Model-driven regularization approach to straight line program genetic programming

•A regularization method for linear genetic programming is proposed.•Straight line programs with transcendental elementary functions are used.•A sharp bound for the Vapnik–Chervonenkis dimension of programs is encountered.•Our approach is empirically better than other statistical regularization meth...

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Bibliographic Details
Published in:Expert systems with applications 2016-09, Vol.57, p.76-90
Main Authors: Montaña, José L., Alonso, César L., Borges, Cruz E., Tîrnăucă, Cristina
Format: Article
Language:English
Subjects:
Criteria
Evolutionary
Fitness
Genetic algorithms
Genetic programming
Mathematical models
Pfaffian operator
Regression
Regularization
Straight line program
Straight lines
Symbolic regression
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Summary:•A regularization method for linear genetic programming is proposed.•Straight line programs with transcendental elementary functions are used.•A sharp bound for the Vapnik–Chervonenkis dimension of programs is encountered.•Our approach is empirically better than other statistical regularization methods. 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.
ISSN:0957-4174
1873-6793
DOI:10.1016/j.eswa.2016.03.003