Vehicle Routing Problem with Backhauls (VRPB)

import hexaly.optimizer
import sys
import math


def read_elem(filename):
    with open(filename) as f:
        return [str(elem) for elem in f.read().split()]


def main(instance_file, str_time_limit, output_file):

    #
    # Read instance data
    #
    nb_customers, nb_trucks, truck_capacity, dist_matrix_data, dist_depot_data, \
        delivery_demands_data, pickup_demands_data, backhaul_data = read_input_vrpb(
            instance_file)

    with hexaly.optimizer.HexalyOptimizer() as optimizer:
        #
        # Declare the optimization model
        #
        model = optimizer.model

        # Sequence of customers visited by each truck
        customers_sequences = [model.list(nb_customers)
                               for _ in range(nb_trucks)]

        # All customers must be visited by exactly one truck
        model.constraint(model.partition(customers_sequences))

        # Create Hexaly arrays to be able to access them with an "at" operator
        delivery_demands = model.array(delivery_demands_data)
        pickup_demands = model.array(pickup_demands_data)
        dist_matrix = model.array(dist_matrix_data)
        dist_depot = model.array(dist_depot_data)

        # A truck is used if it visits at least one customer
        trucks_used = [(model.count(customers_sequences[k]) > 0)
                       for k in range(nb_trucks)]

        dist_routes = [None] * nb_trucks
        is_backhaul = model.array(backhaul_data.values())
        for k in range(nb_trucks):
            sequence = customers_sequences[k]
            c = model.count(sequence)

            # A pickup cannot be followed by a delivery
            precedency_lambda = model.lambda_function(lambda i: model.or_(model.not_(
                model.at(is_backhaul, sequence[i-1])), model.at(is_backhaul, sequence[i])))
            model.constraint(model.and_(model.range(1, c), precedency_lambda))

            # The quantity needed in each route must not exceed the truck capacity
            delivery_demand_lambda = model.lambda_function(
                lambda j: delivery_demands[j])
            route_pickup_quantity = model.sum(sequence, delivery_demand_lambda)
            model.constraint(route_pickup_quantity <= truck_capacity)

            pickup_demand_lambda = model.lambda_function(
                lambda j: pickup_demands[j])
            route_pickup_quantity = model.sum(sequence, pickup_demand_lambda)
            model.constraint(route_pickup_quantity <= truck_capacity)

            # Distance traveled by each truck
            dist_lambda = model.lambda_function(lambda i:
                                                model.at(dist_matrix,
                                                         sequence[i - 1],
                                                         sequence[i]))
            dist_routes[k] = model.sum(model.range(1, c), dist_lambda) \
                + model.iif(c > 0,
                            dist_depot[sequence[0]] +
                            dist_depot[sequence[c - 1]],
                            0)

        # Total number of trucks used
        nb_trucks_used = model.sum(trucks_used)

        # Total distance traveled
        total_distance = model.sum(dist_routes)

        # Objective: minimize the number of trucks used, then minimize the distance traveled
        model.minimize(nb_trucks_used)
        model.minimize(total_distance)

        model.close()

        # Parameterize the optimizer
        optimizer.param.time_limit = int(str_time_limit)

        optimizer.solve()

        #
        # Write the solution in a file with the following format:
        #  - number of trucks used and total distance
        #  - for each truck the customers visited (omitting the start/end at the depot)
        #
        if output_file is not None:
            with open(output_file, 'w') as f:
                f.write("%d %d\n" %
                        (nb_trucks_used.value, total_distance.value))
                for k in range(nb_trucks):
                    if trucks_used[k].value != 1:
                        continue
                    # Values in sequence are in 0...nbCustomers. +2 is to put it back
                    # in 2...nbCustomers+2 as in the data files (1 being the depot)
                    for customer in customers_sequences[k].value:
                        f.write("%d " % (customer + 2))
                    f.write("\n")


# The input files follow the "CVRPLib" format
def read_input_vrpb(filename):
    file_it = iter(read_elem(filename))

    nb_nodes = 0
    while True:
        token = next(file_it)
        if token == "DIMENSION":
            next(file_it)  # Removes the ":"
            nb_nodes = int(next(file_it))
            nb_customers = nb_nodes - 1
        elif token == "VEHICLES":
            next(file_it)  # Removes the ":"
            nb_trucks = int(next(file_it))
        elif token == "CAPACITY":
            next(file_it)  # Removes the ":"
            truck_capacity = int(next(file_it))
        elif token == "EDGE_WEIGHT_TYPE":
            next(file_it)  # Removes the ":"
            token = next(file_it)
            if token != "EXACT_2D":
                print("Edge Weight Type " + token +
                      " is not supported (only EXACT_2D)")
                sys.exit(1)
        elif token == "NODE_COORD_SECTION":
            break

    customers_x = [None] * nb_customers
    customers_y = [None] * nb_customers
    depot_x = 0
    depot_y = 0
    for n in range(nb_nodes):
        node_id = int(next(file_it))
        if node_id != n + 1:
            print("Unexpected index")
            sys.exit(1)
        if node_id == 1:
            depot_x = int(next(file_it))
            depot_y = int(next(file_it))
        else:
            # -2 because original customer indices are in 2..nbNodes
            customers_x[node_id - 2] = int(next(file_it))
            customers_y[node_id - 2] = int(next(file_it))

    distance_matrix = compute_distance_matrix(customers_x, customers_y)
    distance_depots = compute_distance_depots(
        depot_x, depot_y, customers_x, customers_y)

    token = next(file_it)
    if token != "DEMAND_SECTION":
        print("Expected token DEMAND_SECTION")
        sys.exit(1)

    demands = [None] * nb_customers
    for n in range(nb_nodes):
        node_id = int(next(file_it))
        if node_id != n + 1:
            print("Unexpected index")
            sys.exit(1)
        if node_id == 1:
            if int(next(file_it)) != 0:
                print("Demand for depot should be 0")
                sys.exit(1)
        else:
            # -2 because original customer indices are in 2..nbNodes
            demands[node_id - 2] = int(next(file_it))

    token = next(file_it)
    if token != "BACKHAUL_SECTION":
        print("Expected token BACKHAUL_SECTION")
        sys.exit(1)

    is_backhaul = {i: False for i in range(nb_customers)}
    while True:
        node_id = int(next(file_it))
        if node_id == -1:
            break
        # -2 because original customer indices are in 2..nbNodes
        is_backhaul[node_id - 2] = True
    delivery_demands = [0 if is_backhaul[i] else demands[i]
                        for i in range(nb_customers)]
    pickup_demands = [demands[i] if is_backhaul[i]
                      else 0 for i in range(nb_customers)]

    token = next(file_it)
    if token != "DEPOT_SECTION":
        print("Expected token DEPOT_SECTION")
        sys.exit(1)

    depot_id = int(next(file_it))
    if depot_id != 1:
        print("Depot id is supposed to be 1")
        sys.exit(1)

    end_of_depot_section = int(next(file_it))
    if end_of_depot_section != -1:
        print("Expecting only one depot, more than one found")
        sys.exit(1)

    return nb_customers, nb_trucks, truck_capacity, distance_matrix, distance_depots, \
        delivery_demands, pickup_demands, is_backhaul


# Compute the distance matrix
def compute_distance_matrix(customers_x, customers_y):
    nb_customers = len(customers_x)
    distance_matrix = [[None for i in range(
        nb_customers)] for j in range(nb_customers)]
    for i in range(nb_customers):
        distance_matrix[i][i] = 0
        for j in range(nb_customers):
            dist = compute_dist(
                customers_x[i], customers_x[j], customers_y[i], customers_y[j])
            distance_matrix[i][j] = dist
            distance_matrix[j][i] = dist
    return distance_matrix


# Compute the distances to depot
def compute_distance_depots(depot_x, depot_y, customers_x, customers_y):
    nb_customers = len(customers_x)
    distance_depots = [None] * nb_customers
    for i in range(nb_customers):
        dist = compute_dist(depot_x, customers_x[i], depot_y, customers_y[i])
        distance_depots[i] = dist
    return distance_depots


def compute_dist(xi, xj, yi, yj):
    exact_dist = math.sqrt(math.pow(xi - xj, 2) + math.pow(yi - yj, 2))
    return int(math.floor(exact_dist + 0.5))


if __name__ == '__main__':
    if len(sys.argv) < 2:
        print(
            "Usage: python vehicle_routing_backhauls.py input_file [output_file] [time_limit]")
        sys.exit(1)

    instance_file = sys.argv[1]
    output_file = sys.argv[2] if len(sys.argv) > 2 else None
    str_time_limit = sys.argv[3] if len(sys.argv) > 3 else "20"

    main(instance_file, str_time_limit, output_file)

#include "optimizer/hexalyoptimizer.h"
#include <cmath>
#include <cstring>
#include <fstream>
#include <iostream>
#include <vector>

using namespace hexaly;
using namespace std;

class VehicleRoutingWithBackhauls
{
public:
    // Hexaly Optimizer
    HexalyOptimizer optimizer;

    // Number of customers
    int nbCustomers;

    // Capacity of the trucks
    int truckCapacity;

    // Demand on each customer
    vector<int> pickupDemandsData;
    vector<int> deliveryDemandsData;

    // Type of each customer
    vector<int> isBackhaulData;

    // Distance matrix between customers
    vector<vector<int>> distMatrixData;

    // Distances between customers and depot
    vector<int> distDepotData;

    // Number of trucks
    int nbTrucks;

    // Decision variables
    vector<HxExpression> customersSequences;

    // Are the trucks actually used
    vector<HxExpression> trucksUsed;

    // Number of trucks used in the solution
    HxExpression nbTrucksUsed;

    // Distance traveled by all the trucks
    HxExpression totalDistance;

    /* Read instance data */
    void readInstance(const string &fileName)
    {
        readInputVrpb(fileName);
    }

    void solve(int limit)
    {
        // Declare the optimization model
        HxModel model = optimizer.getModel();

        // Sequence of customers visited by each truck
        customersSequences.resize(nbTrucks);
        for (int k = 0; k < nbTrucks; ++k)
        {
            customersSequences[k] = model.listVar(nbCustomers);
        }

        // All customers must be visited by exactly one truck
        model.constraint(model.partition(customersSequences.begin(), customersSequences.end()));

        // Create Hexaly arrays to be able to access them with an "at" operator
        HxExpression deliveryDemands = model.array(deliveryDemandsData.begin(), deliveryDemandsData.end());
        HxExpression pickupDemands = model.array(pickupDemandsData.begin(), pickupDemandsData.end());
        HxExpression isBackhaul = model.array(isBackhaulData.begin(), isBackhaulData.end());
        HxExpression distMatrix = model.array();
        for (int n = 0; n < nbCustomers; ++n)
        {
            distMatrix.addOperand(model.array(distMatrixData[n].begin(), distMatrixData[n].end()));
        }
        HxExpression distDepot = model.array(distDepotData.begin(), distDepotData.end());

        trucksUsed.resize(nbTrucks);
        vector<HxExpression> distRoutes(nbTrucks);

        for (int k = 0; k < nbTrucks; ++k)
        {
            HxExpression sequence = customersSequences[k];
            HxExpression c = model.count(sequence);

            // A truck is used if it visits at least one customer
            trucksUsed[k] = c > 0;

            // A pickup cannot be followed by a delivery
            HxExpression precedencyLambda =
                model.createLambdaFunction([&](HxExpression i)
                                           { return model.leq(model.at(isBackhaul, sequence[i - 1]), model.at(isBackhaul, sequence[i])); });
            model.constraint(model.and_(model.range(1, c), precedencyLambda));

            // The quantity needed in each route must not exceed the truck capacity
            HxExpression deliveryDemandLambda =
                model.createLambdaFunction([&](HxExpression j)
                                           { return deliveryDemands[j]; });
            HxExpression routeDeliveryQuantity = model.sum(sequence, deliveryDemandLambda);
            model.constraint(routeDeliveryQuantity <= truckCapacity);
            HxExpression pickupDemandLambda =
                model.createLambdaFunction([&](HxExpression j)
                                           { return pickupDemands[j]; });
            HxExpression routePickupQuantity = model.sum(sequence, pickupDemandLambda);
            model.constraint(routePickupQuantity <= truckCapacity);

            // Distance traveled by truck k
            HxExpression distLambda = model.createLambdaFunction(
                [&](HxExpression i)
                { return model.at(distMatrix, sequence[i - 1], sequence[i]); });
            distRoutes[k] = model.sum(model.range(1, c), distLambda) +
                            model.iif(c > 0, distDepot[sequence[0]] + distDepot[sequence[c - 1]], 0);
        }

        // Total number of trucks used
        nbTrucksUsed = model.sum(trucksUsed.begin(), trucksUsed.end());

        // Total distance traveled
        totalDistance = model.sum(distRoutes.begin(), distRoutes.end());

        // Objective: minimize the number of trucks used, then minimize the distance traveled
        model.minimize(nbTrucksUsed);
        model.minimize(totalDistance);

        model.close();

        // Parametrize the optimizer
        optimizer.getParam().setTimeLimit(limit);

        optimizer.solve();
    }

    /* Write the solution in a file with the following format:
     *  - number of trucks used and total distance
     *  - for each truck the customers visited (omitting the start/end at the depot) */
    void writeSolution(const string &fileName)
    {
        ofstream outfile;
        outfile.exceptions(ofstream::failbit | ofstream::badbit);
        outfile.open(fileName.c_str());

        outfile << nbTrucksUsed.getValue() << " " << totalDistance.getValue() << endl;
        for (int k = 0; k < nbTrucks; ++k)
        {
            if (trucksUsed[k].getValue() != 1)
                continue;
            // Values in sequence are in 0...nbCustomers. +2 is to put it back in 2...nbCustomers+2
            // as in the data files (1 being the depot)
            HxCollection customersCollection = customersSequences[k].getCollectionValue();
            for (int i = 0; i < customersCollection.count(); ++i)
            {
                outfile << customersCollection[i] + 2 << " ";
            }
            outfile << endl;
        }
    }

private:
    // The input files follow the "CVRPLib" format
    void readInputVrpb(const string &fileName)
    {
        ifstream infile(fileName.c_str());
        if (!infile.is_open())
        {
            throw std::runtime_error("File cannot be opened.");
        }

        string str;
        char *pch;
        char *line;
        int nbNodes;
        while (true)
        {
            getline(infile, str);
            line = strdup(str.c_str());
            pch = strtok(line, " :");
            if (strcmp(pch, "DIMENSION") == 0)
            {
                pch = strtok(NULL, " :");
                nbNodes = atoi(pch);
                nbCustomers = nbNodes - 1;
            }
            else if (strcmp(pch, "VEHICLES") == 0)
            {
                pch = strtok(NULL, " :");
                nbTrucks = atoi(pch);
            }
            else if (strcmp(pch, "CAPACITY") == 0)
            {
                pch = strtok(NULL, " :");
                truckCapacity = atoi(pch);
            }
            else if (strcmp(pch, "EDGE_WEIGHT_TYPE") == 0)
            {
                pch = strtok(NULL, " :");
                if (strcmp(pch, "EXACT_2D") != 0)
                {
                    throw std::runtime_error("Only Edge Weight Type EXACT_2D is supported");
                }
            }
            else if (strcmp(pch, "NODE_COORD_SECTION") == 0)
            {
                break;
            }
        }

        vector<int> customersX(nbCustomers);
        vector<int> customersY(nbCustomers);
        int depotX, depotY;
        for (int n = 1; n <= nbNodes; ++n)
        {
            int id;
            infile >> id;
            if (id != n)
            {
                throw std::runtime_error("Unexpected index");
            }
            if (n == 1)
            {
                infile >> depotX;
                infile >> depotY;
            }
            else
            {
                // -2 because original customer indices are in 2..nbNodes
                infile >> customersX[n - 2];
                infile >> customersY[n - 2];
            }
        }

        computeDistanceMatrix(depotX, depotY, customersX, customersY);

        getline(infile, str); // End the last line
        getline(infile, str);
        line = strdup(str.c_str());
        pch = strtok(line, " :");
        if (strcmp(pch, "DEMAND_SECTION") != 0)
        {
            throw std::runtime_error("Expected keyword DEMAND_SECTION");
        }

        vector<int> demandsData(nbCustomers);
        for (int n = 1; n <= nbNodes; ++n)
        {
            int id;
            infile >> id;
            if (id != n)
            {
                throw std::runtime_error("Unexpected index");
            }
            int demand;
            infile >> demand;
            if (n == 1)
            {
                if (demand != 0)
                {
                    throw std::runtime_error("Demand for depot should be O");
                }
            }
            else
            {
                // -2 because original customer indices are in 2..nbNodes
                demandsData[n - 2] = demand;
            }
        }

        isBackhaulData.resize(nbCustomers);
        fill(isBackhaulData.begin(), isBackhaulData.end(), 0);
        getline(infile, str); // End the last line
        getline(infile, str);
        line = strdup(str.c_str());
        pch = strtok(line, " :");
        if (strcmp(pch, "BACKHAUL_SECTION") != 0)
        {
            throw std::runtime_error("Expected keyword BACKHAUL_SECTION");
        }
        while (true)
        {
            int id;
            infile >> id;
            if (id == -1)
                break;
            // -2 because original customer indices are in 2..nbNodes
            isBackhaulData[id - 2] = 1;
        }

        deliveryDemandsData.resize(nbCustomers);
        pickupDemandsData.resize(nbCustomers);
        for (int i = 0; i <= nbCustomers; ++i)
        {
            if (isBackhaulData[i])
            {
                deliveryDemandsData[i] = 0;
                pickupDemandsData[i] = demandsData[i];
            }
            else
            {
                deliveryDemandsData[i] = demandsData[i];
                pickupDemandsData[i] = 0;
            }
        }

        getline(infile, str); // End the last line
        getline(infile, str);
        line = strdup(str.c_str());
        pch = strtok(line, " :");
        if (strcmp(pch, "DEPOT_SECTION") != 0)
        {
            throw std::runtime_error("Expected keyword DEPOT_SECTION");
        }

        int depotId;
        infile >> depotId;
        if (depotId != 1)
        {
            throw std::runtime_error("Depot id is supposed to be 1");
        }

        int endOfDepotSection;
        infile >> endOfDepotSection;
        if (endOfDepotSection != -1)
        {
            throw std::runtime_error("Expecting only one depot, more than one found");
        }

        infile.close();
    }

    // Compute the distance matrix
    void computeDistanceMatrix(int depotX, int depotY, const vector<int> &customersX, const vector<int> &customersY)
    {
        distMatrixData.resize(nbCustomers);
        for (int i = 0; i < nbCustomers; ++i)
        {
            distMatrixData[i].resize(nbCustomers);
        }
        for (int i = 0; i < nbCustomers; ++i)
        {
            distMatrixData[i][i] = 0;
            for (int j = i + 1; j < nbCustomers; ++j)
            {
                int distance = computeDist(customersX[i], customersX[j], customersY[i], customersY[j]);
                distMatrixData[i][j] = distance;
                distMatrixData[j][i] = distance;
            }
        }

        distDepotData.resize(nbCustomers);
        for (int i = 0; i < nbCustomers; ++i)
        {
            distDepotData[i] = computeDist(depotX, customersX[i], depotY, customersY[i]);
        }
    }

    int computeDist(int xi, int xj, int yi, int yj)
    {
        double exactDist = sqrt(pow((double)xi - xj, 2) + pow((double)yi - yj, 2));
        return floor(exactDist + 0.5);
    }
};

int main(int argc, char **argv)
{
    if (argc < 2)
    {
        cerr << "Usage: vehicle_routing_backhauls inputFile [outputFile] [timeLimit]" << endl;
        return 1;
    }

    const char *instanceFile = argv[1];
    const char *solFile = argc > 2 ? argv[2] : NULL;
    const char *strTimeLimit = argc > 3 ? argv[3] : "20";

    try
    {
        VehicleRoutingWithBackhauls model;
        model.readInstance(instanceFile);
        model.solve(atoi(strTimeLimit));
        if (solFile != NULL)
            model.writeSolution(solFile);
        return 0;
    }
    catch (const exception &e)
    {
        cerr << "An error occurred: " << e.what() << endl;
        return 1;
    }
}

using System;
using System.IO;
using Hexaly.Optimizer;

public class VehicleRoutingWithBackhauls : IDisposable
{
    // Hexaly Optimizer
    HexalyOptimizer optimizer;

    // Number of customers
    int nbCustomers;

    // Capacity of the trucks
    int truckCapacity;

    // Demand on each customer
    long[] deliveryDemandsData;
    long[] pickupDemandsData;

    // Type of each customer
    int[] isBackhaulData;

    // Distance matrix between customers
    long[][] distMatrixData;

    // Distances between customers and depot
    long[] distDepotData;

    // Number of trucks
    int nbTrucks;

    // Decision variables
    HxExpression[] customersSequences;

    // Are the trucks actually used
    HxExpression[] trucksUsed;

    // Number of trucks used in the solution
    HxExpression nbTrucksUsed;

    // Distance traveled by all the trucks
    HxExpression totalDistance;

    public VehicleRoutingWithBackhauls()
    {
        optimizer = new HexalyOptimizer();
    }

    /* Read instance data */
    void ReadInstance(string fileName)
    {
        ReadInputVrpb(fileName);
    }

    public void Dispose()
    {
        if (optimizer != null)
            optimizer.Dispose();
    }

    void Solve(int limit)
    {
        // Declare the optimization model
        HxModel model = optimizer.GetModel();

        trucksUsed = new HxExpression[nbTrucks];
        customersSequences = new HxExpression[nbTrucks];
        HxExpression[] distRoutes = new HxExpression[nbTrucks];

        // Sequence of customers visited by each truck
        for (int k = 0; k < nbTrucks; ++k)
            customersSequences[k] = model.List(nbCustomers);

        // All customers must be visited by exactly one truck
        model.Constraint(model.Partition(customersSequences));

        // Create HexalyOptimizer arrays to be able to access them with an "at" operator
        HxExpression deliveryDemands = model.Array(deliveryDemandsData);
        HxExpression pickupDemands = model.Array(pickupDemandsData);
        HxExpression isBackhaul = model.Array(isBackhaulData);
        HxExpression distDepot = model.Array(distDepotData);
        HxExpression distMatrix = model.Array(distMatrixData);

        for (int k = 0; k < nbTrucks; ++k)
        {
            HxExpression sequence = customersSequences[k];
            HxExpression c = model.Count(sequence);

            // A truck is used if it visits at least one customer
            trucksUsed[k] = c > 0;

            // A pickup cannot be followed by a delivery
            HxExpression precedencyLambda = model.LambdaFunction(
                i => isBackhaul[sequence[i - 1]] <= isBackhaul[sequence[i]]
            );
            model.Constraint(model.And(model.Range(1, c), precedencyLambda));

            // The quantity needed in each route must not exceed the truck capacity
            HxExpression deliveryDemandLambda = model.LambdaFunction(j => deliveryDemands[j]);
            HxExpression routeDeliveryQuantity = model.Sum(sequence, deliveryDemandLambda);
            model.Constraint(routeDeliveryQuantity <= truckCapacity);
            HxExpression pickupDemandLambda = model.LambdaFunction(j => pickupDemands[j]);
            HxExpression routePickupQuantity = model.Sum(sequence, pickupDemandLambda);
            model.Constraint(routePickupQuantity <= truckCapacity);

            // Distance traveled by truck k
            HxExpression distLambda = model.LambdaFunction(
                i => distMatrix[sequence[i - 1], sequence[i]]
            );
            distRoutes[k] =
                model.Sum(model.Range(1, c), distLambda)
                + model.If(c > 0, distDepot[sequence[0]] + distDepot[sequence[c - 1]], 0);
        }

        nbTrucksUsed = model.Sum(trucksUsed);
        totalDistance = model.Sum(distRoutes);

        // Objective: minimize the number of trucks used, then minimize the distance traveled
        model.Minimize(nbTrucksUsed);
        model.Minimize(totalDistance);

        model.Close();

        // Parametrize the optimizer
        optimizer.GetParam().SetTimeLimit(limit);

        optimizer.Solve();
    }

    /* Write the solution in a file with the following format:
     *  - number of trucks used and total distance
     *  - for each truck the customers visited (omitting the start/end at the depot) */
    void WriteSolution(string fileName)
    {
        using (StreamWriter output = new StreamWriter(fileName))
        {
            output.WriteLine(nbTrucksUsed.GetValue() + " " + totalDistance.GetValue());
            for (int k = 0; k < nbTrucks; ++k)
            {
                if (trucksUsed[k].GetValue() != 1)
                    continue;
                // Values in sequence are in 0...nbCustomers. +2 is to put it back in 2...nbCustomers+2
                // as in the data files (1 being the depot)
                HxCollection customersCollection = customersSequences[k].GetCollectionValue();
                for (int i = 0; i < customersCollection.Count(); ++i)
                    output.Write((customersCollection[i] + 2) + " ");
                output.WriteLine();
            }
        }
    }

    public static void Main(string[] args)
    {
        if (args.Length < 1)
        {
            Console.WriteLine("Usage: VehicleRoutingWithBackhauls inputFile [solFile] [timeLimit]");
            Environment.Exit(1);
        }
        string instanceFile = args[0];
        string outputFile = args.Length > 1 ? args[1] : null;
        string strTimeLimit = args.Length > 2 ? args[2] : "20";

        using (VehicleRoutingWithBackhauls model = new VehicleRoutingWithBackhauls())
        {
            model.ReadInstance(instanceFile);
            model.Solve(int.Parse(strTimeLimit));
            if (outputFile != null)
                model.WriteSolution(outputFile);
        }
    }

    // The input files follow the "CVRPLib" format
    private void ReadInputVrpb(string fileName)
    {
        using (StreamReader input = new StreamReader(fileName))
        {
            int nbNodes = 0;
            string[] splitted;
            while (true)
            {
                splitted = input.ReadLine().Split(':');
                if (splitted[0].Contains("DIMENSION"))
                {
                    nbNodes = int.Parse(splitted[1]);
                    nbCustomers = nbNodes - 1;
                }
                else if (splitted[0].Contains("VEHICLES"))
                    nbTrucks = int.Parse(splitted[1]);
                else if (splitted[0].Contains("CAPACITY"))
                    truckCapacity = int.Parse(splitted[1]);
                else if (splitted[0].Contains("EDGE_WEIGHT_TYPE"))
                {
                    if (!splitted[1].Trim().Equals("EXACT_2D"))
                        throw new Exception(
                            "Edge Weight Type " + splitted[1] + " is not supported (only EXACT_2D)"
                        );
                }
                else if (splitted[0].Contains("NODE_COORD_SECTION"))
                    break;
            }
            int[] customersX = new int[nbCustomers];
            int[] customersY = new int[nbCustomers];
            int depotX = 0,
                depotY = 0;
            for (int n = 1; n <= nbNodes; ++n)
            {
                splitted = input
                    .ReadLine()
                    .Split((char[])null, StringSplitOptions.RemoveEmptyEntries);
                if (int.Parse(splitted[0]) != n)
                    throw new Exception("Unexpected index");
                if (n == 1)
                {
                    depotX = int.Parse(splitted[1]);
                    depotY = int.Parse(splitted[2]);
                }
                else
                {
                    // -2 because original customer indices are in 2..nbNodes
                    customersX[n - 2] = int.Parse(splitted[1]);
                    customersY[n - 2] = int.Parse(splitted[2]);
                }
            }

            ComputeDistanceMatrix(depotX, depotY, customersX, customersY);

            splitted = input.ReadLine().Split(':');
            if (!splitted[0].Contains("DEMAND_SECTION"))
                throw new Exception("Expected keyword DEMAND_SECTION");

            long[] demandsData = new long[nbCustomers];
            for (int n = 1; n <= nbNodes; ++n)
            {
                splitted = input
                    .ReadLine()
                    .Split((char[])null, StringSplitOptions.RemoveEmptyEntries);
                if (int.Parse(splitted[0]) != n)
                    throw new Exception("Unexpected index");
                var demand = int.Parse(splitted[1]);
                if (n == 1)
                {
                    if (demand != 0)
                        throw new Exception("Depot demand is supposed to be 0");
                }
                else
                {
                    // -2 because original customer indices are in 2..nbNodes
                    demandsData[n - 2] = demand;
                }
            }

            splitted = input.ReadLine().Split(':');
            if (!splitted[0].Contains("BACKHAUL_SECTION"))
                throw new Exception("Expected keyword BACKHAUL_SECTION");

            isBackhaulData = new int[nbCustomers];
            splitted = input.ReadLine().Split((char[])null, StringSplitOptions.RemoveEmptyEntries);
            foreach (var item in splitted)
            {
                var node_id = int.Parse(item);
                if (node_id == -1)
                    continue;
                // -2 because original customer indices are in 2..nbNodes
                isBackhaulData[node_id - 2] = 1;
            }

            deliveryDemandsData = new long[nbCustomers];
            pickupDemandsData = new long[nbCustomers];
            for (int i = 0; i < nbCustomers; ++i)
            {
                if (isBackhaulData[i] == 1)
                {
                    pickupDemandsData[i] = demandsData[i];
                }
                else
                {
                    deliveryDemandsData[i] = demandsData[i];
                }
            }

            splitted = input.ReadLine().Split(':');
            if (!splitted[0].Contains("DEPOT_SECTION"))
                throw new Exception("Expected keyword DEPOT_SECTION");

            int depotId = int.Parse(input.ReadLine());
            if (depotId != 1)
                throw new Exception("Depot id is supposed to be 1");

            int endOfDepotSection = int.Parse(input.ReadLine());
            if (endOfDepotSection != -1)
                throw new Exception("Expecting only one depot, more than one found");
        }
    }

    // Compute the distance matrix
    private void ComputeDistanceMatrix(int depotX, int depotY, int[] customersX, int[] customersY)
    {
        distMatrixData = new long[nbCustomers][];
        for (int i = 0; i < nbCustomers; ++i)
            distMatrixData[i] = new long[nbCustomers];

        for (int i = 0; i < nbCustomers; ++i)
        {
            distMatrixData[i][i] = 0;
            for (int j = i + 1; j < nbCustomers; ++j)
            {
                long dist = ComputeDist(customersX[i], customersX[j], customersY[i], customersY[j]);
                distMatrixData[i][j] = dist;
                distMatrixData[j][i] = dist;
            }
        }

        distDepotData = new long[nbCustomers];
        for (int i = 0; i < nbCustomers; ++i)
            distDepotData[i] = ComputeDist(depotX, customersX[i], depotY, customersY[i]);
    }

    private long ComputeDist(int xi, int xj, int yi, int yj)
    {
        double exactDist = Math.Sqrt(Math.Pow(xi - xj, 2) + Math.Pow(yi - yj, 2));
        return Convert.ToInt64(Math.Round(exactDist));
    }
}

import java.util.*;

import org.w3c.dom.ls.LSException;

import java.io.*;
import com.hexaly.optimizer.*;

public class VehicleRoutingWithBackhauls {
    // Hexaly Optimizer
    private final HexalyOptimizer optimizer;

    // Number of customers
    int nbCustomers;

    // Capacity of the trucks
    private int truckCapacity;

    // Demand on each customer
    private long[] deliveryDemandsData;
    private long[] pickupDemandsData;

    // Type of each customer
    private int[] isBackhaulData;

    // Distance matrix between customers
    private long[][] distMatrixData;

    // Distances between customers and depot
    private long[] distDepotData;

    // Number of trucks
    private int nbTrucks;

    // Decision variables
    private HxExpression[] customersSequences;

    // Are the trucks actually used
    private HxExpression[] trucksUsed;

    // Number of trucks used in the solution
    private HxExpression nbTrucksUsed;

    // Distance traveled by all the trucks
    private HxExpression totalDistance;

    private VehicleRoutingWithBackhauls(HexalyOptimizer optimizer) {
        this.optimizer = optimizer;
    }

    private void solve(int limit) {
        // Declare the optimization model
        HxModel model = optimizer.getModel();

        trucksUsed = new HxExpression[nbTrucks];
        customersSequences = new HxExpression[nbTrucks];
        HxExpression[] distRoutes = new HxExpression[nbTrucks];

        // Sequence of customers visited by each truck
        for (int k = 0; k < nbTrucks; ++k)
            customersSequences[k] = model.listVar(nbCustomers);

        // All customers must be visited by exactly one truck
        model.constraint(model.partition(customersSequences));

        // Create HexalyOptimizer arrays to be able to access them with an "at" operator
        HxExpression deliveryDemands = model.array(deliveryDemandsData);
        HxExpression pickupDemands = model.array(pickupDemandsData);
        HxExpression isBackhaul = model.array(isBackhaulData);
        HxExpression distDepot = model.array(distDepotData);
        HxExpression distMatrix = model.array(distMatrixData);

        for (int k = 0; k < nbTrucks; ++k) {
            HxExpression sequence = customersSequences[k];
            HxExpression c = model.count(sequence);

            // A truck is used if it visits at least one customer
            trucksUsed[k] = model.gt(c, 0);

            // A pickup cannot be followed by a delivery
            HxExpression precedencyLambda = model.lambdaFunction(
                    i -> model.leq(
                            model.at(isBackhaul, model.at(sequence, model.sub(i, 1))),
                            model.at(isBackhaul, model.at(sequence, i))));
            model.constraint(model.and(model.range(1, c), precedencyLambda));

            // The quantity needed in each route must not exceed the truck capacity
            HxExpression deliveryDemandLambda = model.lambdaFunction(j -> model.at(deliveryDemands, j));
            HxExpression routeDeliveryQuantity = model.sum(sequence, deliveryDemandLambda);
            model.constraint(model.leq(routeDeliveryQuantity, truckCapacity));
            HxExpression pickupDemandLambda = model.lambdaFunction(j -> model.at(pickupDemands, j));
            HxExpression routePickupQuantity = model.sum(sequence, pickupDemandLambda);
            model.constraint(model.leq(routePickupQuantity, truckCapacity));

            // Distance traveled by truck k
            HxExpression distLambda = model
                    .lambdaFunction(
                            i -> model.at(distMatrix, model.at(sequence, model.sub(i, 1)), model.at(sequence, i)));
            distRoutes[k] = model.sum(model.sum(model.range(1, c), distLambda),
                    model.iif(model.gt(c, 0), model.sum(model.at(distDepot, model.at(sequence, 0)),
                            model.at(distDepot, model.at(sequence, model.sub(c, 1)))), 0));
        }

        nbTrucksUsed = model.sum(trucksUsed);
        totalDistance = model.sum(distRoutes);

        // Objective: minimize the number of trucks used, then minimize the distance
        // traveled
        model.minimize(nbTrucksUsed);
        model.minimize(totalDistance);

        model.close();

        // Parametrize the optimizer
        optimizer.getParam().setTimeLimit(limit);

        optimizer.solve();
    }

    /*
     * Write the solution in a file with the following format:
     * - number of trucks used and total distance
     * - for each truck the customers visited (omitting the start/end at the depot)
     */
    private void writeSolution(String fileName) throws IOException {
        try (PrintWriter output = new PrintWriter(fileName)) {
            output.println(nbTrucksUsed.getValue() + " " + totalDistance.getValue());
            for (int k = 0; k < nbTrucks; ++k) {
                if (trucksUsed[k].getValue() != 1)
                    continue;
                // Values in sequence are in 0...nbCustomers. +2 is to put it back in
                // 2...nbCustomers as in the data files (1 being the depot)
                HxCollection customersCollection = customersSequences[k].getCollectionValue();
                for (int i = 0; i < customersCollection.count(); ++i) {
                    output.print((customersCollection.get(i) + 2) + " ");
                }
                output.println();
            }
        }
    }

    // The input files follow the "CVRPLib" format
    private void readInstance(String fileName) throws IOException {
        try (Scanner input = new Scanner(new File(fileName))) {
            int nbNodes = 0;
            String[] splitted;
            while (true) {
                splitted = input.nextLine().split(":");
                if (splitted[0].contains("DIMENSION")) {
                    nbNodes = Integer.parseInt(splitted[1].trim());
                    nbCustomers = nbNodes - 1;
                } else if (splitted[0].contains("VEHICLES")) {
                    nbTrucks = Integer.parseInt(splitted[1].trim());
                } else if (splitted[0].contains("CAPACITY")) {
                    truckCapacity = Integer.parseInt(splitted[1].trim());
                } else if (splitted[0].contains("EDGE_WEIGHT_TYPE")) {
                    if (splitted[1].trim().compareTo("EXACT_2D") != 0) {
                        throw new RuntimeException(
                                "Edge Weight Type " + splitted[1] + " is not supported (only EXACT_2D)");
                    }
                } else if (splitted[0].contains("NODE_COORD_SECTION")) {
                    break;
                }
            }

            int[] customersX = new int[nbCustomers];
            int[] customersY = new int[nbCustomers];
            int depotX = 0, depotY = 0;
            for (int n = 1; n <= nbNodes; ++n) {
                int id = input.nextInt();
                if (id != n)
                    throw new IOException("Unexpected index");
                if (n == 1) {
                    depotX = input.nextInt();
                    depotY = input.nextInt();
                } else {
                    // -2 because original customer indices are in 2..nbNodes
                    customersX[n - 2] = input.nextInt();
                    customersY[n - 2] = input.nextInt();
                }
            }

            computeDistanceMatrix(depotX, depotY, customersX, customersY);

            input.nextLine().split(":"); // End the last line
            splitted = input.nextLine().split(":");
            if (!splitted[0].contains("DEMAND_SECTION")) {
                throw new RuntimeException("Expected keyword DEMAND_SECTION");
            }

            long[] demandsData = new long[nbCustomers];
            for (int n = 1; n <= nbNodes; ++n) {
                int id = input.nextInt();
                if (id != n)
                    throw new IOException("Unexpected index");
                int demand = input.nextInt();
                if (n == 1) {
                    if (demand != 0)
                        throw new IOException("Depot demand is supposed to be 0");
                } else {
                    // -2 because original customer indices are in 2..nbNodes
                    demandsData[n - 2] = demand;
                }
            }

            input.nextLine().split(":"); // End the last line
            splitted = input.nextLine().split(":");
            if (!splitted[0].contains("BACKHAUL_SECTION")) {
                throw new RuntimeException("Expected keyword DEPOT_SECTION");
            }

            isBackhaulData = new int[nbCustomers];
            while (true) {
                int id = input.nextInt();
                if (id == -1)
                    break;
                // -2 because original customer indices are in 2..nbNodes
                isBackhaulData[id - 2] = 1;
            }

            deliveryDemandsData = new long[nbCustomers];
            pickupDemandsData = new long[nbCustomers];
            for (int i = 0; i < nbCustomers; ++i) {
                if (isBackhaulData[i] == 1) {
                    pickupDemandsData[i] = demandsData[i];
                } else {
                    deliveryDemandsData[i] = demandsData[i];
                }
            }

            input.nextLine().split(":"); // End the last line
            splitted = input.nextLine().split(":");
            if (!splitted[0].contains("DEPOT_SECTION")) {
                throw new RuntimeException("Expected keyword DEPOT_SECTION");
            }

            int depotId = input.nextInt();
            if (depotId != 1)
                throw new IOException("Depot id is supposed to be 1");

            int endOfDepotSection = input.nextInt();
            if (endOfDepotSection != -1) {
                throw new RuntimeException("Expecting only one depot, more than one found");
            }
        }
    }

    // Compute the distance matrix
    private void computeDistanceMatrix(int depotX, int depotY, int[] customersX, int[] customersY) {
        distMatrixData = new long[nbCustomers][nbCustomers];
        for (int i = 0; i < nbCustomers; ++i) {
            distMatrixData[i][i] = 0;
            for (int j = i + 1; j < nbCustomers; ++j) {
                long dist = computeDist(customersX[i], customersX[j], customersY[i], customersY[j]);
                distMatrixData[i][j] = dist;
                distMatrixData[j][i] = dist;
            }
        }

        distDepotData = new long[nbCustomers];
        for (int i = 0; i < nbCustomers; ++i) {
            distDepotData[i] = computeDist(depotX, customersX[i], depotY, customersY[i]);
        }
    }

    private long computeDist(int xi, int xj, int yi, int yj) {
        double exactDist = Math.sqrt(Math.pow(xi - xj, 2) + Math.pow(yi - yj, 2));
        return Math.round(exactDist);
    }

    public static void main(String[] args) {
        if (args.length < 1) {
            System.err.println("Usage: java VehicleRoutingWithBackhauls inputFile [outputFile] [timeLimit]");
            System.exit(1);
        }

        try (HexalyOptimizer optimizer = new HexalyOptimizer()) {
            String instanceFile = args[0];
            String outputFile = args.length > 1 ? args[1] : null;
            String strTimeLimit = args.length > 2 ? args[2] : "20";

            VehicleRoutingWithBackhauls model = new VehicleRoutingWithBackhauls(optimizer);
            model.readInstance(instanceFile);
            model.solve(Integer.parseInt(strTimeLimit));
            if (outputFile != null) {
                model.writeSolution(outputFile);
            }
        } catch (Exception ex) {
            System.err.println(ex);
            ex.printStackTrace();
            System.exit(1);
        }
    }
}