Abstract: This paper presents a regularization method for program complexity control of linear genetic programming tuned for transcendental elementary functions. Our goal is to improve the performance of evolutionary methods when solving symbolic regression tasks involving Pfaffian functions such as polynomials, analytic algebraic and transcendental operations like sigmoid, inverse trigonometric and radial basis functions. We propose the use of straight line programs as the underlying structure for representing symbolic expressions. Our main result is a sharp upper bound for the Vapnik Chervonenkis dimension of families of straight line programs containing transcendental elementary functions. This bound leads to a penalization criterion for the mean square error based fitness function often used in genetic programming for solving inductive learning problems. Our experiments show that the new fitness function gives very good results when compared with classical statistical regularization methods (such as Akaike and Bayesian Information Criteria) in almost all studied situations, including some benchmark real-world regression problems.

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