1 | using System;
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2 | using System.Collections.Generic;
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3 | using System.Linq;
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4 | using System.Security;
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5 | using System.Security.AccessControl;
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6 | using System.Text;
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7 |
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8 | namespace HeuristicLab.Problems.GrammaticalOptimization {
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9 | public class SymbolicRegressionPoly10Problem : IProblem {
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10 | // length of the longest palindrome in the sentence + number of different symbols occurring in the palindrome
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11 | private const string grammarString = @"
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12 | G(E):
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13 | E -> V | V+E | V-E | V*E | V/E | (E)
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14 | V -> a .. j
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15 | ";
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16 |
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17 | private readonly IGrammar grammar;
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18 | private readonly ExpressionInterpreter interpreter;
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19 |
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20 | private readonly int N;
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21 | private readonly double[][] x;
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22 | private readonly double[] y;
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23 |
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24 | public SymbolicRegressionPoly10Problem() {
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25 | this.grammar = new Grammar(grammarString);
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26 | this.interpreter = new ExpressionInterpreter();
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27 |
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28 | this.N = 500;
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29 | this.x = new double[N][];
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30 | this.y = new double[N];
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31 |
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32 | GenerateData();
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33 | }
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34 |
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35 | private void GenerateData() {
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36 | // generate data with fixed seed to make sure that data is always the same
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37 | var rand = new Random(31415);
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38 | for (int i = 0; i < N; i++) {
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39 | x[i] = new double[10];
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40 | for (int j = 0; j < 10; j++) {
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41 | x[i][j] = rand.NextDouble() * 2 - 1;
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42 | }
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43 | // poly-10 no noise
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44 | y[i] = x[i][0] * x[i][1] +
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45 | x[i][2] * x[i][3] +
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46 | x[i][4] * x[i][5] +
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47 | x[i][0] * x[i][6] * x[i][8] +
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48 | x[i][2] * x[i][5] * x[i][9];
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49 | }
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50 | }
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51 |
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52 | public double GetBestKnownQuality(int maxLen) {
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53 | // for now only an upper bound is returned, ideally we have an R² of 1.0
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54 | // the optimal R² can only be reached for sentences of at least 23 symbols
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55 | return 1.0;
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56 | }
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57 |
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58 | public IGrammar Grammar {
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59 | get { return grammar; }
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60 | }
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61 |
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62 | public double Evaluate(string sentence) {
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63 | return RSq(y, Enumerable.Range(0, N).Select(i => interpreter.Interpret(sentence, x[i])).ToArray());
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64 | }
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65 |
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66 | private double RSq(IEnumerable<double> xs, IEnumerable<double> ys) {
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67 | // two pass implementation, but we don't care
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68 | var meanX = xs.Average();
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69 | var meanY = ys.Average();
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70 |
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71 | var s = 0.0;
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72 | var ssX = 0.0;
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73 | var ssY = 0.0;
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74 | foreach (var p in xs.Zip(ys, (x, y) => new { x, y })) {
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75 | s += (p.x - meanX) * (p.y - meanY);
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76 | ssX += Math.Pow(p.x - meanX, 2);
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77 | ssY += Math.Pow(p.y - meanY, 2);
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78 | }
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79 |
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80 | if (s.IsAlmost(0)) return 0;
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81 | if (ssX.IsAlmost(0) || ssY.IsAlmost(0)) return 0;
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82 | return s * s / (ssX * ssY);
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83 | }
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84 | }
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85 | }
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