Learning Probabilistic Tree Grammars for Genetic Programming

Genetic Programming (GP) provides evolutionary methods for problems with tree representations. A recent development in Genetic Algorithms (GAs) has led to principled algorithms called Estimation-of-Distribution Algorithms (EDAs). EDAs identify and exploit structural features of a problem’s structure during optimization. Here, we investigate the use of a specific EDA for GP. We develop a probabilistic model that employs transformations of production rules in a context-free grammar to represent local structures. The results of performing experiments on two benchmark problems demonstrate the feasibility of the approach.

[1]  Wray L. Buntine.  A Guide to the Literature on Learning Probabilistic Networks from Data , 1996, IEEE Trans. Knowl. Data Eng..

[2]  D. Goldberg,et al.  Probabilistic Model Building and Competent Genetic Programming , 2003 .

[3]  Fernando G. Lobo,et al.  A Survey of Optimization by Building and Using Probabilistic Models , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[4]  Emin Erkan Korkmaz,et al.  Design and Usage of a New Benchmark Problem for Genetic Programming , 2003, ISCIS.

[5]  Vidroha Debroy,et al.  Genetic Programming , 1998, Lecture Notes in Computer Science.

[6]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

[7]  J. Pollack,et al.  The Evolutionary Induction of Subroutines , 1997 .

[8]  Peter J. Angeline,et al.  The Royal Tree Problem, a Benchmark for Single and Multiple Population Genetic Programming , 1996 .

[9]  Justinian P. Rosca,et al.  Discovery of subroutines in genetic programming , 1996 .

[10]  Nichael Lynn Cramer,et al.  A Representation for the Adaptive Generation of Simple Sequential Programs , 1985, ICGA.

[11]  Jorma Rissanen,et al.  Hypothesis Selection and Testing by the MDL Principle , 1999, Comput. J..

[12]  David E. Goldberg,et al.  Bayesian Optimization Algorithm: From Single Level to Hierarchy , 2002 .

[13]  Peter A. N. Bosman,et al.  Design and Application of iterated Density-Estimation Evolutionary Algorithms , 2003 .

[14]  David E. Goldberg,et al.  A Survey of Optimization by Building and Using Probabilistic Models , 2002, Comput. Optim. Appl..

[15]  Rafal Salustowicz,et al.  Probabilistic Incremental Program Evolution , 1997, Evolutionary Computation.

[16]  Hussein A. Abbass,et al.  Grammar model-based program evolution , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[17]  John R. Koza,et al.  Genetic programming 2 - automatic discovery of reusable programs , 1994, Complex Adaptive Systems.

[18]  Peter A. N. Bosman,et al.  Grammar Transformations in an EDA for Genetic Programming , 2004 .