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Neutral Fitness Landscape in the Cellular Automata Majority Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4173))

Abstract

We study in detail the fitness landscape of a difficult cellular automata computational task: the majority problem. Our results show why this problem landscape is so hard to search, and we quantify the large degree of neutrality found in various ways. We show that a particular subspace of the solution space, called the ”Olympus”, is where good solutions concentrate, and give measures to quantitatively characterize this subspace.

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References

  1. Wolfram, S.: A New Kind of Science. Wolfram Media (2002)

    Google Scholar 

  2. Land, M., Belew, R.K.: No perfect two-state cellular automata for density classification exists. Physical Review Letters 74, 5148–5150 (1995)

    Article  Google Scholar 

  3. Mitchell, M., Crutchfield, J.P., Hraber, P.T.: Evolving cellular automata to perform computations: Mechanisms and impediments. Physica D 75, 361–391 (1994)

    Article  MATH  Google Scholar 

  4. Andre, D., Bennett III, F.H., Koza, J.R.: Discovery by genetic programming of a cellular automata rule that is better than any known rule for the majority classification problem. In: Koza, J.R., Goldberg, D.E., Fogel, D.B., Riolo, R.L. (eds.) Genetic Programming 1996: Proceedings of the First Annual Conference, pp. 3–11. MIT Press, Cambridge (1996)

    Google Scholar 

  5. Juillé, H., Pollack, J.B.: Coevolutionary learning: a case study. In: ICML 1998 Proceedings of the Fifteenth International Conference on Machine Learning, pp. 251–259. Morgan Kaufmann, San Francisco (1998)

    Google Scholar 

  6. Crutchfield, J.P., Mitchell, M., Das, R.: Evolutionary design of collective computation in cellular automata. In: Crutchfield, J.P., Schuster, P. (eds.) Evolutionary Dynamics: Exploring the Interplay of Selection, Accident, Neutrality, and Function, pp. 361–411. Oxford University Press, Oxford (2003)

    Google Scholar 

  7. Packard, N.H.: Adaptation toward the edge of chaos. In: Kelso, J.A.S., Mandell, A.J., Shlesinger, M.F. (eds.) Dynamic Patterns in Complex Systems, pp. 293–301. World Scientific, Singapore (1988)

    Google Scholar 

  8. Pagie, L., Mitchell, M.: A comparison of evolutionary and coevolutionary search. In: Belew, R.K., Juillè, H. (eds.) Coevolution: Turning Adaptive Algorithms upon Themselves, San Francisco, California, USA, pp. 20–25 (2001)

    Google Scholar 

  9. Das, R., Mitchell, M., Crutchfield, J.P.: A genetic algorithm discovers particle-based computation in cellular automata. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 344–353. Springer, Heidelberg (1994)

    Google Scholar 

  10. Hanson, J.E., Crutchfield, J.P.: Computational mechanics of cellular automata: An example. Technical Report 95-10-95, Santa Fe Institute Working Paper (1995)

    Google Scholar 

  11. Gacs, P., Kurdyumov, G.L., Levin, L.A.: One-dimensional uniform arrays that wash out finite islands. Problemy Peredachi Informatsii 14, 92–98 (1978)

    Google Scholar 

  12. Reidys, C.M., Stadler, P.F.: Neutrality in fitness landscapes. Applied Mathematics and Computation 117, 321–350 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kimura, M.: The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge (1983)

    Book  Google Scholar 

  14. Rosé, H., Ebeling, W., Asselmeyer, T.: The density of states - a measure of the difficulty of optimisation problems. In: Parallel Problem Solving from Nature, pp. 208–217 (1996)

    Google Scholar 

  15. Van Nimwegen, E., Crutchfield, J., Huynen, M.: Neutral evolution of mutational robustness. Proc. Nat. Acad. Sci. USA 96, 9716–9720 (1999)

    Article  Google Scholar 

  16. Bastolla, U., Porto, M., Roman, H.E., Vendruscolo, M.: Statiscal properties of neutral evolution. Journal Molecular Evolution 57, 103–119 (2003)

    Article  Google Scholar 

  17. Vanneschi, L., Clergue, M., Collard, P., Tomassini, M., Verel, S.: Fitness clouds and problem hardness in genetic programming. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3102, Springer, Heidelberg (2004)

    Google Scholar 

  18. Barnett, L.: Netcrawling - optimal evolutionary search with neutral networks. In: Proceedings of the 2001 Congress on Evolutionary Computation CEC2001, COEX, World Trade Center, 159 Samseong-dong, Gangnam-gu, Seoul, Korea, pp. 30–37. IEEE Press, Los Alamitos (2001)

    Chapter  Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Verel, S., Collard, P., Tomassini, M., Vanneschi, L. (2006). Neutral Fitness Landscape in the Cellular Automata Majority Problem. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds) Cellular Automata. ACRI 2006. Lecture Notes in Computer Science, vol 4173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11861201_31

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  • DOI: https://doi.org/10.1007/11861201_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40929-8

  • Online ISBN: 978-3-540-40932-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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