68 lines
1.5 KiB
Plaintext
68 lines
1.5 KiB
Plaintext
+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+
|
|
|
|
Symbolic regression (symbreg): A simple GP example with Open BEAGLE
|
|
|
|
Copyright (C) 2001-2003
|
|
by Christian Gagne <cgagne@gmail.com>
|
|
and Marc Parizeau <parizeau@gel.ulaval.ca>
|
|
|
|
+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+
|
|
|
|
|
|
Getting started
|
|
===============
|
|
|
|
Example is compiled in binary 'symbreg'. Usage options is described by
|
|
executing it with command-line argument '-OBusage'. The detailed help can
|
|
also be obtained with argument '-OBhelp'.
|
|
|
|
Objective
|
|
=========
|
|
|
|
Find a function of one independent variable and one dependent variable, in
|
|
symbolic form, that fits a given sample of 20 $(x_i,y_i)$ data points,
|
|
where the target function is the quadratic polynomial $x^4 + x^3 + x^2 + x$.
|
|
|
|
Terminal set
|
|
============
|
|
|
|
X (the independent variable)
|
|
PI
|
|
Ephemeral constants randomly generated in $[-1,1]$
|
|
|
|
Function set
|
|
============
|
|
|
|
+
|
|
-
|
|
*
|
|
/ (protected division)
|
|
SIN
|
|
COS
|
|
EXP
|
|
LOG (protected logarithm)
|
|
|
|
Fitness cases
|
|
=============
|
|
|
|
The given sample of 20 data points $(x_i,y_i)$, randomly chosen within
|
|
interval [-1,1].
|
|
|
|
Fitness
|
|
=======
|
|
|
|
$\frac{1.}{1.+RMSE}$ where RMSE is the Root Mean Square Error on the
|
|
fitness cases.
|
|
|
|
Stopping criteria
|
|
=================
|
|
|
|
When the evolution reaches the maximum number of generations.
|
|
|
|
Reference
|
|
=========
|
|
|
|
John R. Koza, "Genetic Programming: On the Programming of Computers by Means
|
|
of Natural Selection", MIT Press, 1992, pages 162-169.
|
|
|