On dynamical genetic programming: simple Boolean networks in learning classifier systems

Many representations have been presented to enable the effective evolution of computer programs. Turing was perhaps the first to present a general scheme by which to achieve this end. Significantly, Turing proposed a form of discrete dynamical system and yet dynamical representations remain almost unexplored within conventional genetic programming (GP). This paper presents results from an initial investigation into using simple dynamical GP representations within a learning classifier system. It is shown possible to evolve ensembles of dynamical Boolean function networks to solve versions of the well-known multiplexer problem. Both synchronous and asynchronous systems are considered.

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

[2]  John R. Koza,et al.  Genetic Programming II , 1992 .

[3]  Ada YUEN,et al.  Applications of Cellular Automata , 2010 .

[4]  W S McCulloch,et al.  A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.

[5]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[6]  H. Crichton-Miller.  Adaptation , 1926 .

[7]  Hod Lipson,et al.  Comparison of tree and graph encodings as function of problem complexity , 2007, GECCO '07.

[8]  Christof Teuscher Dipl-Ing Epfl,et al.  Turing’s Connectionism , 2002, Discrete Mathematics and Theoretical Computer Science.

[9]  J. Reed,et al.  Simulation of biological evolution and machine learning. I. Selection of self-reproducing numeric patterns by data processing machines, effects of hereditary control, mutation type and crossing. , 1967, Journal of theoretical biology.

[10]  Kotaro Hirasawa,et al.  Comparison between Genetic Network Programming (GNP) and Genetic Programming (GP) , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[11]  T. E. Ingerson,et al.  Structure in asynchronous cellular automata , 1984 .

[12]  Larry Bull,et al.  Coevolutionary Species Adaptation Genetic Algorithms: A Continuing SAGA on Coupled Fitness Landscapes , 2005, ECAL.

[13]  O. Bhabha.  The Essential Turing , 2011 .

[14]  Yao-Chen Hung,et al.  Chaos synchronization of two stochastically coupled random Boolean networks , 2006 .

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

[16]  Martin V. Butz,et al.  Toward a theory of generalization and learning in XCS , 2004, IEEE Transactions on Evolutionary Computation.

[17]  Larry Bull,et al.  On Using Constructivism in Neural Classifier Systems , 2002, PPSN.

[18]  Manuel Valenzuela-Rendón,et al.  The Fuzzy Classifier System: A Classifier System for Continuously Varying Variables , 1991, ICGA.

[19]  Larry Bull,et al.  Self-adaptive mutation in classifier system controllers , 2000 .

[20]  SAGAInman HarveyCSRP.  Species Adaptation Genetic Algorithms: A Basis for a Continuing SAGA , 1992 .

[21]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[22]  Kenneth L. Artis.  Design for a Brain , 1961 .

[23]  Astro Teller,et al.  Neural Programming and an Internal Reinforcement Policy , 1996 .

[24]  Thomas Bck,et al.  Self-adaptation in genetic algorithms , 1991 .

[25]  Jan Drugowitsch.  Design and Analysis of Learning Classifier Systems - A Probabilistic Approach , 2008, Studies in Computational Intelligence.

[26]  Larry Bull,et al.  Two simple learning classifier systems , 2005 .

[27]  Tim Kovacs,et al.  Advances in Learning Classifier Systems , 2001, Lecture Notes in Computer Science.

[28]  David M. W. Powers,et al.  Graph composition in a graph grammar-based method for automata network evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[29]  Lee Spector,et al.  Evolving Graphs and Networks with Edge Encoding: Preliminary Report , 1996 .

[30]  Ney Lemke,et al.  A numerical investigation of adaptation in populations of random boolean networks , 2001 .

[31]  Jia Di,et al.  Cellular Array-based Delay-insensitive Asynchronous Circuits Design and Test for Nanocomputing Systems , 2007, J. Electron. Test..

[32]  Larry Bull,et al.  A Self-Adaptive Classifier System , 2000, IWLCS.

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

[34]  John R. Koza,et al.  Hierarchical Genetic Algorithms Operating on Populations of Computer Programs , 1989, IJCAI.

[35]  Carlos Gershenson,et al.  Classification of Random Boolean Networks , 2002, ArXiv.

[36]  Moshe Sipper,et al.  Evolution of Parallel Cellular Machines , 1997, Lecture Notes in Computer Science.

[37]  Richard M. Friedberg,et al.  A Learning Machine: Part I , 1958, IBM J. Res. Dev..

[38]  James P. Crutchfield,et al.  Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations , 1993, Complex Syst..

[39]  Edgar Galvan-Lopez.  Efficient graph-based genetic programming representation with multiple outputs , 2008 .

[40]  Stephen Wolfram,et al.  Theory and Applications of Cellular Automata , 1986 .

[41]  S. Kauffman.  Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[42]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[43]  Wolfgang Banzhaf,et al.  Genetic Programming for Pedestrians , 1993, ICGA.

[44]  Van den Broeck C,et al.  Learning in feedforward Boolean networks. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[45]  Günter P. Wagner,et al.  Complex Adaptations and the Evolution of Evolvability , 2005 .

[46]  Jean-Jacques Chabrier,et al.  Research of a Cellular Automaton Simulating Logic Gates by Evolutionary Algorithms , 2003, EuroGP.

[47]  J. Miller.  An empirical study of the efficiency of learning boolean functions using a Cartesian Genetic Programming approach , 1999 .

[48]  T. Gelder,et al.  Mind as Motion: Explorations in the Dynamics of Cognition , 1995 .

[49]  Christof Teuscher,et al.  Deducing local rules for solving global tasks with random Boolean networks , 2005 .

[50]  David B. Fogel,et al.  Meta-evolutionary programming , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[51]  L. Bull,et al.  Dynamic control and information processing in the Belousov-Zhabotinsky reaction using a coevolutionary algorithm. , 2008, The Journal of chemical physics.

[52]  Stewart W. Wilson.  Mining Oblique Data with XCS , 2000, IWLCS.

[53]  Chrystopher L. Nehaniv,et al.  Evolving Embodied Genetic Regulatory Network-Driven Control Systems , 2003, ECAL.

[54]  Marco Tomassini,et al.  Evolving Asynchronous and Scalable Non-uniform Cellular Automata , 1997, ICANNGA.

[55]  Stewart W. Wilson.  Classifier Fitness Based on Accuracy , 1995, Evolutionary Computation.

[56]  Richard S. Forsyth,et al.  BEAGLE—A DARWINIAN APPROACH TO PATTERN RECOGNITION , 1981 .

[57]  Wolfgang Banzhaf,et al.  Adaption of Operator Probabilities in Genetic Programming , 2001, EuroGP.

[58]  Venkatesh Akella,et al.  Asynchronous Processor Survey , 1997, Computer.

[59]  E. D. Paolo,et al.  Rhythmic and non-rhythmic attractors in asynchronous random Boolean networks , 2001 .

[60]  John Dickinson,et al.  Using the Genetic Algorithm to Generate LISP Source Code to Solve the Prisoner's Dilemma , 1987, ICGA.

[61]  Juan Julián Merelo Guervós,et al.  Parallel Problem Solving from Nature — PPSN VII , 2002, Lecture Notes in Computer Science.

[62]  D. M. Hutton,et al.  The Essential Turing , 2007 .

[63]  Pier Luca Lanzi,et al.  System Level Hardware-Software Design Exploration with XCS , 2004, GECCO.

[64]  Marco Tomassini,et al.  Evolution of Asynchronous Cellular Automata for the Density Task , 2002, PPSN.

[65]  Marco Dorigo,et al.  New Ideas in Optimisation , 1999 .

[66]  Luca Lanzi Pier,et al.  Extending the Representation of Classifier Conditions Part II: From Messy Coding to S-Expressions , 1999 .

[67]  Rodney A. Brooks,et al.  Asynchrony induces stability in cellular automata based models , 1994 .

[68]  Riccardo Poli,et al.  Parallel Distributed Genetic Programming , 1996 .

[69]  Larry Bull,et al.  A Neural Learning Classifier System with Self-Adaptive Constructivism for Mobile Robot Control , 2006, Artificial Life.

[70]  Thomas S. Ray,et al.  An Approach to the Synthesis of Life , 1991 .

[71]  B. Jack Copeland,et al.  On Alan Turing's anticipation of connectionism , 1996, Synthese.

[72]  Riccardo Poli,et al.  Efficient Evolution of Asymmetric Recurrent Neural Networks Using a PDGP-inspired Two-Dimensional Representation , 1998, EuroGP.

[73]  L. Darrell Whitley,et al.  Adding Learning to the Cellular Development of Neural Networks: Evolution and the Baldwin Effect , 1993, Evolutionary Computation.