source: branches/HeuristicLab.Problems.GPDL/Examples/symbreg Koza.txt @ 12002

PROBLEM SymbRegKoza
CODE <<
  double[,] x;
  double[] y;
  int[] rows;
  int[] variables;
  double[] randomConsts;

  double RSquared(IEnumerable<double> xs, IEnumerable<double> ys) {
    // calculate Pearson's correlation in one pass over xs and ys
    double sumx = 0.0;
    double sumy = 0.0;
    double sumxSq = 0.0;
    double sumySq = 0.0;
    double sumxy = 0.0;
    int n = 0;
    var xEnum = xs.GetEnumerator();
    var yEnum = ys.GetEnumerator();
    while(xEnum.MoveNext() & yEnum.MoveNext()) {
      sumx += xEnum.Current;
      sumy += yEnum.Current;
      sumxSq += xEnum.Current * xEnum.Current;
      sumySq += yEnum.Current * yEnum.Current;
      sumxy += xEnum.Current * yEnum.Current;
      n++;
    }
    System.Diagnostics.Debug.Assert(!(xEnum.MoveNext() | yEnum.MoveNext()));

    double num;
    double den;
    double r = 0.0;
    num = sumxy - ( ( sumx * sumy ) / n );
    den = Math.Sqrt( ( sumxSq - ( sumx*sumx ) / n ) *
                     ( sumySq - ( sumy*sumy ) / n ) );
    if(den > 0){
      r = num / den;
    }
    return r*r;
  } 
>>

INIT <<
  // generate 500 cases of poly-10 benchmark function
  int n = 500;
  variables = new int[] {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
  var rand = new System.Random(31415);
  x = new double[n, 10];
  y = new double[n];
  for(int row = 0; row < n; row++) {
    for(int col = 0; col < 10; col++) {
      x[row, col] = rand.NextDouble() * 2.0 - 1.0;
    }
    y[row] = x[row, 0] * x[row, 1] +
             x[row, 2] * x[row, 3] +
             x[row, 4] * x[row, 5] +
             x[row, 0] * x[row, 6] + x[row, 8] +
             x[row, 2] * x[row, 5] + x[row, 9];
  }
 
  rows = System.Linq.Enumerable.Range(0, n).ToArray();
  
  // generate 100 random constants in [-10.0 .. 10.0[
  randomConsts = Enumerable.Range(0, 100).Select(i => rand.NextDouble()*20.0 - 10.0).ToArray();
>>

NONTERMINALS
  Model<<int row, out double val>>.
  RPB<<int row, out double val>>.
  Addition<<int row, out double val>>.
  Subtraction<<int row, out double val>>.
  Multiplication<<int row, out double val>>.
  Division<<int row, out double val>>.

TERMINALS
  ERC<<out double val>> 
    CONSTRAINTS
      val IN SET << randomConsts >>
  .

  Var<<out int variable>> 
    CONSTRAINTS
      variable IN SET << variables >>
  .

RULES
  Model<<int row, out double val>> =
    RPB<<row, out val>> .

  RPB<<int row, out double val>> =                         LOCAL << int variable; >>
    Addition<<row, out val>>
    | Subtraction<<row, out val>>
    | Division<<row, out val>>
    | Multiplication<<row, out val>>
    | Var<<out variable>>                                  SEM << val = x[row, variable]; >>
    | ERC<<out val>> 
  .

  Addition<<int row, out double val>> =                    LOCAL << double x1, x2; >>
      RPB<<row, out x1>> RPB<<row, out x2>>                SEM<< val = x1 + x2; >>
  .
  Subtraction<<int row, out double val>> =                 LOCAL << double x1, x2; >>
      RPB<<row, out x1>> RPB<<row, out x2>>                SEM<< val = x1 - x2; >>
  .
  Division<<int row, out double val>> =                    LOCAL << double x1, x2; >>
      RPB<<row, out x1>> RPB<<row, out x2>>                SEM<< val = x1 / x2; >>
  .
  Multiplication<<int row, out double val>> =              LOCAL << double x1, x2; >>
      RPB<<row, out x1>> RPB<<row, out x2>>                SEM<< val = x1 * x2; >>
  .

MAXIMIZE
  << 
    var predicted = rows.Select(r => {
      double result;
      Model(r, out result);                                /* we can call the root symbol directly */
      return result;
    });
    return RSquared(predicted, y);
  >>
END SymbRegKoza.