/// <summary>
/// Calculates how much hypervolume each point dominates exclusively. The points
/// have to be transformed beforehand, to accommodate the assumptions of Zitzler's
/// hypervolume code.
/// </summary>
/// <param name="front">transformed objective values</param>
/// <returns>HV contributions</returns>
private double[] HvContributions(double[][] front)
{
int numberOfObjectives = Problem.NumberOfObjectives;
double[] contributions = new double[front.Length];
double[][] frontSubset = new double[front.Length - 1][];
for (int i = 0; i < front.Length - 1; i++)
{
frontSubset[i] = new double[front[0].Length];
}
List <double[]> frontCopy = new List <double[]>();
frontCopy.AddRange(front);
double[][] totalFront = frontCopy.ToArray <double[]>();
double totalVolume = hv.CalculateHypervolume(totalFront, totalFront.Length, numberOfObjectives);
for (int i = 0; i < front.Length; i++)
{
double[] evaluatedPoint = frontCopy[i];
frontCopy.RemoveAt(i);
frontSubset = frontCopy.ToArray <double[]>();
// STEP4. The hypervolume (control is passed to java version of Zitzler code)
double chv = hv.CalculateHypervolume(frontSubset, frontSubset.Length, numberOfObjectives);
double contribution = totalVolume - chv;
contributions[i] = contribution;
// put point back
frontCopy.Insert(i, evaluatedPoint);
}
return(contributions);
}
/// <summary>
/// Calculates the hv contribution of different populations. Receives an
/// array of populations and computes the contribution to HV of the
/// population consisting in the union of all of them
/// </summary>
/// <param name="archive"></param>
/// <param name="populations">Consisting in all the populatoins</param>
/// <returns>HV contributions of each population</returns>
public double[] HVContributions(SolutionSet archive, SolutionSet[] populations)
{
SolutionSet union;
int size = 0;
double offset_ = 0.0;
//determining the global size of the population
foreach (SolutionSet population in populations)
{
size += population.Size();
}
//allocating space for the union
union = archive;
//determining the number of objectives
int numberOfObjectives = union.Get(0).NumberOfObjectives;
//writing everything in matrices
double[][][] frontValues = new double[populations.Length + 1][][];
frontValues[0] = union.WriteObjectivesToMatrix();
for (int i = 0; i < populations.Length; i++)
{
if (populations[i].Size() > 0)
{
frontValues[i + 1] = populations[i].WriteObjectivesToMatrix();
}
else
{
frontValues[i + 1] = new double[0][];
}
}
// obtain the maximum and minimum values of the Pareto front
double[] maximumValues = GetMaximumValues(union.WriteObjectivesToMatrix(), numberOfObjectives);
double[] minimumValues = GetMinimumValues(union.WriteObjectivesToMatrix(), numberOfObjectives);
// normalized all the fronts
double[][][] normalizedFront = new double[populations.Length + 1][][];
for (int i = 0; i < normalizedFront.Length; i++)
{
if (frontValues[i].Length > 0)
{
normalizedFront[i] = GetNormalizedFront(frontValues[i], maximumValues, minimumValues);
}
else
{
normalizedFront[i] = new double[0][];
}
}
// compute offsets for reference point in normalized space
double[] offsets = new double[maximumValues.Length];
for (int i = 0; i < maximumValues.Length; i++)
{
offsets[i] = offset_ / (maximumValues[i] - minimumValues[i]);
}
//Inverse all the fronts front. This is needed because the original
//metric by Zitzler is for maximization problems
double[][][] invertedFront = new double[populations.Length + 1][][];
for (int i = 0; i < invertedFront.Length; i++)
{
if (normalizedFront[i].Length > 0)
{
invertedFront[i] = InvertedFront(normalizedFront[i]);
}
else
{
invertedFront[i] = new double[0][];
}
}
// shift away from origin, so that boundary points also get a contribution > 0
foreach (double[][] anInvertedFront in invertedFront)
{
foreach (double[] point in anInvertedFront)
{
for (int i = 0; i < point.Length; i++)
{
point[i] += offsets[i];
}
}
}
// calculate contributions
double[] contribution = new double[populations.Length];
HyperVolume hyperVolume = new HyperVolume();
for (int i = 0; i < populations.Length; i++)
{
if (invertedFront[i + 1].Length == 0)
{
contribution[i] = 0;
}
else
{
int auxSize = 0;
for (int j = 0; j < populations.Length; j++)
{
if (j != i)
{
auxSize += invertedFront[j + 1].Length;
}
}
if (size == archive.Size())
{ // the contribution is the maximum hv
contribution[i] = hyperVolume.CalculateHypervolume(invertedFront[0], invertedFront[0].Length, numberOfObjectives);
}
else
{
//make a front with all the populations but the target one
int index = 0;
double[][] aux = new double[auxSize][];
for (int j = 0; j < populations.Length; j++)
{
if (j != i)
{
for (int k = 0; k < populations[j].Size(); k++)
{
aux[index++] = invertedFront[j + 1][k];
}
}
}
contribution[i] = hyperVolume.CalculateHypervolume(invertedFront[0], invertedFront[0].Length, numberOfObjectives)
- hyperVolume.CalculateHypervolume(aux, aux.Length, numberOfObjectives);
}
}
}
return(contribution);
}
/// <summary>
/// Calculates the hv contribution of different populations. Receives an
/// array of populations and computes the contribution to HV of the
/// population consisting in the union of all of them
/// </summary>
/// <param name="populations">Consisting in all the populatoins</param>
/// <returns>HV contributions of each population</returns>
public double[] HVContributions(SolutionSet[] populations)
{
bool empty = true;
foreach (SolutionSet population2 in populations)
{
if (population2.Size() > 0)
{
empty = false;
}
}
if (empty)
{
double[] contributions = new double[populations.Length];
for (int i = 0; i < populations.Length; i++)
{
contributions[i] = 0;
}
for (int i = 0; i < populations.Length; i++)
{
Logger.Log.Info("Contributions: " + contributions[i]);
Console.WriteLine(contributions[i]);
}
return(contributions);
}
SolutionSet union;
int size = 0;
double offset_ = 0.0;
//determining the global size of the population
foreach (SolutionSet population1 in populations)
{
size += population1.Size();
}
//allocating space for the union
union = new SolutionSet(size);
// filling union
foreach (SolutionSet population in populations)
{
for (int j = 0; j < population.Size(); j++)
{
union.Add(population.Get(j));
}
}
//determining the number of objectives
int numberOfObjectives = union.Get(0).NumberOfObjectives;
//writing everything in matrices
double[][][] frontValues = new double[populations.Length + 1][][];
frontValues[0] = union.WriteObjectivesToMatrix();
for (int i = 0; i < populations.Length; i++)
{
if (populations[i].Size() > 0)
{
frontValues[i + 1] = populations[i].WriteObjectivesToMatrix();
}
else
{
frontValues[i + 1] = new double[0][];
}
}
// obtain the maximum and minimum values of the Pareto front
double[] maximumValues = GetMaximumValues(union.WriteObjectivesToMatrix(), numberOfObjectives);
double[] minimumValues = GetMinimumValues(union.WriteObjectivesToMatrix(), numberOfObjectives);
// normalized all the fronts
double[][][] normalizedFront = new double[populations.Length + 1][][];
for (int i = 0; i < normalizedFront.Length; i++)
{
if (frontValues[i].Length > 0)
{
normalizedFront[i] = GetNormalizedFront(frontValues[i], maximumValues, minimumValues);
}
else
{
normalizedFront[i] = new double[0][];
}
}
// compute offsets for reference point in normalized space
double[] offsets = new double[maximumValues.Length];
for (int i = 0; i < maximumValues.Length; i++)
{
offsets[i] = offset_ / (maximumValues[i] - minimumValues[i]);
}
//Inverse all the fronts front. This is needed because the original
//metric by Zitzler is for maximization problems
double[][][] invertedFront = new double[populations.Length + 1][][];
for (int i = 0; i < invertedFront.Length; i++)
{
if (normalizedFront[i].Length > 0)
{
invertedFront[i] = InvertedFront(normalizedFront[i]);
}
else
{
invertedFront[i] = new double[0][];
}
}
// shift away from origin, so that boundary points also get a contribution > 0
foreach (double[][] anInvertedFront in invertedFront)
{
foreach (double[] point in anInvertedFront)
{
for (int i = 0; i < point.Length; i++)
{
point[i] += offsets[i];
}
}
}
// calculate contributions
double[] contribution = new double[populations.Length];
HyperVolume hyperVolume = new HyperVolume();
for (int i = 0; i < populations.Length; i++)
{
if (invertedFront[i + 1].Length == 0)
{
contribution[i] = 0;
}
else
{
if (invertedFront[i + 1].Length != invertedFront[0].Length)
{
double[][] aux = new double[invertedFront[0].Length - invertedFront[i + 1].Length][];
int startPoint = 0, endPoint;
for (int j = 0; j < i; j++)
{
startPoint += invertedFront[j + 1].Length;
}
endPoint = startPoint + invertedFront[i + 1].Length;
int index = 0;
for (int j = 0; j < invertedFront[0].Length; j++)
{
if (j < startPoint || j >= (endPoint))
{
aux[index++] = invertedFront[0][j];
}
}
contribution[i] = hyperVolume.CalculateHypervolume(invertedFront[0], invertedFront[0].Length, numberOfObjectives)
- hyperVolume.CalculateHypervolume(aux, aux.Length, numberOfObjectives);
}
else
{
contribution[i] = hyperVolume.CalculateHypervolume(invertedFront[0], invertedFront[0].Length, numberOfObjectives);
}
}
}
return(contribution);
}