В этом разделе мы описываем VRP, в котором каждое транспортное средство забирает предметы в разных местах и выгружает их в других. Проблема состоит в том, чтобы назначить маршруты для транспортных средств, чтобы они могли забрать и доставить все предметы, минимизируя при этом длину самого длинного маршрута.
Пример VRP с самовывозом и доставкой
На диаграмме ниже показаны места получения и доставки в сетке, аналогичной той, что была в предыдущем примере VRP . Для каждого товара существует направленная грань от места самовывоза к месту доставки.
Решение примера с помощью OR-Tools
В следующих разделах описано, как решить проблему VRP с самовывозом и доставкой. Большая часть кода заимствована из предыдущего примера VRP , поэтому мы сосредоточимся на новых частях.
Создайте данные
Данные для задачи включают в себя матрицу расстояний из предыдущего примера VRP, а также список пар мест получения и доставки, data['pickups_deliveries'] , соответствующий направленным ребрам на диаграмме выше. Код ниже определяет места получения и доставки.
Питон
data["pickups_deliveries"] = [
[1, 6],
[2, 10],
[4, 3],
[5, 9],
[7, 8],
[15, 11],
[13, 12],
[16, 14],
]С++
const std::vector<std::vector<RoutingIndexManager::NodeIndex>>
pickups_deliveries{
{RoutingIndexManager::NodeIndex{1},
RoutingIndexManager::NodeIndex{6}},
{RoutingIndexManager::NodeIndex{2},
RoutingIndexManager::NodeIndex{10}},
{RoutingIndexManager::NodeIndex{4},
RoutingIndexManager::NodeIndex{3}},
{RoutingIndexManager::NodeIndex{5},
RoutingIndexManager::NodeIndex{9}},
{RoutingIndexManager::NodeIndex{7},
RoutingIndexManager::NodeIndex{8}},
{RoutingIndexManager::NodeIndex{15},
RoutingIndexManager::NodeIndex{11}},
{RoutingIndexManager::NodeIndex{13},
RoutingIndexManager::NodeIndex{12}},
{RoutingIndexManager::NodeIndex{16},
RoutingIndexManager::NodeIndex{14}},
};Ява
public final int[][] pickupsDeliveries = {
{1, 6},
{2, 10},
{4, 3},
{5, 9},
{7, 8},
{15, 11},
{13, 12},
{16, 14},
};С#
public int[][] PickupsDeliveries = {
new int[] { 1, 6 }, new int[] { 2, 10 }, new int[] { 4, 3 }, new int[] { 5, 9 },
new int[] { 7, 8 }, new int[] { 15, 11 }, new int[] { 13, 12 }, new int[] { 16, 14 },
};Для каждой пары первая запись — это индекс места получения, а вторая — индекс места доставки.
Определите запросы на получение и доставку
Следующий код определяет запросы на получение и доставку, используя места получения и доставки в data['pickups_deliveries'] .
Питон
for request in data["pickups_deliveries"]:
pickup_index = manager.NodeToIndex(request[0])
delivery_index = manager.NodeToIndex(request[1])
routing.AddPickupAndDelivery(pickup_index, delivery_index)
routing.solver().Add(
routing.VehicleVar(pickup_index) == routing.VehicleVar(delivery_index)
)
routing.solver().Add(
distance_dimension.CumulVar(pickup_index)
<= distance_dimension.CumulVar(delivery_index)
)С++
Solver* const solver = routing.solver();
for (const auto& request : data.pickups_deliveries) {
const int64_t pickup_index = manager.NodeToIndex(request[0]);
const int64_t delivery_index = manager.NodeToIndex(request[1]);
routing.AddPickupAndDelivery(pickup_index, delivery_index);
solver->AddConstraint(solver->MakeEquality(
routing.VehicleVar(pickup_index), routing.VehicleVar(delivery_index)));
solver->AddConstraint(
solver->MakeLessOrEqual(distance_dimension->CumulVar(pickup_index),
distance_dimension->CumulVar(delivery_index)));
}Ява
Solver solver = routing.solver();
for (int[] request : data.pickupsDeliveries) {
long pickupIndex = manager.nodeToIndex(request[0]);
long deliveryIndex = manager.nodeToIndex(request[1]);
routing.addPickupAndDelivery(pickupIndex, deliveryIndex);
solver.addConstraint(
solver.makeEquality(routing.vehicleVar(pickupIndex), routing.vehicleVar(deliveryIndex)));
solver.addConstraint(solver.makeLessOrEqual(
distanceDimension.cumulVar(pickupIndex), distanceDimension.cumulVar(deliveryIndex)));
}С#
Solver solver = routing.solver();
for (int i = 0; i < data.PickupsDeliveries.GetLength(0); i++)
{
long pickupIndex = manager.NodeToIndex(data.PickupsDeliveries[i][0]);
long deliveryIndex = manager.NodeToIndex(data.PickupsDeliveries[i][1]);
routing.AddPickupAndDelivery(pickupIndex, deliveryIndex);
solver.Add(solver.MakeEquality(routing.VehicleVar(pickupIndex), routing.VehicleVar(deliveryIndex)));
solver.Add(solver.MakeLessOrEqual(distanceDimension.CumulVar(pickupIndex),
distanceDimension.CumulVar(deliveryIndex)));
} Для каждой пары команда routing.AddPickupAndDelivery(pickup_index, delivery_index) создает запрос на получение и доставку товара.
В следующей строке добавляется требование о том, что каждый товар должен быть забран и доставлен одним и тем же транспортным средством.
routing.solver().Add(
routing.VehicleVar(pickup_index) ==
routing.VehicleVar(delivery_index))Наконец, мы добавляем очевидное требование о том, что каждый предмет необходимо забрать до его доставки. Для этого мы требуем, чтобы совокупное расстояние транспортного средства в месте получения товара не превышало его совокупное расстояние в месте доставки.
routing.solver().Add(
distance_dimension.CumulVar(pickup_index) <=
distance_dimension.CumulVar(delivery_index))Запуск программы
Полные программы для ВРП с самовывозом и доставкой показаны в следующем разделе. Когда вы запускаете программу, она отображает следующие маршруты.
Objective: 226116 Route for vehicle 0: 0 -> 13 -> 15 -> 11 -> 12 -> 0 Distance of the route: 1552m Route for vehicle 1: 0 -> 5 -> 2 -> 10 -> 16 -> 14 -> 9 -> 0 Distance of the route: 2192m Route for vehicle 2: 0 -> 4 -> 3 -> 0 Distance of the route: 1392m Route for vehicle 3: 0 -> 7 -> 1 -> 6 -> 8 -> 0 Distance of the route: 1780m Total Distance of all routes: 6916m
На следующей схеме показаны маршруты:
Полные программы
Полные программы представлены ниже.
Питон
"""Simple Pickup Delivery Problem (PDP)."""
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["pickups_deliveries"] = [
[1, 6],
[2, 10],
[4, 3],
[5, 9],
[7, 8],
[15, 11],
[13, 12],
[16, 14],
]
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()}")
total_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)
total_distance += route_distance
print(f"Total Distance of all routes: {total_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["depot"]
)
# Create Routing Model.
routing = pywrapcp.RoutingModel(manager)
# Define cost of each arc.
def distance_callback(from_index, to_index):
"""Returns the manhattan 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)
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)
# Define Transportation Requests.
for request in data["pickups_deliveries"]:
pickup_index = manager.NodeToIndex(request[0])
delivery_index = manager.NodeToIndex(request[1])
routing.AddPickupAndDelivery(pickup_index, delivery_index)
routing.solver().Add(
routing.VehicleVar(pickup_index) == routing.VehicleVar(delivery_index)
)
routing.solver().Add(
distance_dimension.CumulVar(pickup_index)
<= distance_dimension.CumulVar(delivery_index)
)
# Setting first solution heuristic.
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (
routing_enums_pb2.FirstSolutionStrategy.PARALLEL_CHEAPEST_INSERTION
)
# Solve the problem.
solution = routing.SolveWithParameters(search_parameters)
# Print solution on console.
if solution:
print_solution(data, manager, routing, solution)
if __name__ == "__main__":
main()С++
#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 std::vector<std::vector<RoutingIndexManager::NodeIndex>>
pickups_deliveries{
{RoutingIndexManager::NodeIndex{1},
RoutingIndexManager::NodeIndex{6}},
{RoutingIndexManager::NodeIndex{2},
RoutingIndexManager::NodeIndex{10}},
{RoutingIndexManager::NodeIndex{4},
RoutingIndexManager::NodeIndex{3}},
{RoutingIndexManager::NodeIndex{5},
RoutingIndexManager::NodeIndex{9}},
{RoutingIndexManager::NodeIndex{7},
RoutingIndexManager::NodeIndex{8}},
{RoutingIndexManager::NodeIndex{15},
RoutingIndexManager::NodeIndex{11}},
{RoutingIndexManager::NodeIndex{13},
RoutingIndexManager::NodeIndex{12}},
{RoutingIndexManager::NodeIndex{16},
RoutingIndexManager::NodeIndex{14}},
};
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 total_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";
total_distance += route_distance;
}
LOG(INFO) << "Total distance of all routes: " << total_distance << "m";
LOG(INFO) << "";
LOG(INFO) << "Advanced usage:";
LOG(INFO) << "Problem solved in " << routing.solver()->wall_time() << "ms";
}
void VrpGlobalSpan() {
// 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);
// Define cost of each arc.
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];
});
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index);
// Add Distance constraint.
routing.AddDimension(transit_callback_index, // transit callback
0, // no slack
3000, // vehicle maximum travel distance
true, // start cumul to zero
"Distance");
RoutingDimension* distance_dimension =
routing.GetMutableDimension("Distance");
distance_dimension->SetGlobalSpanCostCoefficient(100);
// Define Transportation Requests.
Solver* const solver = routing.solver();
for (const auto& request : data.pickups_deliveries) {
const int64_t pickup_index = manager.NodeToIndex(request[0]);
const int64_t delivery_index = manager.NodeToIndex(request[1]);
routing.AddPickupAndDelivery(pickup_index, delivery_index);
solver->AddConstraint(solver->MakeEquality(
routing.VehicleVar(pickup_index), routing.VehicleVar(delivery_index)));
solver->AddConstraint(
solver->MakeLessOrEqual(distance_dimension->CumulVar(pickup_index),
distance_dimension->CumulVar(delivery_index)));
}
// Setting first solution heuristic.
RoutingSearchParameters searchParameters = DefaultRoutingSearchParameters();
searchParameters.set_first_solution_strategy(
FirstSolutionStrategy::PARALLEL_CHEAPEST_INSERTION);
// 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::VrpGlobalSpan();
return EXIT_SUCCESS;
}Ява
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.Solver;
import com.google.ortools.constraintsolver.main;
import java.util.logging.Logger;
/** Minimal Pickup & Delivery Problem (PDP).*/
public class VrpPickupDelivery {
private static final Logger logger = Logger.getLogger(VrpPickupDelivery.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[][] pickupsDeliveries = {
{1, 6},
{2, 10},
{4, 3},
{5, 9},
{7, 8},
{15, 11},
{13, 12},
{16, 14},
};
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 totalDistance = 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");
totalDistance += routeDistance;
}
logger.info("Total Distance of all routes: " + totalDistance + "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, // transit callback index
0, // no slack
3000, // vehicle maximum travel distance
true, // start cumul to zero
"Distance");
RoutingDimension distanceDimension = routing.getMutableDimension("Distance");
distanceDimension.setGlobalSpanCostCoefficient(100);
// Define Transportation Requests.
Solver solver = routing.solver();
for (int[] request : data.pickupsDeliveries) {
long pickupIndex = manager.nodeToIndex(request[0]);
long deliveryIndex = manager.nodeToIndex(request[1]);
routing.addPickupAndDelivery(pickupIndex, deliveryIndex);
solver.addConstraint(
solver.makeEquality(routing.vehicleVar(pickupIndex), routing.vehicleVar(deliveryIndex)));
solver.addConstraint(solver.makeLessOrEqual(
distanceDimension.cumulVar(pickupIndex), distanceDimension.cumulVar(deliveryIndex)));
}
// Setting first solution heuristic.
RoutingSearchParameters searchParameters =
main.defaultRoutingSearchParameters()
.toBuilder()
.setFirstSolutionStrategy(FirstSolutionStrategy.Value.PARALLEL_CHEAPEST_INSERTION)
.build();
// Solve the problem.
Assignment solution = routing.solveWithParameters(searchParameters);
// Print solution on console.
printSolution(data, routing, manager, solution);
}
}С#
using System;
using System.Collections.Generic;
using Google.OrTools.ConstraintSolver;
/// <summary>
/// Minimal Pickup & Delivery Problem (PDP).
/// </summary>
public class VrpPickupDelivery
{
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[][] PickupsDeliveries = {
new int[] { 1, 6 }, new int[] { 2, 10 }, new int[] { 4, 3 }, new int[] { 5, 9 },
new int[] { 7, 8 }, new int[] { 15, 11 }, new int[] { 13, 12 }, new int[] { 16, 14 },
};
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 totalDistance = 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);
totalDistance += routeDistance;
}
Console.WriteLine("Total Distance of all routes: {0}m", totalDistance);
}
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);
// Define Transportation Requests.
Solver solver = routing.solver();
for (int i = 0; i < data.PickupsDeliveries.GetLength(0); i++)
{
long pickupIndex = manager.NodeToIndex(data.PickupsDeliveries[i][0]);
long deliveryIndex = manager.NodeToIndex(data.PickupsDeliveries[i][1]);
routing.AddPickupAndDelivery(pickupIndex, deliveryIndex);
solver.Add(solver.MakeEquality(routing.VehicleVar(pickupIndex), routing.VehicleVar(deliveryIndex)));
solver.Add(solver.MakeLessOrEqual(distanceDimension.CumulVar(pickupIndex),
distanceDimension.CumulVar(deliveryIndex)));
}
// 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);
}
}