source: branches/2943_MOBasicProblem_MOCMAES/HeuristicLab.Problems.TestFunctions.MultiObjective/3.3/TestFunctions/Misc/SchafferN1.cs

#region License Information
/* HeuristicLab
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 * This file is part of HeuristicLab.
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 * GNU General Public License for more details.
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#endregion
using System;
using System.Collections.Generic;
using System.Linq;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Encodings.RealVectorEncoding;
using HeuristicLab.Optimization;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;

namespace HeuristicLab.Problems.TestFunctions.MultiObjective {
  [Item("SchafferN1", "Schaffer function N.1 for mulitobjective optimization from // https://en.wikipedia.org/wiki/Test_functions_for_optimization [30.11.2015]")]
  [StorableClass]
  public class SchafferN1 : MultiObjectiveTestFunction {
    protected override double[,] GetBounds(int objectives) {
      return new double[,] { { -1e5, 1e5 } };
    }

    protected override bool[] GetMaximization(int objectives) {
      return new bool[2];
    }

    protected override double[] GetReferencePoint(int objectives) {
      return new double[] { 1e5, 1e5 };
    }


    protected override IEnumerable<double[]> GetOptimalParetoFront(int objectives) {
      return ParetoFrontStore.GetParetoFront("Misc.ParetoFronts." + "SchafferN1");
    }

    protected override double GetBestKnownHypervolume(int objectives) {
      return HypervolumeCalculator.CalculateHypervolume(GetOptimalParetoFront(objectives).ToArray(), GetReferencePoint(objectives), GetMaximization(objectives));
    }

    [StorableConstructor]
    protected SchafferN1(bool deserializing) : base(deserializing) { }
    protected SchafferN1(SchafferN1 original, Cloner cloner) : base(original, cloner) { }
    public override IDeepCloneable Clone(Cloner cloner) {
      return new SchafferN1(this, cloner);
    }

    public SchafferN1() : base(minimumObjectives: 2, maximumObjectives: 2, minimumSolutionLength: 1, maximumSolutionLength: 1) { }

    public override double[] Evaluate(RealVector r, int objectives) {
      if (objectives != 2) throw new ArgumentException("The Schaffer N1 problem must always have 2 objectives");
      if (r.Length != 1) return null;
      var x = r[0];

      //objective1
      var f0 = x * x;

      //objective0
      var f1 = x - 2;
      f1 *= f1;

      return new double[] { f0, f1 };
    }
  }
}