Evolution and Dynamics of Small-World Cellular Automata

We study an extension of cellular automata to arbitrary interconnection topologies for the majority and the synchronization problems. By using an evolutionary algorithm, we show that small-world type network topologies consistently evolve from regular and random structures without being designed beforehand. These topologies have better performance than regular lattice structures and are easier to evolve, which could explain in part their ubiquity. Moreover, we show experimentally that general graph topologies are much more robust in the face of random faults than lattice structures for these problems.

[1]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

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

[3]  Capcarrere,et al.  Two-state, r=1 Cellular Automaton that Classifies Density. , 1996, Physical review letters.

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

[5]  James P. Crutchfield,et al.  The Evolutionary Design of Collective Computation in Cellular Automata , 1998, adap-org/9809001.

[6]  Enrique Alba,et al.  The influence of grid shape and asynchronicity on cellular evolutionary algorithms , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[7]  Marco Tomassini,et al.  Evolving robust asynchronous CA for the density task. , 2002 .

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

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

[10]  Max H. Garzon,et al.  Models of massive parallelism: analysis of cellular automata and neural networks , 1995 .

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

[12]  Marco Tomassini,et al.  Studying Probabilistic Faults in Evolved Non-Uniform Cellular Automata , 1996 .

[13]  Mike Mannion,et al.  Complex systems , 1997, Proceedings International Conference and Workshop on Engineering of Computer-Based Systems.

[14]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[15]  Kojima.  Structure and function , 2005 .

[16]  Enrique Alba,et al.  Modeling Selection Intensity for Toroidal Cellular Evolutionary Algorithms , 2004, GECCO.

[17]  Jie Wu,et al.  Small Worlds: The Dynamics of Networks between Order and Randomness , 2003 .

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

[19]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[20]  Marco Tomassini,et al.  Evolution of Small-World Networks of Automata for Computation , 2004, PPSN.

[21]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[22]  Marco Tomassini,et al.  Soft computing - integrating evolutionary, neural, and fuzzy systems , 2001 .

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

[24]  J. Pollack,et al.  Coevolving the "Ideal" Trainer: Application to the Discovery of Cellular Automata Rules , 1998 .

[25]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.