रूटिंग से जुड़े सामान्य टास्क

नीचे दिए गए सेक्शन में वाहनों को रूट करने से जुड़ी समस्याओं को हल करने से जुड़े कुछ सामान्य काम करने के तरीके बताए गए हैं.

खोज की सीमाएं

कई जगहों पर, वाहन रूटिंग से जुड़ी समस्याएं हल होने में ज़्यादा समय लग सकता है. ऐसी समस्याओं के लिए, खोज सीमा सेट करना एक अच्छा उपाय है, जो दी गई समयावधि या दिए गए समाधानों की संख्या के बाद खोज को खत्म कर देता है.

समयसीमा

किसी खोज के लिए 30 सेकंड की समयसीमा सेट करने का तरीका नीचे दिए गए उदाहरणों में बताया गया है.

Python

search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.time_limit.seconds = 30

C++

RoutingSearchParameters searchParameters = DefaultRoutingSearchParameters();
searchParameters.mutable_time_limit()->set_seconds(30);

Java

प्रोग्राम की शुरुआत में यह `इंपोर्ट` जोड़ें:

import com.google.protobuf.Duration;

इसके बाद, खोज पैरामीटर इस तरह सेट करें:

RoutingSearchParameters searchParameters =
        main.defaultRoutingSearchParameters()
            .toBuilder()
            .setTimeLimit(Duration.newBuilder().setSeconds(30).build())
            .build();

C#

कार्यक्रम की शुरुआत में नीचे दी गई लाइन जोड़ें:

using Google.Protobuf.WellKnownTypes; // Duration

इसके बाद, खोज पैरामीटर इस तरह सेट करें:

RoutingSearchParameters searchParameters =
  operations_research_constraint_solver.DefaultRoutingSearchParameters();
searchParameters.TimeLimit = new Duration { Seconds = 10 };

समय सीमा सेट करने वाले उदाहरण के लिए खोज रणनीति बदलना देखें.

समाधान की सीमाएं

नीचे दिए गए उदाहरणों में, खोज के लिए 100 की सीमा तय करने का तरीका बताया गया है.

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);

किसी खोज के लिए शुरुआती रूट सेट करना

कुछ समस्याओं के लिए, ऐसा हो सकता है कि आप वीआरपी के लिए शुरुआती रास्तों का एक सेट बताएं, न कि सॉल्वर को कोई शुरुआती हल ढूंढने के लिए. उदाहरण के लिए, अगर आपको समस्या का अच्छा हल पहले ही मिल गया है और आप उसका इस्तेमाल शुरुआती समस्या को हल करने की शुरुआत करने के लिए करना चाहते हैं.

शुरुआती रास्ते बनाने के लिए यह तरीका अपनाएं:

1. शुरुआती रास्तों वाली एक श्रेणी तय करें.
2. ReadAssignmentFromRoutes तरीके का इस्तेमाल करके शुरुआती हल बनाएं.

कोड में, डेटा के शुरुआती रूट के बारे में बताया गया है.

ध्यान दें: शुरुआती रास्तों में डिपो शामिल नहीं है.

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 },
        };

नीचे दिया गया कोड, रास्तों से शुरुआत करने वाला समाधान बनाता है और फिर शुरुआती हल से शुरू करते हुए खोज करता है.

प्रोग्राम में शुरुआती समाधान के साथ-साथ, खोज के ज़रिए मिले समाधान, दोनों दिखते हैं.

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);

इस कोड को पिछले VRP प्रोग्राम में जोड़ने और प्रोग्राम को चलाने पर, यह आउटपुट दिखाता है:

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

यहां वे सभी प्रोग्राम दिए गए हैं जो शुरुआती रूट सेट करते हैं.

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);
    }
}

रास्तों के लिए शुरू और खत्म होने की जगह सेट करना

अब तक, हमने यह माना है कि सभी वाहन एक ही जगह से शुरू और खत्म होते हैं, डिपो. इस समस्या में, हर वाहन के लिए, शुरू और खत्म होने की अलग-अलग जगहें भी सेट की जा सकती हैं. ऐसा करने के लिए, मुख्य फ़ंक्शन में RoutingModel मैथड में इनपुट के तौर पर, दो वेक्टर पास करें जिनमें स्टार्ट और एंड लोकेशन के इंडेक्स शामिल हैं. यहां प्रोग्राम के डेटा सेक्शन में स्टार्ट और एंड वेक्टर बनाने का तरीका बताया गया है:

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 };

यहां ऐसे सभी प्रोग्राम दिए गए हैं जो इस तरह से, शुरू और खत्म होने की जगह सेट करते हैं.

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);
    }
}

जब आप प्रोग्राम चलाते हैं, तो आपको नीचे दिया गया आउटपुट मिलता है, जिसमें रास्ते तय जगहों पर शुरू और खत्म होते हैं:

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

कुल दूरी पिछले उदाहरण से कम है, क्योंकि वाहनों को डिपो से शुरू या खत्म करने की ज़रूरत नहीं है.

आर्बिट्रेरी शुरू और खत्म होने की जगहों को अनुमति देना

वाहन रूटिंग की समस्या के अन्य वर्शन में, वाहन आर्बिट्रेरी स्थान पर प्रारंभ और समाप्ति करने की अनुमति देते हैं. इस तरीके से प्रॉब्लम सेट अप करने के लिए, डिस्टेंस मैट्रिक्स में बदलाव करें, ताकि डिपो से किसी अन्य जगह पर दूरी 0 हो. ऐसा करने के लिए, मैट्रिक्स की पहली पंक्ति और कॉलम को ज़ीरो पर सेट करें. इससे डिपो उस डमी जगह में बदल जाता है जिस पर सबसे अच्छे रास्तों का कोई असर नहीं होता.

यहां एक उदाहरण दिया गया है, जिसमें VRP उदाहरण से दूरी के मैट्रिक्स में बदलाव किया गया है, ताकि डिपो से सभी अन्य नोड 0 तक दूरी बनाई जा सके.

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
        ],
    ]

जब आप VRP प्रोग्राम चलाते हैं, जिसमें बदलाव किया गया दूरी का मैट्रिक्स हो (और डिपो छोड़ने के लिए सॉल्यूशन प्रिंटर में बदलाव करें) , तो प्रोग्राम में इन रास्तों को दिखाया जाता है:

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