work in progress ...

How to ... implement a new VRPEncoding

Goals

One way to implement a new VRP variant is by implementing a new VRPEncoding and new Operators. This is a suitable possibility if the VRP variant requires additional decision variables to optimize. Based on these new decision variables, new Operators for crossing and mutating solutions in the search process of algorithms (e.g. a Genetic Algorithm) are required.

A VRPEncoding is the representation of a solution candidate for a given ProblemInstance (see How to ... implement a new VRP ProblemInstance?). There are different ways of representing and operating on tours of a VRP solution. (​source) Different Encodings require different Operators to work on. This way of extending the vehicle routing problem allows you to modify the search process and yielding results with additinal decition variables.

After this tutorial you will be able to implement you own VRP variants that require additional decision variables. You will also have a basic understanding of the concepts and architecture concerning the VRPEncoding, the VRPOperator concepts and related components.

The Multi Trip Vehicle Routing Problem

To show the procedure of implementing a new VRPEncoding, the implementation of the Multi Trip Vehicle Routing Problem (MTVRP) (​source) is demonstrated. The MTVRP allows vehicles to return to the depot, refill their cargo and therefore can satisfy multiple tours. In addition the maximum driving distance of each vehicle is limited. Usually MTVRP solutions require much fewer vehicles compared to standard VRP variants because a vehicle can drive multiple tours.

In this tutorial, the MTVRP is based on the Capacitated Vehicle Routing Problem (CVRP). In addition we have to specify the maximum distance a vehicle can drive as well the penalty for exceeding the maximum distance.

To implement the new Encoding we extend the existing PotvingEncoding (​source). In addition, the available operators for the PotvinEncoding will be extended in order to make use of the new data in the encoding. The advantage of extending an existing encoding is that we can reuse the original operators in the algorithm. If you like to implement a complete new encoding you also have to implement all operators yourself.

Prerequisites

Before you start, make sure you have the latest version of the HeuristicLab source code ready. Then create a new plugin called HeuristicLab.MultiTripVRP. For additional help for creating a new plugin, see How to ... create HeuristicLab plugins (step by step)?.

Your plugin need an additional dependency onto the HeuristicLab.Problems.VehicleRouting plugin. The plugin should look like this:

[Plugin("HeuristicLab.MultiTripVRP", "1.0.0.0")]
[PluginFile("HeuristicLab.MultiTripVRP.dll", PluginFileType.Assembly)]
[PluginDependency("HeuristicLab.Problems.VehicleRouting", "3.4")]
public class MultiTripVRPPlugin : PluginBase {
}

In addition you will need references onto following HeuristicLab assemblies:

• HeuristicLab.Collections
• HeuristicLab.Common
• HeuristicLab.Core
• HeuristicLab.Data
• HeuristicLab.Encodings.PermutationEncoding
• HeuristicLab.Operators
• HeuristicLab.Optimization
• HeuristicLab.Parameters
• HeuristicLab.Persistence
• HeuristicLab.Problems.VehicleRouting

Implementing new Encoding

The first thing to do is to create the new encoding. If you want to implement a whole new encoding, you start by deriving from TourEncoding. Then you have to store the assignments vehicles to tours as well as additional data, like our tour delimiters for the multi trip VRP. In the case of this tutorial we derive from the existing PotvinEncoding which stores the vehicle assignments already.

[Item("MultiTripEncoding", "Represents a potvin encoding of VRP solutions adapted for multi trip VRPs.")]
[StorableClass]
public class MultiTripEncoding
  : PotvinEncoding {
 
  [StorableConstructor]
  protected MultiTripEncoding(bool serializing)
    : base(serializing) {
  }
 
  public override IDeepCloneable Clone(Cloner cloner) {
    return new MultiTripEncoding(this, cloner);
  }
 
  [StorableHook(HookType.AfterDeserialization)]
  private void AfterDeserialization() {
    AttachEventHandlers();
  }
}

To implement the multi trip VRP we need to store when a tour is interrupted and the vehicle drives back to the depot. We store this information in a List<list<bool>> which indicates whether the tour is interrupted after the stop or not. A more compact possibility is to store the delimiters as bit in an integer, but then you are limited by the size of an integer (32 bit).

[Storable]
public List<List<bool>> TripDelimiters { get; private set; }
 
public MultiTripEncoding(IVRPProblemInstance instance)
  : base(instance) {
  TripDelimiters = new List<List<bool>>();
  AttachEventHandlers();
}

protected MultiTripEncoding(MultiTripEncoding original, Cloner cloner)
  : base(original, cloner) {
  TripDelimiters = new List<List<bool>>(original.TripDelimiters.Count);
  foreach (var delimiters in original.TripDelimiters) {
    TripDelimiters.Add(new List<bool>(delimiters));
  }
}

protected MultiTripEncoding(MultiTripEncoding original, Cloner cloner)
  : base(original, cloner) {
  TripDelimiters = new List<List<bool>>(original.TripDelimiters.Count);
  foreach (var delimiters in original.TripDelimiters) {
    TripDelimiters.Add(new List<bool>(delimiters));
  }
}

In order to keep the delimiters synchronized with the actual tours we need to register event handlers on the Tours collection. When a tour is added or removed we also have to add or remove the delimiters.

private void AttachEventHandlers() {
  Tours.ItemsAdded += new CollectionItemsChangedEventHandler<IndexedItem<Tour>>(Tours_ItemsAdded);
  Tours.ItemsRemoved += new CollectionItemsChangedEventHandler<IndexedItem<Tour>>(Tours_ItemsRemoved);
}
 
void Tours_ItemsAdded(object sender, CollectionItemsChangedEventArgs<IndexedItem<Tour>> e) {
  foreach (var added in e.Items.Except(e.OldItems).OrderBy(x => x.Index)) {
    TripDelimiters.Insert(added.Index, new List<bool>());
  }
}
 
void Tours_ItemsRemoved(object sender, CollectionItemsChangedEventArgs<IndexedItem<Tour>> e) {
  foreach (var removed in e.OldItems.Except(e.Items).OrderByDescending(x => x.Index)) {
    TripDelimiters.RemoveAt(removed.Index);
  }
}

In addition we implement a method for retrieving the delimiters for a tour as array, and to flip a delimiter on specific position in a tour. These methods are used for the VRPOperators and the VRPEvaluator later. We also specify a method for converting an existing PotvinEncoding and new delimiters to a new MultiTripEncoding.

public bool[] GetDelimiters(int tour) {
  if (tour < TripDelimiters.Count) {
    return TripDelimiters[tour].ToArray();
  } else {
    return new bool[0];
  }
}
 
public void FlipDelimiter(int tour, int index) {
  if (tour < TripDelimiters.Count) {
    if (TripDelimiters[tour].Count <= index) {
      for (int i = TripDelimiters[tour].Count; i <= index; i++) {
        TripDelimiters[tour].Add(false);
      }
    }
 
    TripDelimiters[tour][index] = !TripDelimiters[tour][index];
  }
}

public static MultiTripEncoding ConvertFrom(IVRPProblemInstance instance, PotvinEncoding orig, List<List<bool>> tripDelimiters = null) {
  MultiTripEncoding result = new MultiTripEncoding(instance);
 
  result.Tours.AddRange(orig.Tours);
  for (int i = 0; i < result.Tours.Count; i++) {
    result.VehicleAssignment[i] = orig.VehicleAssignment[i];
  }
 
  if (tripDelimiters != null)
    result.TripDelimiters = tripDelimiters;
 
  return result;
}

Sample Foundations

In order to implement the sample we need a new ProblemInstance and a new Evaluator for the MultiTrip VRP variant. For detailed information about creating new VRPInstances and VRPEvaluators see How to ... implement a new VRP ProblemInstance? and How to ... implement a new VRP Evaluator?.

MultiTripVRPInstance

The MultiTripVRPInstance only needs to store the additional MaxDistance parameter for the vehicle as well as the penalty for exceeding it.

public interface IMultiTripProblemInstance {
  DoubleValue MaxDistance { get; set; }
  DoubleValue MaxDistancePenalty { get; set; }
}

For the implementation the usual HL specific cloning and persistence code is necessary.

[Item("MultiTripVRPInstance", "Represents a single depot multi trip CVRP instance.")]
[StorableClass]
public class MultiTripVRPInstance : CVRPProblemInstance, IMultiTripProblemInstance {
  protected IValueParameter<DoubleValue> MaxDistanceParameter {
    get { return (IValueParameter<DoubleValue>)Parameters["MaxDistance"]; }
  }
 
  public DoubleValue MaxDistance {
    get { return MaxDistanceParameter.Value; }
    set { MaxDistanceParameter.Value = value; }
  }
 
  protected IValueParameter<DoubleValue> MaxDistancePenaltyParameter {
    get { return (IValueParameter<DoubleValue>)Parameters["MaxDistancePenalty"]; }
  }
 
  public DoubleValue MaxDistancePenalty {
    get { return MaxDistancePenaltyParameter.Value; }
    set { MaxDistancePenaltyParameter.Value = value; }
  }
 
  [StorableConstructor]
  protected MultiTripVRPInstance(bool deserializing) : base(deserializing) { }
 
  public MultiTripVRPInstance() {
    Parameters.Add(new ValueParameter<DoubleValue>("MaxDistance", "The max distance of each vehicle.", new DoubleValue(100)));
    Parameters.Add(new ValueParameter<DoubleValue>("MaxDistancePenalty", "The distance penalty considered in the evaluation.", new DoubleValue(100)));
 
    AttachEventHandlers();
  }
 
  public override IDeepCloneable Clone(Cloner cloner) {
    return new MultiTripVRPInstance(this, cloner);
  }
 
  protected MultiTripVRPInstance(MultiTripVRPInstance original, Cloner cloner)
    : base(original, cloner) {
    AttachEventHandlers();
  }
 
  [StorableHook(HookType.AfterDeserialization)]
  private void AfterDeserialization() {
    AttachEventHandlers();
  }
 
  private void AttachEventHandlers() {
    MaxDistanceParameter.ValueChanged += new EventHandler(MaxDistanceParameter_ValueChanged);
    MaxDistancePenaltyParameter.ValueChanged += new EventHandler(MaxDistancePenaltyParameter_ValueChanged);
  }
 
  void MaxDistancePenaltyParameter_ValueChanged(object sender, EventArgs e) {
    MaxDistancePenaltyParameter.Value.ValueChanged += new EventHandler(ValueChanged);
    EvalBestKnownSolution();
  }
 
  void MaxDistanceParameter_ValueChanged(object sender, EventArgs e) {
    MaxDistanceParameter.Value.ValueChanged += new EventHandler(ValueChanged);
    EvalBestKnownSolution();
  }
 
  void ValueChanged(object sender, EventArgs e) {
    EvalBestKnownSolution();
  }
 }

We will override more methods in the MultiTripProblemInstance class when we deal with operators in this tutorial later.

MultiTripEvaluator

For the evaluator we copy the CVRPEvaluator and modify it. Now we consider the travel distance after a stopover on the depot and calculate the maximum distance violation.

public class MultiTripEvaluation : CVRPEvaluation {
  public double MaxDistanceViolation { get; set; }
}
 
[Item("MultiTripEvaluator", "Represents a single depot CVRP evaluator with multiple trips.")]
[StorableClass]
public class MultiTripEvaluator : CVRPEvaluator {
  public ILookupParameter<DoubleValue> MaxDistanceViolationParameter {
    get { return (ILookupParameter<DoubleValue>)Parameters["MaxDistanceViolation"]; }
  }
 
  protected override VRPEvaluation CreateTourEvaluation() {
    return new MultiTripEvaluation();
  }
  
  protected override void InitResultParameters() {
    base.InitResultParameters();
 
    MaxDistanceViolationParameter.ActualValue = new DoubleValue(0);
  }
 
  protected override void SetResultParameters(VRPEvaluation tourEvaluation) {
    base.SetResultParameters(tourEvaluation);
 
    MaxDistanceViolationParameter.ActualValue.Value = (tourEvaluation as MultiTripEvaluation).MaxDistanceViolation;
  }
 
  [StorableConstructor]
  protected MultiTripEvaluator(bool deserializing) : base(deserializing) { }
 
  public MultiTripEvaluator() {
    Parameters.Add(new LookupParameter<DoubleValue>("MaxDistanceViolation", "The distance violation."));
  }
 
  public override IDeepCloneable Clone(Cloner cloner) {
    return new MultiTripEvaluator(this, cloner);
  }
 
  protected MultiTripEvaluator(MultiTripEvaluator original, Cloner cloner)
    : base(original, cloner) {
  }
}

In the evaluation process we need to consider the additional travel distance after a vehicle drives back to the depot. Therefore we add the distance from the current stop to the depot and the distance between the depot and the next stop instead of the direct distance.

After a tour we have to check the maximum driven distance whether it exceeds the maximum driven distance of a vehicle or not. In case of a violation of the limit we increment the penalty.

protected override void EvaluateTour(VRPEvaluation eval, IVRPProblemInstance instance, Tour tour, IVRPEncoding solution) {
  TourInsertionInfo tourInfo = new TourInsertionInfo(solution.GetVehicleAssignment(solution.GetTourIndex(tour))); ;
  eval.InsertionInfo.AddTourInsertionInfo(tourInfo);
  double originalQuality = eval.Quality;
 
  IHomogenousCapacitatedProblemInstance cvrpInstance = instance as IHomogenousCapacitatedProblemInstance;
  MultiTripVRPInstance multiTripInstance = instance as MultiTripVRPInstance;
  DoubleArray demand = instance.Demand;
 
  double overweight = 0.0;
  double distance = 0.0;
 
  double capacity = cvrpInstance.Capacity.Value;
  double spareCapacity = capacity;
 
  var tripDelimiters = new bool[0];
  if(solution is MultiTripEncoding)
    tripDelimiters = ((MultiTripEncoding)solution).GetDelimiters(solution.GetTourIndex(tour));
 
  //simulate a tour, start and end at depot
  for (int i = 0; i <= tour.Stops.Count; i++) {
    int start = 0;
    if (i > 0)
      start = tour.Stops[i - 1];
    int end = 0;
    if (i < tour.Stops.Count)
      end = tour.Stops[i];
 
    //drive there
    double currentDistace = 0;
 
    if (i > 0 && tripDelimiters.Length >= i && tripDelimiters[i - 1]) {
      currentDistace += instance.GetDistance(start, 0, solution);
      currentDistace += instance.GetDistance(0, end, solution);
 
      spareCapacity = capacity;
    } else {
      currentDistace += instance.GetDistance(start, end, solution);
    }
    distance += currentDistace;
 
    spareCapacity -= demand[end];
    if (spareCapacity < 0) {
      overweight += -spareCapacity;
      spareCapacity = 0;
    }
 
    CVRPInsertionInfo stopInfo = new CVRPInsertionInfo(start, end, spareCapacity);
    tourInfo.AddStopInsertionInfo(stopInfo);
  }
 
  eval.Quality += instance.FleetUsageFactor.Value;
  eval.Quality += instance.DistanceFactor.Value * distance;
 
  eval.Distance += distance;
  eval.VehicleUtilization += 1;
 
  (eval as CVRPEvaluation).Overload += overweight;
  double penalty = overweight * cvrpInstance.OverloadPenalty.Value;
  eval.Penalty += penalty;
  eval.Quality += penalty;
  tourInfo.Penalty = penalty;
  tourInfo.Quality = eval.Quality - originalQuality;
 
  if (distance > multiTripInstance.MaxDistance.Value) {
    double maxDistanceViolation = (distance - (multiTripInstance.MaxDistance.Value));
    penalty = maxDistanceViolation * multiTripInstance.MaxDistancePenalty.Value;
    eval.Penalty += penalty;
    eval.Quality += penalty;
    (eval as MultiTripEvaluation).MaxDistanceViolation += maxDistanceViolation;
  }
}

Because the increment based implementation is not trivial and not topic of this tutorial, we evaluate the tour at whole and calculate the distance to the previous solution.

protected override double GetTourInsertionCosts(IVRPProblemInstance instance, IVRPEncoding solution, TourInsertionInfo tourInsertionInfo, int index, int customer,
  out bool feasible) {
    if (!(solution is MultiTripEncoding)) {
      return base.GetTourInsertionCosts(instance, solution, tourInsertionInfo, index, customer, out feasible);
    } else {
      MultiTripEncoding individual = (solution as MultiTripEncoding);
 
      int tourIdx = -1;
      for (int i = 0; i < individual.Tours.Count; i++) {
        if (solution.GetVehicleAssignment(i) == tourInsertionInfo.Vehicle)
          tourIdx = i;
      }
      Tour tour = individual.Tours[tourIdx];
 
      tour.Stops.Insert(index, customer);
      VRPEvaluation newEval = instance.EvaluateTour(tour, individual);
      tour.Stops.RemoveAt(index);
 
      feasible = instance.Feasible(newEval);
      return newEval.Quality - tourInsertionInfo.Quality;
    }
}

Implementing new Operators

Foundations

Link Encoding/Operators to VRP variants

Implementing new MultiTripOperator

Implementing new Creator

Implementing new Manipulator

Implement new Crossover

Result

Configure Algorithm

Interpretation