Abstract
We study an extension of cellular automata to arbitrary interconnection topologies for the majority problem. By using an evolutionary algorithm, we show that small-world 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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Albert, R., Barabasi, A.-L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74, 47–97 (2002)
Capcarrère, M.S., Sipper, M., Tomassini, M.: Two-state, r=1 cellular automaton that classifies density. Physical Review Letters 77(24), 4969–4971 (1996)
Dorronsoro, B., Alba, E., Giacobini, M., Tomassini, M.: The influence of grid shape and asynchronicity in cellular evolutionary algorithms. In: Congress on Evolutionary Computation (CEC 2004) (to appear)
Garzon, M. (ed.): Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks. Springer, Berlin (1995)
Kauffman, S.A.: The Origins of Order. Oxford University Press, New York (1993)
Land, M., Belew, R.K.: No perfect two-state cellular automata for density classification exists. Physical Review Letters 74(25), 5148–5150 (1995)
Thomson Leighton, F.: Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann, San Mateo (1992)
Mitchell, M., Crutchfield, J.P., Hraber, P.T.: Evolving cellular automata to perform computations: Mechanisms and impediments. Physica D 75, 361–391 (1994)
Mitchell, M., Hraber, P.T., Crutchfield, J.P.: Revisiting the edge of chaos: Evolving cellular automata to perform computations. Complex Systems 7, 89–130 (1993)
Serra, R., Villani, M.: Perturbing the regular topology of cellular automata: implications for the dynamics. In: Bandini, S., Chopard, B., Tomassini, M. (eds.) ACRI 2002. LNCS, vol. 2493, pp. 168–177. Springer, Heidelberg (2002)
Sipper, M.: Evolution of Parallel Cellular Machines: The Cellular Programming Approach. Springer, Heidelberg (1997)
Sipper, M., Ruppin, E.: Co-evolving architectures for cellular machines. Physica D 99, 428–441 (1997)
Watts, D.J.: Small worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press, Princeton (1999)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tomassini, M., Giacobini, M., Darabos, C. (2004). Evolution of Small-World Networks of Automata for Computation. In: Yao, X., et al. Parallel Problem Solving from Nature - PPSN VIII. PPSN 2004. Lecture Notes in Computer Science, vol 3242. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30217-9_68
Download citation
DOI: https://doi.org/10.1007/978-3-540-30217-9_68
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23092-2
Online ISBN: 978-3-540-30217-9
eBook Packages: Springer Book Archive