When I first started on my project, a few years ago, I decided to save time by making use of an existing tree-based GP system. I did some research into the various alternatives and by far the best framework I came across was Christian Gagné's Open BEAGLE. It is well-designed, flexible, easily extendable and very efficient.
Open BEAGLE also has a Yahoo mailing list offering help and support along the way.
As an initial test of the system, and my understanding of it, I played around with symbolic and numerical regression, where the input and output to a mathematical function is known but the function itself must be evolved.
All you need to do is loop over a series of input data (e.g. the integers 1 to 100), run some function (e.g. x2+x+1) on the input, store the output for fitness evaluation, and then provide only the input data to your population along with some basic operators (e.g. addition, subtraction, multiplication and division). Fitness is determined as the negated magnitude of the error when comparing an individual's output with the known output - the closer the error is to zero, the fitter the individual. Thus, if the error is exactly zero, you have a perfect fitness case.
If everything works you will end up with a program that matches the function exactly, after a few generations of evolution, e.g. for x2+x+1:
Next, I tried if this system could evolve more elaborate functions like 4x3+2x-27. I played around with how many generations were required and how large a population was necessary to get exact solutions. I also tried using a square root function without exposing a square root operator to the GP system, and was amazed when the GP system found very good approximate solutions within a few dozen generations of a few thousand individuals!
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