Adapting learning classifier systems to symbolic regression

Genetic programming (GP) approaches have been widely studied for symbolic regression problems and have achieved substantial progress. This work investigates the effectiveness of niching property and multiple learned solutions of a Learning Classifier System (LCS) to symbolic regression benchmark problems. Specifically, an XCS with real-valued interval based conditions and code fragmented action termed as XCS-SR is proposed for tackling symbolic regression problem. This is the first LCS ever to address the problem of symbolic regression. The results on nine standard symbolic regression benchmarks show that the proposed XCS-SR method consistently obtains statistically better results on a majority of the benchmarks, in terms of average absolute error together with an increased number of exact solutions as compared with the GP benchmark.

[1]  Ester Bernadó-Mansilla,et al.  Accuracy-Based Learning Classifier Systems: Models, Analysis and Applications to Classification Tasks , 2003, Evolutionary Computation.

[2]  Martin V. Butz,et al.  Automated Global Structure Extraction for Effective Local Building Block Processing in XCS , 2006, Evolutionary Computation.

[3]  Leonardo Vanneschi,et al.  Multi-optimization improves genetic programming generalization ability , 2007, GECCO '07.

[4]  Krzysztof Krawiec,et al.  Multiple regression genetic programming , 2014, GECCO.

[5]  Michael O'Neill,et al.  Genetic Programming and Evolvable Machines Manuscript No. Semantically-based Crossover in Genetic Programming: Application to Real-valued Symbolic Regression , 2022 .

[6]  Stewart W. Wilson.  Three Architectures for Continuous Action , 2005, IWLCS.

[7]  Michael O'Neill,et al.  Semantic Aware Crossover for Genetic Programming: The Case for Real-Valued Function Regression , 2009, EuroGP.

[8]  Daniele Loiacono,et al.  Generalization in the XCSF Classifier System: Analysis, Improvement, and Extension , 2007, Evolutionary Computation.

[9]  Stewart W. Wilson.  Get Real! XCS with Continuous-Valued Inputs , 1999, Learning Classifier Systems.

[10]  Daniele Loiacono,et al.  Classifier systems that compute action mappings , 2007, GECCO '07.

[11]  Larry Bull,et al.  A Genetic Programming-based Classifier System , 1999, GECCO.

[12]  Will N. Browne,et al.  Learning overlapping natured and niche imbalance boolean problems using XCS classifier systems , 2013, 2013 IEEE Congress on Evolutionary Computation.

[13]  Stewart W. Wilson.  Function approximation with a classifier system , 2001 .

[14]  Mengjie Zhang,et al.  Evolving optimum populations with XCS classifier systems , 2012, Soft Computing.

[15]  Nguyen Xuan Hoai,et al.  Solving the symbolic regression problem with tree-adjunct grammar guided genetic programming: the comparative results , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[16]  Kalyan Veeramachaneni,et al.  Learning regression ensembles with genetic programming at scale , 2013, GECCO '13.

[17]  Leonardo Vanneschi,et al.  A comparison of the generalization ability of different genetic programming frameworks , 2010, IEEE Congress on Evolutionary Computation.

[18]  Maarten Keijzer,et al.  Improving Symbolic Regression with Interval Arithmetic and Linear Scaling , 2003, EuroGP.

[19]  Riccardo Poli,et al.  Genetic Programming: An Introduction and Tutorial, with a Survey of Techniques and Applications , 2008, Computational Intelligence: A Compendium.

[20]  Anisa W. Ragalo,et al.  A building block conservation and extension mechanism for improved performance in Polynomial Symbolic Regression tree-based Genetic Programming , 2012, 2012 Fourth World Congress on Nature and Biologically Inspired Computing (NaBIC).

[21]  Mark Kotanchek,et al.  Scalable Symbolic Regression by Continuous Evolution with Very Small Populations , 2011 .

[22]  Mengjie Zhang,et al.  Reusing Building Blocks of Extracted Knowledge to Solve Complex, Large-Scale Boolean Problems , 2014, IEEE Transactions on Evolutionary Computation.

[23]  Sean Luke,et al.  A Comparison of Bloat Control Methods for Genetic Programming , 2006, Evolutionary Computation.

[24]  Kenneth Chiu,et al.  Prioritized grammar enumeration: symbolic regression by dynamic programming , 2013, GECCO '13.

[25]  Colin G. Johnson.  Genetic Programming Crossover: Does It Cross over? , 2009, EuroGP.

[26]  Michael F. Korns.  Accuracy in Symbolic Regression , 2011 .

[27]  Martin V. Butz,et al.  An algorithmic description of XCS , 2000, Soft Comput..

[28]  Martin V. Butz,et al.  Function Approximation With XCS: Hyperellipsoidal Conditions, Recursive Least Squares, and Compaction , 2008, IEEE Transactions on Evolutionary Computation.