Model Complexity Control in Straight Line Program Genetic Programming

In this paper we propose a tool for controlling the complexity of Genetic Programming models. The tool is supported by the theory of VapnikChervonekis dimension and is combined with a novel representation of models named straight line program. Experimental results, implemented on conventional algebraic structures (such as polynomials) and real problems, show that the empirical risk, penalized by suitable upper bounds for the Vapnik-Chervonenkis dimension, gives a generalization error smaller than the use of statistical conventional techniques such as Bayesian or Akaike information criteria.