.
لغة 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;
}
لغة 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);
}
}
تعيين مواقع البداية والنهاية للمسارات
لقد افترضنا حتى الآن أن جميع المركبات تبدأ وتنتهي في موقع واحد، المستودع. يمكنك أيضًا تعيين مواقع مختلفة للبدء والانتهاء لكل مركبة في المشكلة. للقيام بذلك، مرِّر متّجهين يحتويان على مؤشرات مواقع البداية والنهاية كإدخالات في طريقة RoutingModel في الدالة الرئيسية. في ما يلي كيفية إنشاء متّجهي البداية والنهاية في قسم البيانات من البرنامج:
لغة 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},
};
لغة 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 };
وفي ما يلي البرامج الكاملة التي تعيّن مواقع البدء والانتهاء بهذه الطريقة.
لغة 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;
}
لغة 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);
}
}
عند تشغيل البرنامج، تحصل على الإخراج التالي، حيث تبدأ المسارات وتنتهي في المواقع المحددة:
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
إجمالي المسافة أقصر من المثال السابق لأن المركبات غير مطلوبة لبدء تشغيل المستودع أو إنهاؤه.
السماح بمواقع البدء والانتهاء بشكل عشوائي
في الإصدارات الأخرى من مشكلة توجيه المركبة، يُسمح للمركبات بأن تبدأ وتنتهي في المواقع العشوائية. ولإعداد المشكلة بهذه الطريقة، ما عليك سوى تعديل مصفوفة المسافة بحيث تصبح المسافة من المستودع إلى أي موقع آخر 0، عن طريق تعيين الصف والعمود الأول من المصفوفة على جميع الأصفار. ويؤدي هذا إلى تحويل المستودع إلى موقع وهمي ليس له أي تأثير على المسارات المثلى.
في ما يلي مثال تم فيه تعديل مصفوفة المسافة من مثال VRP لتجعل المسافة من المستودع إلى جميع العقد الأخرى 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
],
]
عند تشغيل برنامج VRP مع مصفوفة المسافة المعدلة (وتعديل طابعة الحلول لحذف المستودع)، يعرض البرنامج المسارات التالية:
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