Evolving Uniform and Non-Uniform Cellular Automata Networks

Natural evolution has “created” many parallel cellular systems, in which emergent computation gives rise to impressive computational capabilities. In recent years we are witness to a rapidly growing interest in such complex adaptive systems, addressing, among others, the major problem of designing them to exhibit a specific behavior or solve a given problem. One possible approach, which we explore in this paper, is to employ artificial evolution. The systems studied are based on the cellular automata (CA) model, where a regular grid of cells is updated synchronously in discrete time steps, according to a local, identical interaction rule. We first present the application of a standard genetic algorithm to the evolution of CAs to perform two non-trivial computational tasks, density and synchronization, showing that high-performance systems can be attained. The evolutionary process as well as the resulting emergent computation are then discussed. Next we study two generalizations of the CA model, the first consisting of non-uniform CAs, where cellular rules need not be identical for all cells. Introducing the cellular programming evolutionary algorithm, we apply it to six computational tasks, demonstrating that high-performance systems can be evolved. The second generalization involves non-standard, evolving connectivity architectures, where we demonstrate that yet better systems can be attained. Evolving, cellular systems hold potential both scientifically, as vehicles for studying phenomena of interest in areas such as complex adaptive systems and artificial life, as well as practically, showing a range of potential future applications ensuing the construction of adaptive systems, and in particular ‘evolving ware’, evolware.

[1]  James P. Crutchfield,et al.  A Genetic Algorithm Discovers Particle-Based Computation in Cellular Automata , 1994, PPSN.

[2]  N. B. Wilding,et al.  Errors In Monte Carlo Simulations Using Shift Register Random Number Generators , 1995 .

[3]  E. Berlekamp,et al.  Winning Ways for Your Mathematical Plays , 1983 .

[4]  S H Strogatz,et al.  Coupled oscillators and biological synchronization. , 1993, Scientific American.

[5]  K. Eric Drexler,et al.  Nanosystems - molecular machinery, manufacturing, and computation , 1992 .

[6]  Mats G. Nordahl,et al.  Universal Computation in Simple One-Dimensional Cellular Automata , 1990, Complex Syst..

[7]  S. K. Park,et al.  Random number generators: good ones are hard to find , 1988, CACM.

[8]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[9]  N. Margolus Physics-like models of computation☆ , 1984 .

[10]  J. Buck Synchronous Rhythmic Flashing of Fireflies. II. , 1938, The Quarterly Review of Biology.

[11]  Tommaso Toffoli,et al.  Cellular Automata as an Alternative to (Rather than an Approximation of) Differential Equations in M , 1984 .

[12]  Paula Gonzaga Sá,et al.  The Gacs-Kurdyumov-Levin automaton revisited , 1992 .

[13]  Marco Tomassini,et al.  Generating Parallel Random Number Generators By Cellular Programming , 1996 .

[14]  Moshe Sipper An Introduction To Artificial Life , 1995 .

[15]  J. Crutchfield,et al.  Turbulent pattern bases for cellular automata , 1993 .

[16]  G. Vichniac Simulating physics with cellular automata , 1984 .

[17]  Wentian Li,et al.  Transition phenomena in cellular automata rule space , 1991 .

[18]  H. Pagels,et al.  Dreams of Reason: The Computer and the Rise of the Sciences of Complexity , 1989 .

[19]  M Mitchell,et al.  The evolution of emergent computation. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Moshe Sipper,et al.  Co-evolving cellular architectures by cellular programming , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[21]  Bennett,et al.  Role of irreversibility in stabilizing complex and nonergodic behavior in locally interacting discrete systems. , 1985, Physical review letters.

[22]  Marco Tomassini,et al.  Co-evolving Parallel Random Number Generators , 1996, PPSN.

[23]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[24]  Moshe Sipper,et al.  Evolution of Parallel Cellular Machines: The Cellular Programming Approach , 1997 .

[25]  Richard K. Belew,et al.  Towards a Self-Replicating Language for Computation , 1995, Evolutionary Programming.

[26]  Marco Tomassini,et al.  The Parallel Genetic Cellular Automata: Application to Global Function Optimization , 1993 .

[27]  Melanie Mitchell,et al.  Evolving cellular automata to perform computations: mechanisms and impediments , 1994 .

[28]  Tommaso Toffoli,et al.  Cellular Automata Machines , 1987, Complex Syst..

[29]  G. Y. Vichniac,et al.  Annealed and quenched inhomogeneous cellular automata (INCA) , 1986 .

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

[31]  Reiko Tanese,et al.  Parallel Genetic Algorithms for a Hypercube , 1987, ICGA.

[32]  S. Wolfram Statistical mechanics of cellular automata , 1983 .

[33]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[34]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[35]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

[36]  Dietrich Stauffer,et al.  Dynamics and Strong Size Effects of a Bootstrap Percolation Problem , 1996 .

[37]  Moshe Sipper,et al.  Designing Evolware by Cellular Programming , 1996, ICES.

[38]  D Stauffer,et al.  Size effects in Kauffman type evolution for rugged fitness landscapes. , 1994, Journal of theoretical biology.

[39]  Stephen Wolfram,et al.  Universality and complexity in cellular automata , 1983 .

[40]  Max H. Garzon,et al.  Cellular automata and discrete neural networks , 1990 .

[41]  Y. Pomeau,et al.  Molecular dynamics of a classical lattice gas: Transport properties and time correlation functions , 1976 .

[42]  Moshe Sipper,et al.  Co-evolving architectures for cellular machines , 1997 .

[43]  Frank Harary,et al.  Distance in graphs , 1990 .

[44]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[45]  Howard C. Card,et al.  Parallel Random Number Generation for VLSI Systems Using Cellular Automata , 1989, IEEE Trans. Computers.

[46]  Alvy Ray Smith,et al.  Cellular automata theory , 1969 .

[47]  Chris Langton,et al.  Mean Field Theory of the Edge of Chaos , 1995, ECAL.

[48]  Tommaso Toffoli,et al.  Reversible Computing , 1980, ICALP.

[49]  S. Wolfram Random sequence generation by cellular automata , 1986 .

[50]  Christopher G. Langton,et al.  Computation at the edge of chaos: Phase transitions and emergent computation , 1990 .

[51]  Marco Tomassini,et al.  a Survey of Genetic Algorithms , 1995 .

[52]  L. Darrell Whitley,et al.  Optimization Using Distributed Genetic Algorithms , 1990, PPSN.

[53]  Land,et al.  No perfect two-state cellular automata for density classification exists. , 1995, Physical review letters.

[54]  Bernard Manderick,et al.  Fine-Grained Parallel Genetic Algorithms , 1989, ICGA.

[55]  Marco Tomassini,et al.  Online Autonomous Evolware , 1996, ICES.

[56]  G B Ermentrout,et al.  Cellular automata approaches to biological modeling. , 1993, Journal of theoretical biology.

[57]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

[58]  F. H. Bennett,et al.  Discovery by genetic programming of a cellular automata rule that is better than any known rule for the majority classification problem , 1996 .

[59]  Christopher G. Langton,et al.  Life at the Edge of Chaos , 1992 .

[60]  James P. Crutchfield,et al.  Evolving Globally Synchronized Cellular Automata , 1995, ICGA.

[61]  Tommaso Toffoli,et al.  Cellular automata mechanics. , 1977 .

[62]  Moshe Sipper Quasi-Uniform Computation-Universal Cellular Automata , 1995, ECAL.

[63]  Peter V. Coveney,et al.  Frontiers of Complexity: The Search for Order in a Chaotic World, Peter Coveney and Roger Highfield. 1995. Random House, Inc., New York, NY. 480 pages. ISBN: 0-449-90832-1. $27.50 , 1996 .

[64]  Marco Tomassini,et al.  Evolutionary Algorithms , 1995, Towards Evolvable Hardware.

[65]  Zicheng Guo,et al.  Parallel thinning with two-subiteration algorithms , 1989, Commun. ACM.

[66]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .

[67]  Moshe Sipper Studying artificial life using a simple, general cellular model , 1995 .

[68]  K. Culík,et al.  Computation theoretic aspects of cellular automata , 1990 .

[69]  Stephen Wolfram,et al.  Cellular automata as models of complexity , 1984, Nature.

[70]  Moshe Sipper,et al.  Toward a viable, self-reproducing universal computer , 1996 .

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

[72]  M. Sipper Co-evolving non-uniform cellular automata to perform computations , 1996 .

[73]  Vincenzo D'Andrea,et al.  CELLULAR AUTOMATA AS A COMPUTATIONAL MODEL FOR LOW-LEVEL VISION , 1993 .

[74]  Stuart A. Kauffman,et al.  ORIGINS OF ORDER , 2019, Origins of Order.

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

[76]  J. Crutchfield,et al.  The attractor—basin portrait of a cellular automaton , 1992 .

[77]  Y. Pomeau,et al.  Lattice-gas automata for the Navier-Stokes equation. , 1986, Physical review letters.

[78]  James P. Crutchfield,et al.  Dynamics, computation, and the “edge of chaos”: a re-examination , 1993, adap-org/9306003.

[79]  P. Bak,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[80]  Marco Tomassini,et al.  Designing cellular automata using a parallel evolutionary algorithm , 1997 .