source: branches/2886_SymRegGrammarEnumeration/Test/GrammarEnumerationTest.cs @ 15716

using System;
using System.Collections.Generic;
using System.Linq;
using HeuristicLab.Algorithms.DataAnalysis.SymRegGrammarEnumeration;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Problems.DataAnalysis;
using HeuristicLab.Random;
using Microsoft.VisualStudio.TestTools.UnitTesting;

namespace HeuristicLab.Algorithms.DataAnalysis.MctsSymbolicRegression {
  //[TestClass()]
  public class MctsSymbolicRegressionTest {
    private const int Seed = 1234;
    private IRandom rand;

    private const double SuccessThreshold = 0.99999;

    [TestInitialize]
    public void InitTest() {
      Console.Write("init called... ");
      rand = new FastRandom(Seed);
    }

    #region test structure search (no constants)
    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_Nguyen1() {
      // x³ + x² + x
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F1 ")));
      TestGrammarEnumeration(regProblem);
    }
    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_Nguyen2() {
      // x^4 + x³ + x² + x
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F2 ")));
      TestGrammarEnumeration(regProblem);
    }
    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_Nguyen3() {
      // x^5 + x^4 + x³ + x² + x
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F3 ")));
      TestGrammarEnumeration(regProblem);
    }
    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_Nguyen4() {
      // x^6 + x^5 + x^4 + x³ + x² + x
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F4 ")));
      TestGrammarEnumeration(regProblem);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_Nguyen7() {
      // log(x + 1) + log(x² + 1)
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F7 ")));
      TestGrammarEnumeration(regProblem);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_Poly10_Part1() {
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.VariousInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Poly-10")));

      //  Y = X1*X2 + X3*X4 + X5*X6 + X1*X7*X9 + X3*X6*X10
      //  Y' = X1*X2 + X3*X4 + X5*X6
      // simplify problem by changing target
      var ds = ((Dataset)regProblem.Dataset).ToModifiable();
      var ys = ds.GetDoubleValues("Y").ToArray();
      var x1 = ds.GetDoubleValues("X1").ToArray();
      var x2 = ds.GetDoubleValues("X2").ToArray();
      var x3 = ds.GetDoubleValues("X3").ToArray();
      var x4 = ds.GetDoubleValues("X4").ToArray();
      var x5 = ds.GetDoubleValues("X5").ToArray();
      var x6 = ds.GetDoubleValues("X6").ToArray();
      var x7 = ds.GetDoubleValues("X7").ToArray();
      var x8 = ds.GetDoubleValues("X8").ToArray();
      var x9 = ds.GetDoubleValues("X9").ToArray();
      var x10 = ds.GetDoubleValues("X10").ToArray();
      for (int i = 0; i < ys.Length; i++) {
        ys[i] -= x1[i] * x7[i] * x9[i];
        ys[i] -= x3[i] * x6[i] * x10[i];
      }
      ds.ReplaceVariable("Y", ys.ToList());

      var modifiedProblemData = new RegressionProblemData(ds, regProblem.AllowedInputVariables, regProblem.TargetVariable);

      TestGrammarEnumeration(modifiedProblemData);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_Poly10_Part2() {
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.VariousInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Poly-10")));

      //  Y = X1*X2 + X3*X4 + X5*X6 + X1*X7*X9 + X3*X6*X10
      //  Y' = X1*X7*X9 + X3*X6*X10
      // simplify problem by changing target
      var ds = ((Dataset)regProblem.Dataset).ToModifiable();
      var ys = ds.GetDoubleValues("Y").ToArray();
      var x1 = ds.GetDoubleValues("X1").ToArray();
      var x2 = ds.GetDoubleValues("X2").ToArray();
      var x3 = ds.GetDoubleValues("X3").ToArray();
      var x4 = ds.GetDoubleValues("X4").ToArray();
      var x5 = ds.GetDoubleValues("X5").ToArray();
      var x6 = ds.GetDoubleValues("X6").ToArray();
      var x7 = ds.GetDoubleValues("X7").ToArray();
      var x8 = ds.GetDoubleValues("X8").ToArray();
      var x9 = ds.GetDoubleValues("X9").ToArray();
      var x10 = ds.GetDoubleValues("X10").ToArray();
      for (int i = 0; i < ys.Length; i++) {
        ys[i] -= x1[i] * x2[i];
        ys[i] -= x3[i] * x4[i];
        ys[i] -= x5[i] * x6[i];
      }
      ds.ReplaceVariable("Y", ys.ToList());

      var modifiedProblemData = new RegressionProblemData(ds, regProblem.AllowedInputVariables, regProblem.TargetVariable);

      TestGrammarEnumeration(modifiedProblemData);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_Poly10_Part3() {
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.VariousInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Poly-10")));

      //  Y = X1*X2 + X3*X4 + X5*X6 + X1*X7*X9 + X3*X6*X10
      //  Y' = X1*X2 + X1*X7*X9
      // simplify problem by changing target
      var ds = ((Dataset)regProblem.Dataset).ToModifiable();
      var ys = ds.GetDoubleValues("Y").ToArray();
      var x1 = ds.GetDoubleValues("X1").ToArray();
      var x2 = ds.GetDoubleValues("X2").ToArray();
      var x3 = ds.GetDoubleValues("X3").ToArray();
      var x4 = ds.GetDoubleValues("X4").ToArray();
      var x5 = ds.GetDoubleValues("X5").ToArray();
      var x6 = ds.GetDoubleValues("X6").ToArray();
      var x7 = ds.GetDoubleValues("X7").ToArray();
      var x8 = ds.GetDoubleValues("X8").ToArray();
      var x9 = ds.GetDoubleValues("X9").ToArray();
      var x10 = ds.GetDoubleValues("X10").ToArray();
      for (int i = 0; i < ys.Length; i++) {
        ys[i] -= x3[i] * x4[i];
        ys[i] -= x5[i] * x6[i];
        ys[i] -= x3[i] * x6[i] * x10[i];
      }
      ds.ReplaceVariable("Y", ys.ToList());

      var modifiedProblemData = new RegressionProblemData(ds, regProblem.AllowedInputVariables, regProblem.TargetVariable);

      TestGrammarEnumeration(modifiedProblemData);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_Poly10_Part4() {
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.VariousInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Poly-10")));

      //  Y = X1*X2 + X3*X4 + X5*X6 + X1*X7*X9 + X3*X6*X10
      //  Y' = X3*X4 + X5*X6 + X3*X6*X10
      // simplify problem by changing target
      var ds = ((Dataset)regProblem.Dataset).ToModifiable();
      var ys = ds.GetDoubleValues("Y").ToArray();
      var x1 = ds.GetDoubleValues("X1").ToArray();
      var x2 = ds.GetDoubleValues("X2").ToArray();
      var x3 = ds.GetDoubleValues("X3").ToArray();
      var x4 = ds.GetDoubleValues("X4").ToArray();
      var x5 = ds.GetDoubleValues("X5").ToArray();
      var x6 = ds.GetDoubleValues("X6").ToArray();
      var x7 = ds.GetDoubleValues("X7").ToArray();
      var x8 = ds.GetDoubleValues("X8").ToArray();
      var x9 = ds.GetDoubleValues("X9").ToArray();
      var x10 = ds.GetDoubleValues("X10").ToArray();
      for (int i = 0; i < ys.Length; i++) {
        ys[i] -= x1[i] * x2[i];
        ys[i] -= x1[i] * x7[i] * x9[i];
      }
      ds.ReplaceVariable("Y", ys.ToList());
      var modifiedProblemData = new RegressionProblemData(ds, regProblem.AllowedInputVariables, regProblem.TargetVariable);


      TestGrammarEnumeration(modifiedProblemData);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_Poly10_Part5() {
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.VariousInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Poly-10")));

      //  Y = X1*X2 + X3*X4 + X5*X6 + X1*X7*X9 + X3*X6*X10
      //  Y' = X1*X2 + X3*X4 + X5*X6 + X1*X7*X9
      // simplify problem by changing target
      var ds = ((Dataset)regProblem.Dataset).ToModifiable();
      var ys = ds.GetDoubleValues("Y").ToArray();
      var x1 = ds.GetDoubleValues("X1").ToArray();
      var x2 = ds.GetDoubleValues("X2").ToArray();
      var x3 = ds.GetDoubleValues("X3").ToArray();
      var x4 = ds.GetDoubleValues("X4").ToArray();
      var x5 = ds.GetDoubleValues("X5").ToArray();
      var x6 = ds.GetDoubleValues("X6").ToArray();
      var x7 = ds.GetDoubleValues("X7").ToArray();
      var x8 = ds.GetDoubleValues("X8").ToArray();
      var x9 = ds.GetDoubleValues("X9").ToArray();
      var x10 = ds.GetDoubleValues("X10").ToArray();
      for (int i = 0; i < ys.Length; i++) {
        ys[i] -= x3[i] * x6[i] * x10[i];
      }
      ds.ReplaceVariable("Y", ys.ToList());
      var modifiedProblemData = new RegressionProblemData(ds, regProblem.AllowedInputVariables, regProblem.TargetVariable);


      TestGrammarEnumeration(modifiedProblemData);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_Poly10_Part6() {
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.VariousInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Poly-10")));

      //  Y = X1*X2 + X3*X4 + X5*X6 + X1*X7*X9 + X3*X6*X10
      //  Y' = X1*X2 + X3*X4 + X5*X6 + X3*X6*X10
      // simplify problem by changing target
      var ds = ((Dataset)regProblem.Dataset).ToModifiable();
      var ys = ds.GetDoubleValues("Y").ToArray();
      var x1 = ds.GetDoubleValues("X1").ToArray();
      var x2 = ds.GetDoubleValues("X2").ToArray();
      var x3 = ds.GetDoubleValues("X3").ToArray();
      var x4 = ds.GetDoubleValues("X4").ToArray();
      var x5 = ds.GetDoubleValues("X5").ToArray();
      var x6 = ds.GetDoubleValues("X6").ToArray();
      var x7 = ds.GetDoubleValues("X7").ToArray();
      var x8 = ds.GetDoubleValues("X8").ToArray();
      var x9 = ds.GetDoubleValues("X9").ToArray();
      var x10 = ds.GetDoubleValues("X10").ToArray();
      for (int i = 0; i < ys.Length; i++) {
        ys[i] -= x1[i] * x7[i] * x9[i];
      }
      ds.ReplaceVariable("Y", ys.ToList());
      var modifiedProblemData = new RegressionProblemData(ds, regProblem.AllowedInputVariables, regProblem.TargetVariable);

      TestGrammarEnumeration(modifiedProblemData);
    }


    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "long")]
    public void MctsSymbReg_NoConstants_Poly10_250rows() {
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.VariousInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Poly-10")));
      regProblem.TrainingPartition.Start = 0;
      regProblem.TrainingPartition.End = regProblem.Dataset.Rows;
      regProblem.TestPartition.Start = 0;
      regProblem.TestPartition.End = 2;
      TestGrammarEnumeration(regProblem);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "long")]
    public void MctsSymbReg_NoConstants_Poly10_10000rows() {
      // as poly-10 but more rows
      var x1 = Enumerable.Range(0, 10000).Select(_ => rand.NextDouble()).ToList();
      var x2 = Enumerable.Range(0, 10000).Select(_ => rand.NextDouble()).ToList();
      var x3 = Enumerable.Range(0, 10000).Select(_ => rand.NextDouble()).ToList();
      var x4 = Enumerable.Range(0, 10000).Select(_ => rand.NextDouble()).ToList();
      var x5 = Enumerable.Range(0, 10000).Select(_ => rand.NextDouble()).ToList();
      var x6 = Enumerable.Range(0, 10000).Select(_ => rand.NextDouble()).ToList();
      var x7 = Enumerable.Range(0, 10000).Select(_ => rand.NextDouble()).ToList();
      var x8 = Enumerable.Range(0, 10000).Select(_ => rand.NextDouble()).ToList();
      var x9 = Enumerable.Range(0, 10000).Select(_ => rand.NextDouble()).ToList();
      var x10 = Enumerable.Range(0, 10000).Select(_ => rand.NextDouble()).ToList();
      var ys = new List<double>();
      for (int i = 0; i < x1.Count; i++) {
        ys.Add(x1[i] * x2[i] + x3[i] * x4[i] + x5[i] * x6[i] + x1[i] * x7[i] * x9[i] + x3[i] * x6[i] * x10[i]);
      }

      var ds = new Dataset(new string[] { "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "y" },
        new[] { x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, ys });


      var problemData = new RegressionProblemData(ds, new string[] { "a", "b", "c", "d", "e", "f", "g", "h", "i", "j" }, "y");

      problemData.TrainingPartition.Start = 0;
      problemData.TrainingPartition.End = problemData.Dataset.Rows;
      problemData.TestPartition.Start = 0;
      problemData.TestPartition.End = 2; // must not be empty


      TestGrammarEnumeration(problemData);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_TwoVars() {

      // y = x1 + x2 + x1*x2 + x1*x2*x2 + x1*x1*x2
      var x1 = Enumerable.Range(0, 100).Select(_ => rand.NextDouble()).ToList();
      var x2 = Enumerable.Range(0, 100).Select(_ => rand.NextDouble()).ToList();
      var ys = x1.Zip(x2, (x1i, x2i) => x1i + x2i + x1i * x2i + x1i * x2i * x2i + x1i * x1i * x2i).ToList();

      var ds = new Dataset(new string[] { "a", "b", "y" }, new[] { x1, x2, ys });
      var problemData = new RegressionProblemData(ds, new string[] { "a", "b" }, "y");

      TestGrammarEnumeration(problemData);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbReg_NoConstants_Misleading() {

      // y = a + baaaaa (the effect of the second term should be very small)
      // the alg will quickly find that a has big effect and will search below a
      // since we prevent a + a... the algorithm must find the correct expression via a + b...
      // however b has a small effect so the branch might not be identified as relevant
      var @as = Enumerable.Range(0, 100).Select(_ => rand.NextDouble()).ToList();
      var bs = Enumerable.Range(0, 100).Select(_ => rand.NextDouble()).ToList();
      var cs = Enumerable.Range(0, 100).Select(_ => rand.NextDouble() * 1.0e-3).ToList();
      var ds = Enumerable.Range(0, 100).Select(_ => rand.NextDouble()).ToList();
      var es = Enumerable.Range(0, 100).Select(_ => rand.NextDouble()).ToList();
      var ys = new double[@as.Count];
      for (int i = 0; i < ys.Length; i++)
        ys[i] = @as[i] + bs[i] + @as[i] * bs[i] * cs[i];

      var dataset = new Dataset(new string[] { "a", "b", "c", "d", "e", "y" }, new[] { @as, bs, cs, ds, es, ys.ToList() });

      var problemData = new RegressionProblemData(dataset, new string[] { "a", "b", "c", "d", "e" }, "y");

      TestGrammarEnumeration(problemData);
    }
    #endregion

    #region restricted structure but including numeric constants

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegKeijzer7() {
      // ln(x)
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.KeijzerInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Keijzer 7 f(")));
      // some Keijzer problem instances have very large test partitions (here we are not concerened about test performance)
      if (regProblem.TestPartition.End - regProblem.TestPartition.Start > 1000) regProblem.TestPartition.End = regProblem.TestPartition.Start + 1000;
      TestGrammarEnumeration(regProblem);
    }

    
    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkNguyen5() {
      // sin(x²)cos(x) - 1
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider();
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F5 ")));
      TestGrammarEnumeration(regProblem);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkNguyen6() {
      // sin(x) + sin(x + x²)
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider();
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F6 ")));
      TestGrammarEnumeration(regProblem);
    }
    
    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkNguyen7() {
      //  log(x + 1) + log(x² + 1)
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F7 ")));
      TestGrammarEnumeration(regProblem);
    }
    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkNguyen8() {
      // Sqrt(x)
      // = x ^ 0.5
      // = exp(0.5 * log(x))
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F8 ")));
      TestGrammarEnumeration(regProblem);
    }
    
    // [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkNguyen9() {
      //  sin(x) + sin(y²)
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider();
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F9 ")));
      TestGrammarEnumeration(regProblem);
    }

    // [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkNguyen10() {
      // 2sin(x)cos(y)
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider();
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F10 ")));
      TestGrammarEnumeration(regProblem);
    }
    
    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkNguyen11() {
      // x ^ y  , x > 0, y > 0   
      // = exp(y * log(x))
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F11 ")));
      TestGrammarEnumeration(regProblem);
    }
    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkNguyen12() {
      // x^4 - x³ + y²/2 - y
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.NguyenInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("F12 ")));
      TestGrammarEnumeration(regProblem);
    }

    #endregion

    #region keijzer
    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "long")]
    public void MctsSymbRegBenchmarkKeijzer5() {
      // (30 * x * z) / ((x - 10)  * y²)
      // = 30 x z / (xy² - y²)
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.KeijzerInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Keijzer 5 f(")));
      // some Keijzer problem instances have very large test partitions (here we are not concerened about test performance)
      if (regProblem.TestPartition.End - regProblem.TestPartition.Start > 1000) regProblem.TestPartition.End = regProblem.TestPartition.Start + 1000;
      TestGrammarEnumeration(regProblem);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkKeijzer6() {
      // Keijzer 6 f(x) = Sum(1 / i) From 1 to X  , x \in [0..120]
      // we can only approximate this
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.KeijzerInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Keijzer 6 f(")));
      // some Keijzer problem instances have very large test partitions (here we are not concerened about test performance)
      if (regProblem.TestPartition.End - regProblem.TestPartition.Start > 1000) regProblem.TestPartition.End = regProblem.TestPartition.Start + 1000;
      TestGrammarEnumeration(regProblem);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkKeijzer8() {
      // sqrt(x)
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.KeijzerInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Keijzer 8 f(")));
      // some Keijzer problem instances have very large test partitions (here we are not concerened about test performance)
      if (regProblem.TestPartition.End - regProblem.TestPartition.Start > 1000) regProblem.TestPartition.End = regProblem.TestPartition.Start + 1000;
      TestGrammarEnumeration(regProblem);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkKeijzer9() {
      // arcsinh(x)  i.e. ln(x + sqrt(x² + 1))
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.KeijzerInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Keijzer 9 f(")));
      // some Keijzer problem instances have very large test partitions (here we are not concerened about test performance)
      if (regProblem.TestPartition.End - regProblem.TestPartition.Start > 1000) regProblem.TestPartition.End = regProblem.TestPartition.Start + 1000;
      TestGrammarEnumeration(regProblem);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkKeijzer11() {
      // xy + sin( (x-1) (y-1) )
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.KeijzerInstanceProvider();
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Keijzer 11 f(")));
      // some Keijzer problem instances have very large test partitions (here we are not concerened about test performance)
      if (regProblem.TestPartition.End - regProblem.TestPartition.Start > 1000) regProblem.TestPartition.End = regProblem.TestPartition.Start + 1000;
      TestGrammarEnumeration(regProblem);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkKeijzer12() {
      // x^4 - x³ + y² / 2 - y,  same as Nguyen 12             
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.KeijzerInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Keijzer 12 f(")));
      // some Keijzer problem instances have very large test partitions (here we are not concerened about test performance)
      if (regProblem.TestPartition.End - regProblem.TestPartition.Start > 1000) regProblem.TestPartition.End = regProblem.TestPartition.Start + 1000;
      TestGrammarEnumeration(regProblem);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkKeijzer14() {
      // 8 / (2 + x² + y²)
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.KeijzerInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Keijzer 14 f(")));
      // some Keijzer problem instances have very large test partitions (here we are not concerened about test performance)
      if (regProblem.TestPartition.End - regProblem.TestPartition.Start > 1000) regProblem.TestPartition.End = regProblem.TestPartition.Start + 1000;
      TestGrammarEnumeration(regProblem);
    }

    [TestMethod]
    [TestCategory("Algorithms.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void MctsSymbRegBenchmarkKeijzer15() {
      // x³ / 5 + y³ / 2 - y - x
      var provider = new HeuristicLab.Problems.Instances.DataAnalysis.KeijzerInstanceProvider(Seed);
      var regProblem = provider.LoadData(provider.GetDataDescriptors().Single(x => x.Name.Contains("Keijzer 15 f(")));
      // some Keijzer problem instances have very large test partitions (here we are not concerened about test performance)
      if (regProblem.TestPartition.End - regProblem.TestPartition.Start > 1000) regProblem.TestPartition.End = regProblem.TestPartition.Start + 1000;
      TestGrammarEnumeration(regProblem);
    }
    #endregion

    private void TestGrammarEnumeration(IRegressionProblemData problemData)
    {
      // Configure algorithm and problem
      var alg = new GrammarEnumerationAlgorithm();
      var problem = new RegressionProblem();
      alg.Problem = problem;
      problem.ProblemData = problemData;
      
      // Run
      alg.Start();

      // Evaluate results
      var eps = 1.0 - SuccessThreshold;

      // Check if algorithm terminated correctly
      Assert.IsTrue(alg.Results.ContainsKey("Best solution quality (training)"), "No training solution returned!");
      Assert.IsTrue(alg.Results.ContainsKey("Best solution quality (test)"), "No test solution returned!");

      // Check resultss
      Assert.AreEqual(1.0, ((DoubleValue)alg.Results["Best solution quality (training)"].Value).Value, eps, "Training quality too low!");
      Assert.AreEqual(1.0, ((DoubleValue)alg.Results["Best solution quality (test)"].Value).Value, eps, "Test quality too low!");
    }
  }
}