Symbolic Regression by Means of Grammatical Evolution with Estimation Distribution Algorithms as Search Engine

Grammatical Evolution (GE) is a Grammar-based form of Genetic Programming (GP) and it has been used to evolve programs or rules. The GE uses a population of linear genotypic strings and it is transformed by mapping process, those string are evolved using a search engine like the Genetic Algorithm (GA), Differential Evolution (DE), Particle Swarm Optimization (PSO), among others. One of the big trouble of these algorithms is the parameter tuning. In this paper is proposed an Estimation Distribution Algorithm (EDA) as search engine using the Symbolic Regression as a benchmark, due to the few parameters used by the EDA. The results were compared against the obtained by DE as search engine using the Friedman nonparametric test.

[1]  Jonathan M. Garibaldi,et al.  GP challenge: evolving energy function for protein structure prediction , 2010, Genetic Programming and Evolvable Machines.

[2]  Terence Soule,et al.  Genetic Programming Theory and Practice IV , 2007 .

[3]  Helio J. C. Barbosa,et al.  Symbolic regression via genetic programming , 2000, Proceedings. Vol.1. Sixth Brazilian Symposium on Neural Networks.

[4]  Paul A. Viola,et al.  MIMIC: Finding Optima by Estimating Probability Densities , 1996, NIPS.

[5]  Athanasios Tsakonas,et al.  Symbolic regression via genetic programming in the optimization of a controlled release pharmaceutical formulation , 2011 .

[6]  Alberto Moraglio,et al.  Geometric Differential Evolution on the Space of Genetic Programs , 2010, EuroGP.

[7]  Rajkumar Roy,et al.  Advances in Soft Computing , 2018, Lecture Notes in Computer Science.

[8]  Anthony Brabazon,et al.  Foundations in Grammatical Evolution for Dynamic Environments , 2009, Studies in Computational Intelligence.

[9]  Taghi M. Khoshgoftaar,et al.  Genetic programming-based decision trees for software quality classification , 2003, Proceedings. 15th IEEE International Conference on Tools with Artificial Intelligence.

[10]  Heinz Mühlenbein,et al.  The Equation for Response to Selection and Its Use for Prediction , 1997, Evolutionary Computation.

[11]  A. E. Eiben,et al.  Parameter tuning for configuring and analyzing evolutionary algorithms , 2011, Swarm Evol. Comput..

[12]  Anthony Brabazon,et al.  Grammatical Differential Evolution , 2006, IC-AI.

[13]  Shumeet Baluja,et al.  A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning , 1994 .

[14]  Julian Togelius,et al.  Geometric PSO + GP = Particle Swarm Programming , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[15]  Pedro Larrañaga,et al.  Estimation of Distribution Algorithms , 2002, Genetic Algorithms and Evolutionary Computation.

[16]  Juan Martín Carpio Valadez,et al.  Evolutionary Indirect Design of Feed-Forward Spiking Neural Networks , 2015, Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization.

[17]  Michael O'Neill,et al.  Grammatical Evolution: Evolving Programs for an Arbitrary Language , 1998, EuroGP.

[18]  M. Pelikán,et al.  The Bivariate Marginal Distribution Algorithm , 1999 .

[19]  Juan Martín Carpio Valadez,et al.  Evolving and reusing Bin Packing heuristic through Grammatical Differential Evolution , 2013, 2013 World Congress on Nature and Biologically Inspired Computing.

[20]  Dervis Karaboga,et al.  Artificial bee colony programming for symbolic regression , 2012, Inf. Sci..

[21]  Marco Aurelio Sotelo-Figueroa,et al.  Improving the Bin Packing Heuristic through Grammatical Evolution Based on Swarm Intelligence , 2014 .

[22]  Martin Pelikan,et al.  An introduction and survey of estimation of distribution algorithms , 2011, Swarm Evol. Comput..

[23]  Oscar Castillo,et al.  Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization , 2015, Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization.