Generate random regression benchmark instances

[bburlacu]

The ability to randomly generate symbolic regression benchmarks according to user-defined rules would be useful for testing new algorithms and for the development of knowledge networks.

A previous effort exists (ticket #2083) for generating data according to user specified formulas. This ticket has a different scope as the focus is shifted towards generation of random instances based on user-defined templates.

[bburlacu]

Initial commit of HeuristicLab.ExpressionGenerator plugin. Note that the code depends on #2703 which should be merged first.

[bburlacu]

r14410: Added the possibility to sample possible arguments without repetition when instantiating expression templates.

[bburlacu]

r14411: Slightly improve usage of ExpressionTemplate class.

[bburlacu]

r14448: Rename expression label to name, and remove label from expression template as it should be specified for each individual instance.

[gkronber]

Please add AssemblyInfo frame file

[gkronber]

Please also include a 'reference' template for expressions in the plugin. Instead of the C# script.

[bburlacu]

r14480: Implement export of expressions as infix strings. Include missing AssemblyInfo.cs.frame file and set language version to C# 4.0.

[bburlacu]

14505: Improve expression generation and fix file formatting.

[bburlacu]

r14510: Minor changes (sample template arguments without repetition)

[bburlacu]

r14515: Fix infix formatting bug, refactored generation of polynomial to respect user choices (with or without exp/log).

[bburlacu]

r14520: Improve infix formatting

[gkronber]

TODO:

• Limit the number of variables in 1/x log(x) and exp(x)
• Allow definition of ranges for argument values for 1/x, log(x) and exp(x) and automatically generating constants (e.g. in log(c1 * (x1 + x2 + x3) + c2) c1 and c2 should be set automatically to make sure that taking the logarithm produces useful results. Same for exp(...)

Examples of functions currently produced:

(1 / (x7 * x4 * x3) + x4 + 1 / (x2 + x1 + x9 + x4 + x6 + x10 + x7 + x3) + x8 + 1 / x4 + 1 / (x6 * x10 * x5 * x7 * x1 * x4 * x9 * x3 * x2) + x3 + x6)

(exp(x10) + exp((x4 * x3 * x2)) + log(x9) + 1 / exp(x1) + exp(x2) + exp(x6) + x5 + 1 / x2 + 1 / exp((x9 * x4 * x6 * x5 * x7 * x8)))

• 1 / (x2 + x1 + x9 + x4 + x6 + x10 + x7 + x3) almost imposible to find
• log(x9) might be negative
• exp(x4 * x3 * x2) might become very large
• 1/x2 has an instability

[gkronber]

Script to test the generator:

using System;
using System.Linq;
using System.Collections.Generic;
using HeuristicLab.Core;
using HeuristicLab.Common;
using HeuristicLab.ExpressionGenerator;
using HeuristicLab.Random;
using HeuristicLab.Problems.DataAnalysis;
using HeuristicLab.Problems.DataAnalysis.Symbolic;
using HeuristicLab.Problems.DataAnalysis.Symbolic.Regression;
using HeuristicLab.Optimization;


public class MyScript : HeuristicLab.Scripting.CSharpScriptBase {
  public override void Main() {
    // type your code here
    var urand = new FastRandom(1234);
    var nrand = new NormalDistributedRandom(urand, 0, 1);
    var variables = ExpressionGenerator.GenerateRandomDistributedVariables(10, "x", nrand).ToArray();
    var experiment = new Experiment();
    vars["experiment"] = experiment;
    for(int i=0;i<20;i++) {
      var p = ExpressionGenerator.RationalExpression(urand, variables, useLog: true, useExp: true);
    // Console.WriteLine(p.PrintDot());
    Console.WriteLine(p.PrintInfix());
    
      var infixParser = new   InfixExpressionParser();
      var t = infixParser.Parse(p.PrintInfix());
      var simplifier = new TreeSimplifier();
      t = simplifier.Simplify(t);
      var formatter = new InfixExpressionFormatter();
      Console.WriteLine(formatter.Format(t));
      vars["t"] = t;


      var dataForDs = new List<List<double>>();
      var variableNames = new List<string>();
    
      var eval = new ExpressionEvaluator();

      // sample    
      var data = eval.GenerateData(variables.Concat(new [] {p}), 1000);
    
      foreach(var variable in variables) {
        dataForDs.Add(data[variable]);
        variableNames.Add(variable.Name);
      }
      dataForDs.Add(data[p]);
      variableNames.Add("y");
    
      var ds = new Dataset(variableNames, dataForDs);
     
      var problemData = new RegressionProblemData(ds, variables.Select(v => v.Name), "y");
      vars["problemData"] = problemData;
      // var osgp = (IAlgorithm) vars["OSGP"];
      // var regProblem = (SymbolicRegressionSingleObjectiveProblem)osgp.Problem;                                      
      // regProblem.Name =  formatter.Format(t);
      // osgp.Name = "OSGP - " + regProblem.Name;
      // regProblem.ProblemData = problemData;
      // 
      // var br = new BatchRun();
      // br.Repetitions = 5;
      // br.Optimizer = (IOptimizer)osgp.Clone();
      // br.Name = br.Optimizer.Name;
      // experiment.Optimizers.Add(br);      
    }
  }
}

[gkronber]

r14873: added possibility to automatically adjust constants based on the distributions of evaluated expressions to allow limiting distributions for arguments of functions (e.g. log should have positive args only, exp should have rather small args only)

[gkronber]

r14880: added more expression templates

[abeham]

Please rename your branch by prepending it with the ticket number

[bburlacu]

r16136: Rename branch