Changeset 13310 for stable/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective

Timestamp:

11/19/15 19:39:07 (9 years ago)

Author:

mkommend

Message:

#2175: Merged r13241, r13300, r13307, r13308 into stable.

Location:

stable

Files:

• . (modified) (1 prop)
• HeuristicLab.Problems.DataAnalysis.Symbolic.Regression (modified) (1 prop)
• HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4 (modified) (1 prop)
• HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/PearsonRSquaredNestedTreeSizeEvaluator.cs (copied) (copied from trunk/sources/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/PearsonRSquaredNestedTreeSizeEvaluator.cs) (3 diffs)
• HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/PearsonRSquaredNumberOfVariablesEvaluator.cs (copied) (copied from trunk/sources/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/PearsonRSquaredNumberOfVariablesEvaluator.cs) (3 diffs)
• HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/PearsonRSquaredTreeComplexityEvaluator.cs (copied) (copied from trunk/sources/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/PearsonRSquaredTreeComplexityEvaluator.cs) (2 diffs)
• HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/SymbolicRegressionMultiObjectiveEvaluator.cs (modified) (2 diffs)
• HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/SymbolicRegressionMultiObjectiveMeanSquaredErrorTreeSizeEvaluator.cs (modified) (3 diffs)
• HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/SymbolicRegressionMultiObjectivePearsonRSquaredTreeSizeEvaluator.cs (modified) (3 diffs)
• HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/SymbolicRegressionMultiObjectiveTrainingBestSolutionAnalyzer.cs (modified) (5 diffs)

stable/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/PearsonRSquaredNestedTreeSizeEvaluator.cs

@@ -44 +44 @@
     public PearsonRSquaredNestedTreeSizeEvaluator() : base() { }
 
-    public override IEnumerable<bool> Maximization { get { return new bool[2] { true, false }; } }
+    public override IEnumerable<bool> Maximization { get { return new bool[2] { true, false }; } } // maximize R² & minimize nested tree size
 
     public override IOperation InstrumentedApply() {
@@ -67 +67 @@
       if (decimalPlaces >= 0)
         r2 = Math.Round(r2, decimalPlaces);
-      return new double[2] { r2, solution.IterateNodesPostfix().Sum(n => n.GetLength()) };
+      return new double[2] { r2, solution.IterateNodesPostfix().Sum(n => n.GetLength()) }; // sum of the length of the whole sub-tree for each node 
     }
 
@@ -74 +74 @@
       EstimationLimitsParameter.ExecutionContext = context;
       ApplyLinearScalingParameter.ExecutionContext = context;
+      // DecimalPlaces parameter is a FixedValueParameter and doesn't need the context.
 
-      double[] quality = Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, problemData, rows, ApplyLinearScalingParameter.ActualValue.Value, DecimalPlaces);
+      double[] quality = Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, problemData, rows, ApplyLinearScalingParameter.ActualValue.Value, DecimalPlaces); 
 
       SymbolicDataAnalysisTreeInterpreterParameter.ExecutionContext = null;

stable/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/PearsonRSquaredNumberOfVariablesEvaluator.cs

@@ -44 +44 @@
     public PearsonRSquaredNumberOfVariablesEvaluator() : base() { }
 
-    public override IEnumerable<bool> Maximization { get { return new bool[2] { true, false }; } }
+    public override IEnumerable<bool> Maximization { get { return new bool[2] { true, false }; } } // maximize R² and minimize the number of variables
 
     public override IOperation InstrumentedApply() {
@@ -66 +66 @@
       if (decimalPlaces >= 0)
         r2 = Math.Round(r2, decimalPlaces);
-      return new double[2] { r2, solution.IterateNodesPostfix().OfType<VariableTreeNode>().Count() };
+      return new double[2] { r2, solution.IterateNodesPostfix().OfType<VariableTreeNode>().Count() }; // count the number of variables
     }
 
@@ -73 +73 @@
       EstimationLimitsParameter.ExecutionContext = context;
       ApplyLinearScalingParameter.ExecutionContext = context;
+      // DecimalPlaces parameter is a FixedValueParameter and doesn't need the context.
 
       double[] quality = Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, problemData, rows, ApplyLinearScalingParameter.ActualValue.Value, DecimalPlaces);

stable/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/PearsonRSquaredTreeComplexityEvaluator.cs

@@ -43 +43 @@
     public PearsonRSquaredTreeComplexityEvaluator() : base() { }
 
-    public override IEnumerable<bool> Maximization { get { return new bool[2] { true, false }; } }
+    public override IEnumerable<bool> Maximization { get { return new bool[2] { true, false }; } } // maximize R² and minimize model complexity 
 
     public override IOperation InstrumentedApply() {
@@ -72 +72 @@
       EstimationLimitsParameter.ExecutionContext = context;
       ApplyLinearScalingParameter.ExecutionContext = context;
+      // DecimalPlaces parameter is a FixedValueParameter and doesn't need the context.
 
       double[] quality = Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, problemData, rows, ApplyLinearScalingParameter.ActualValue.Value, DecimalPlaces);

stable/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/SymbolicRegressionMultiObjectiveEvaluator.cs

@@ -22 +22 @@
 
 using HeuristicLab.Common;
+using HeuristicLab.Core;
+using HeuristicLab.Data;
+using HeuristicLab.Parameters;
 using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
+
 namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Regression {
+  [StorableClass]
   public abstract class SymbolicRegressionMultiObjectiveEvaluator : SymbolicDataAnalysisMultiObjectiveEvaluator<IRegressionProblemData>, ISymbolicRegressionMultiObjectiveEvaluator {
+    private const string DecimalPlacesParameterName = "Decimal Places";
+    private const string UseConstantOptimizationParameterName = "Use constant optimization";
+    private const string ConstantOptimizationIterationsParameterName = "Constant optimization iterations";
+
+    public IFixedValueParameter<IntValue> DecimalPlacesParameter {
+      get { return (IFixedValueParameter<IntValue>)Parameters[DecimalPlacesParameterName]; }
+    }
+    public IFixedValueParameter<BoolValue> UseConstantOptimizationParameter {
+      get { return (IFixedValueParameter<BoolValue>)Parameters[UseConstantOptimizationParameterName]; }
+    }
+
+    public IFixedValueParameter<IntValue> ConstantOptimizationIterationsParameter {
+      get { return (IFixedValueParameter<IntValue>)Parameters[ConstantOptimizationIterationsParameterName]; }
+    }
+
+
+    public int DecimalPlaces {
+      get { return DecimalPlacesParameter.Value.Value; }
+      set { DecimalPlacesParameter.Value.Value = value; }
+    }
+    public bool UseConstantOptimization {
+      get { return UseConstantOptimizationParameter.Value.Value; }
+      set { UseConstantOptimizationParameter.Value.Value = value; }
+    }
+    public int ConstantOptimizationIterations {
+      get { return ConstantOptimizationIterationsParameter.Value.Value; }
+      set { ConstantOptimizationIterationsParameter.Value.Value = value; }
+    }
+
     [StorableConstructor]
     protected SymbolicRegressionMultiObjectiveEvaluator(bool deserializing) : base(deserializing) { }
@@ -31 +65 @@
     }
 
-    protected SymbolicRegressionMultiObjectiveEvaluator() : base() { }
+    protected SymbolicRegressionMultiObjectiveEvaluator()
+      : base() {
+      Parameters.Add(new FixedValueParameter<IntValue>(DecimalPlacesParameterName, "The number of decimal places used for rounding the quality values.", new IntValue(5)) { Hidden = true });
+      Parameters.Add(new FixedValueParameter<BoolValue>(UseConstantOptimizationParameterName, "", new BoolValue(false)));
+      Parameters.Add(new FixedValueParameter<IntValue>(ConstantOptimizationIterationsParameterName, "The number of iterations constant optimization should be applied.", new IntValue(5)));
+    }
+
+    [StorableHook(HookType.AfterDeserialization)]
+    private void AfterDeserialization() {
+      if (!Parameters.ContainsKey(UseConstantOptimizationParameterName)) {
+        Parameters.Add(new FixedValueParameter<BoolValue>(UseConstantOptimizationParameterName, "", new BoolValue(false)));
+      }
+      if (!Parameters.ContainsKey(DecimalPlacesParameterName)) {
+        Parameters.Add(new FixedValueParameter<IntValue>(DecimalPlacesParameterName, "The number of decimal places used for rounding the quality values.", new IntValue(-1)) { Hidden = true });
+      }
+      if (!Parameters.ContainsKey(ConstantOptimizationIterationsParameterName)) {
+        Parameters.Add(new FixedValueParameter<IntValue>(ConstantOptimizationIterationsParameterName, "The number of iterations constant optimization should be applied.", new IntValue(5)));
+      }
+    }
   }
 }

stable/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/SymbolicRegressionMultiObjectiveMeanSquaredErrorTreeSizeEvaluator.cs

@@ -20 +20 @@
 #endregion
 
+using System;
 using System.Collections.Generic;
 using HeuristicLab.Common;
@@ -47 +48 @@
       IEnumerable<int> rows = GenerateRowsToEvaluate();
       var solution = SymbolicExpressionTreeParameter.ActualValue;
-      double[] qualities = Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, ProblemDataParameter.ActualValue, rows, ApplyLinearScalingParameter.ActualValue.Value);
+      var problemData = ProblemDataParameter.ActualValue;
+      var interpreter = SymbolicDataAnalysisTreeInterpreterParameter.ActualValue;
+      var estimationLimits = EstimationLimitsParameter.ActualValue;
+      var applyLinearScaling = ApplyLinearScalingParameter.ActualValue.Value;
+
+      if (UseConstantOptimization) {
+        SymbolicRegressionConstantOptimizationEvaluator.OptimizeConstants(interpreter, solution, problemData, rows, applyLinearScaling, ConstantOptimizationIterations, estimationLimits.Upper, estimationLimits.Lower);
+      }
+
+      double[] qualities = Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, ProblemDataParameter.ActualValue, rows, ApplyLinearScalingParameter.ActualValue.Value, DecimalPlaces);
       QualitiesParameter.ActualValue = new DoubleArray(qualities);
       return base.InstrumentedApply();
     }
 
-    public static double[] Calculate(ISymbolicDataAnalysisExpressionTreeInterpreter interpreter, ISymbolicExpressionTree solution, double lowerEstimationLimit, double upperEstimationLimit, IRegressionProblemData problemData, IEnumerable<int> rows, bool applyLinearScaling) {
-      IEnumerable<double> estimatedValues = interpreter.GetSymbolicExpressionTreeValues(solution, problemData.Dataset, rows);
-      IEnumerable<double> targetValues = problemData.Dataset.GetDoubleValues(problemData.TargetVariable, rows);
-      OnlineCalculatorError errorState;
+    public static double[] Calculate(ISymbolicDataAnalysisExpressionTreeInterpreter interpreter, ISymbolicExpressionTree solution, double lowerEstimationLimit, double upperEstimationLimit, IRegressionProblemData problemData, IEnumerable<int> rows, bool applyLinearScaling, int decimalPlaces) {
+      var mse = SymbolicRegressionSingleObjectiveMeanSquaredErrorEvaluator.Calculate(interpreter, solution, lowerEstimationLimit,
+        upperEstimationLimit, problemData, rows, applyLinearScaling);
 
-      double mse;
-      if (applyLinearScaling) {
-        var mseCalculator = new OnlineMeanSquaredErrorCalculator();
-        CalculateWithScaling(targetValues, estimatedValues, lowerEstimationLimit, upperEstimationLimit, mseCalculator, problemData.Dataset.Rows);
-        errorState = mseCalculator.ErrorState;
-        mse = mseCalculator.MeanSquaredError;
-      } else {
-        IEnumerable<double> boundedEstimatedValues = estimatedValues.LimitToRange(lowerEstimationLimit, upperEstimationLimit);
-        mse = OnlineMeanSquaredErrorCalculator.Calculate(targetValues, boundedEstimatedValues, out errorState);
-      }
-      if (errorState != OnlineCalculatorError.None) mse = double.NaN;
+      if (decimalPlaces >= 0)
+        mse = Math.Round(mse, decimalPlaces);
+
       return new double[2] { mse, solution.Length };
     }
@@ -76 +77 @@
       ApplyLinearScalingParameter.ExecutionContext = context;
 
-      double[] quality = Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, problemData, rows, ApplyLinearScalingParameter.ActualValue.Value);
+      double[] quality = Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, problemData, rows, ApplyLinearScalingParameter.ActualValue.Value, DecimalPlaces);
 
       SymbolicDataAnalysisTreeInterpreterParameter.ExecutionContext = null;

stable/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/SymbolicRegressionMultiObjectivePearsonRSquaredTreeSizeEvaluator.cs

@@ -20 +20 @@
 #endregion
 
+using System;
 using System.Collections.Generic;
 using HeuristicLab.Common;
@@ -47 +48 @@
       IEnumerable<int> rows = GenerateRowsToEvaluate();
       var solution = SymbolicExpressionTreeParameter.ActualValue;
-      double[] qualities = Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, ProblemDataParameter.ActualValue, rows, ApplyLinearScalingParameter.ActualValue.Value);
+      var problemData = ProblemDataParameter.ActualValue;
+      var interpreter = SymbolicDataAnalysisTreeInterpreterParameter.ActualValue;
+      var estimationLimits = EstimationLimitsParameter.ActualValue;
+      var applyLinearScaling = ApplyLinearScalingParameter.ActualValue.Value;
+
+      if (UseConstantOptimization) {
+        SymbolicRegressionConstantOptimizationEvaluator.OptimizeConstants(interpreter, solution, problemData, rows, applyLinearScaling, ConstantOptimizationIterations, estimationLimits.Upper, estimationLimits.Lower);
+      }
+      double[] qualities = Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, ProblemDataParameter.ActualValue, rows, ApplyLinearScalingParameter.ActualValue.Value, DecimalPlaces);
       QualitiesParameter.ActualValue = new DoubleArray(qualities);
       return base.InstrumentedApply();
     }
 
-    public static double[] Calculate(ISymbolicDataAnalysisExpressionTreeInterpreter interpreter, ISymbolicExpressionTree solution, double lowerEstimationLimit, double upperEstimationLimit, IRegressionProblemData problemData, IEnumerable<int> rows, bool applyLinearScaling) {
-      IEnumerable<double> estimatedValues = interpreter.GetSymbolicExpressionTreeValues(solution, problemData.Dataset, rows);
-      IEnumerable<double> targetValues = problemData.Dataset.GetDoubleValues(problemData.TargetVariable, rows);
-      OnlineCalculatorError errorState;
-
-      double r;
-      if (applyLinearScaling) {
-        var rCalculator = new OnlinePearsonsRCalculator();
-        CalculateWithScaling(targetValues, estimatedValues, lowerEstimationLimit, upperEstimationLimit, rCalculator, problemData.Dataset.Rows);
-        errorState = rCalculator.ErrorState;
-        r = rCalculator.R;
-      } else {
-        IEnumerable<double> boundedEstimatedValues = estimatedValues.LimitToRange(lowerEstimationLimit, upperEstimationLimit);
-        r = OnlinePearsonsRCalculator.Calculate(targetValues, boundedEstimatedValues, out errorState);
-      }
-
-      if (errorState != OnlineCalculatorError.None) r = double.NaN;
-      return new double[2] { r*r, solution.Length };
+    public static double[] Calculate(ISymbolicDataAnalysisExpressionTreeInterpreter interpreter, ISymbolicExpressionTree solution, double lowerEstimationLimit, double upperEstimationLimit, IRegressionProblemData problemData, IEnumerable<int> rows, bool applyLinearScaling, int decimalPlaces) {
+      double r2 = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(interpreter, solution, lowerEstimationLimit, upperEstimationLimit, problemData, rows, applyLinearScaling);
+      if (decimalPlaces >= 0)
+        r2 = Math.Round(r2, decimalPlaces);
+      return new double[2] { r2, solution.Length };
     }
 
@@ -77 +73 @@
       ApplyLinearScalingParameter.ExecutionContext = context;
 
-      double[] quality = Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, problemData, rows, ApplyLinearScalingParameter.ActualValue.Value);
+      double[] quality = Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, problemData, rows, ApplyLinearScalingParameter.ActualValue.Value, DecimalPlaces);
 
       SymbolicDataAnalysisTreeInterpreterParameter.ExecutionContext = null;

stable/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/MultiObjective/SymbolicRegressionMultiObjectiveTrainingBestSolutionAnalyzer.cs

@@ -20 +20 @@
 #endregion
 
+using System.Collections.Generic;
+using System.Linq;
+using HeuristicLab.Analysis;
 using HeuristicLab.Common;
 using HeuristicLab.Core;
+using HeuristicLab.Data;
 using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
+using HeuristicLab.Optimization;
 using HeuristicLab.Parameters;
 using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
@@ -37 +42 @@
     private const string SymbolicDataAnalysisTreeInterpreterParameterName = "SymbolicDataAnalysisTreeInterpreter";
     private const string EstimationLimitsParameterName = "EstimationLimits";
+    private const string MaximumSymbolicExpressionTreeLengthParameterName = "MaximumSymbolicExpressionTreeLength";
+    private const string ValidationPartitionParameterName = "ValidationPartition";
+
     #region parameter properties
     public ILookupParameter<IRegressionProblemData> ProblemDataParameter {
@@ -47 +55 @@
       get { return (IValueLookupParameter<DoubleLimit>)Parameters[EstimationLimitsParameterName]; }
     }
+    public ILookupParameter<IntValue> MaximumSymbolicExpressionTreeLengthParameter {
+      get { return (ILookupParameter<IntValue>)Parameters[MaximumSymbolicExpressionTreeLengthParameterName]; }
+    }
+
+    public IValueLookupParameter<IntRange> ValidationPartitionParameter {
+      get { return (IValueLookupParameter<IntRange>)Parameters[ValidationPartitionParameterName]; }
+    }
     #endregion
 
@@ -54 +69 @@
     public SymbolicRegressionMultiObjectiveTrainingBestSolutionAnalyzer()
       : base() {
-      Parameters.Add(new LookupParameter<IRegressionProblemData>(ProblemDataParameterName, "The problem data for the symbolic regression solution."));
-      Parameters.Add(new LookupParameter<ISymbolicDataAnalysisExpressionTreeInterpreter>(SymbolicDataAnalysisTreeInterpreterParameterName, "The symbolic data analysis tree interpreter for the symbolic expression tree."));
-      Parameters.Add(new ValueLookupParameter<DoubleLimit>(EstimationLimitsParameterName, "The lower and upper limit for the estimated values produced by the symbolic regression model."));
+      Parameters.Add(new LookupParameter<IRegressionProblemData>(ProblemDataParameterName, "The problem data for the symbolic regression solution.") { Hidden = true });
+      Parameters.Add(new LookupParameter<ISymbolicDataAnalysisExpressionTreeInterpreter>(SymbolicDataAnalysisTreeInterpreterParameterName, "The symbolic data analysis tree interpreter for the symbolic expression tree.") { Hidden = true });
+      Parameters.Add(new ValueLookupParameter<DoubleLimit>(EstimationLimitsParameterName, "The lower and upper limit for the estimated values produced by the symbolic regression model.") { Hidden = true });
+      Parameters.Add(new LookupParameter<IntValue>(MaximumSymbolicExpressionTreeLengthParameterName, "Maximal length of the symbolic expression.") { Hidden = true });
+      Parameters.Add(new ValueLookupParameter<IntRange>(ValidationPartitionParameterName, "The validation partition."));
+    }
+
+    [StorableHook(HookType.AfterDeserialization)]
+    private void AfterDeserialization() {
+      if (!Parameters.ContainsKey(MaximumSymbolicExpressionTreeLengthParameterName))
+        Parameters.Add(new LookupParameter<IntValue>(MaximumSymbolicExpressionTreeLengthParameterName, "Maximal length of the symbolic expression.") { Hidden = true });
+      if (!Parameters.ContainsKey(ValidationPartitionParameterName))
+        Parameters.Add(new ValueLookupParameter<IntRange>(ValidationPartitionParameterName, "The validation partition."));
     }
 
@@ -68 +93 @@
       return new SymbolicRegressionSolution(model, (IRegressionProblemData)ProblemDataParameter.ActualValue.Clone());
     }
+
+    public override IOperation Apply() {
+      var operation = base.Apply();
+      var paretoFront = TrainingBestSolutionsParameter.ActualValue;
+
+      IResult result;
+      ScatterPlot qualityToTreeSize;
+      if (!ResultCollection.TryGetValue("Pareto Front Analysis", out result)) {
+        qualityToTreeSize = new ScatterPlot("Quality vs Tree Size", "");
+        qualityToTreeSize.VisualProperties.XAxisMinimumAuto = false;
+        qualityToTreeSize.VisualProperties.XAxisMaximumAuto = false;
+        qualityToTreeSize.VisualProperties.YAxisMinimumAuto = false;
+        qualityToTreeSize.VisualProperties.YAxisMaximumAuto = false;
+
+        qualityToTreeSize.VisualProperties.XAxisMinimumFixedValue = 0;
+        qualityToTreeSize.VisualProperties.XAxisMaximumFixedValue = MaximumSymbolicExpressionTreeLengthParameter.ActualValue.Value;
+        qualityToTreeSize.VisualProperties.YAxisMinimumFixedValue = 0;
+        qualityToTreeSize.VisualProperties.YAxisMaximumFixedValue = 2;
+        ResultCollection.Add(new Result("Pareto Front Analysis", qualityToTreeSize));
+      } else {
+        qualityToTreeSize = (ScatterPlot)result.Value;
+      }
+
+
+      int previousTreeLength = -1;
+      var sizeParetoFront = new LinkedList<ISymbolicRegressionSolution>();
+      foreach (var solution in paretoFront.OrderBy(s => s.Model.SymbolicExpressionTree.Length)) {
+        int treeLength = solution.Model.SymbolicExpressionTree.Length;
+        if (!sizeParetoFront.Any()) sizeParetoFront.AddLast(solution);
+        if (solution.TrainingNormalizedMeanSquaredError < sizeParetoFront.Last.Value.TrainingNormalizedMeanSquaredError) {
+          if (treeLength == previousTreeLength)
+            sizeParetoFront.RemoveLast();
+          sizeParetoFront.AddLast(solution);
+        }
+        previousTreeLength = treeLength;
+      }
+
+      qualityToTreeSize.Rows.Clear();
+      var trainingRow = new ScatterPlotDataRow("Training NMSE", "", sizeParetoFront.Select(x => new Point2D<double>(x.Model.SymbolicExpressionTree.Length, x.TrainingNormalizedMeanSquaredError)));
+      trainingRow.VisualProperties.PointSize = 8;
+      qualityToTreeSize.Rows.Add(trainingRow);
+
+      var validationPartition = ValidationPartitionParameter.ActualValue;
+      if (validationPartition.Size != 0) {
+        var problemData = ProblemDataParameter.ActualValue;
+        var validationIndizes = Enumerable.Range(validationPartition.Start, validationPartition.Size).ToList();
+        var targetValues = problemData.Dataset.GetDoubleValues(problemData.TargetVariable, validationIndizes).ToList();
+        OnlineCalculatorError error;
+        var validationRow = new ScatterPlotDataRow("Validation NMSE", "",
+          sizeParetoFront.Select(x => new Point2D<double>(x.Model.SymbolicExpressionTree.Length,
+          OnlineNormalizedMeanSquaredErrorCalculator.Calculate(targetValues, x.GetEstimatedValues(validationIndizes), out error))));
+        validationRow.VisualProperties.PointSize = 7;
+        qualityToTreeSize.Rows.Add(validationRow);
+      }
+
+      return operation;
+    }
+
   }
 }