+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+

Co-evolutionary Symbolic Regression (coev_symbreg):
Mixed real-valued GA - GP co-evolution example with Open BEAGLE

Copyright (C) 2003
by Jiachuan Wang <jiacwang@ecs.umass.edu>
and Christian Gagne <cgagne@gmail.com>

+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+


Getting started
===============

  Example is compiled in binary 'coev_symbreg'. Configuration file for
  real-valued GA population (the evolving training set) is in file
  'trainset-thread.conf', while configuration file for GP symbolic
  regression population is in file 'symgp-thread.conf'.

Objective
=========

  Two populations competitive co-evolution for symbolic regression.
  First population is made of standard GP mathematical expressions.
  Second population is made of individual representing 20 $(x_i,y_i)$
  samples in the domain $[-1,1]$ of the equation $x^4+x^3+x^2+x$.
  The global objective is to a find symbolic expressions that
  "generalizes" well over the domain sampled.

Terminal set of GP expressions
==============================

  X (the independent variable)
  Ephemeral constants randomly generated in $[-1,1]$

Function set of GP expressions
==============================

  +
  -
  *
  /     (protected division)
  
Representation of training sets
===============================

Vector of 20 real-valued numbers in $[-1,1]$.

Fitness
=======

  Root Mean Square (RMS) error of the GP expressions on the 20 samples
  of the training set. GP expression minimizes the RMS error, while
  training set maximizes it. Individuals of one population are
  evaluated against last generation other population best performing
  individual.
  
Reference
=========

Liviu Panait and Sean Luke, Methods for Evolving Robust Programs,
Proceedings of Genetic and Evolutionary Computation -- GECCO-2003,
LNCS, Vol. 2724, pp. 1740-1751, Springer-Verlag, 12-16 July 2003.