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Finding needles in haystacks is harder with neutrality

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Abstract

This research presents an extended analysis of the reported successes of the Cartesian Genetic Programming method on a simplified form of the Boolean parity problem. We show the method of sampling used by the CGP is significantly less effective at locating solutions than the solution density of the corresponding formula space would warrant. We present results indicating that the loss of performance is caused by the sampling bias of the CGP, due to the neutrality friendly representation. We implement a simple intron free random sampling algorithm which performs considerably better on the same problem and then explain how such performance is possible.

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References

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  2. M. Collins, “Monte carlo sampling and counting solutions in reduced boolean parity,” Technical Report, November 2004. EDI-INF-RR-0240.

  3. W.B. Langdon and R. Poli, “Boolean functions fitness spaces,” in Late Breaking Papers at the Genetic Programming 1998 Conference, J. R. Kozai, (ed.), University of Wisconsin, Madison, Wisconsin, USA, 22–25 July 1998. Stanford University Bookstore.

  4. J.F. Miller, “An empirical study of the efficiency of learning boolean functions using a cartesian genetic programming approach,” in Proceedings of the Genetic and Evolutionary Computation Conference, Wolf- gang Banzhaf et al. (eds.), Morgan Kaufmann, 1999, vol. 2, pp. 1135--1142.

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  7. T. Yu and J. Miller, “Neutrality and the evolvability of boolean function landscape,” in Genetic Programming, Proceedings of EuroGP'2001, J.F. Miller, M. Tomassini, P.L. Lanzi, C. Ryan, A.G.B. Tettamanzi, and W.B. Langdon (eds.), vol. 2038 of LNCS, Springer-Verlag, Lake Como, Italy, 18–20 April 2001, pp. 204–217.

  8. T. Yu and J.F. Miller, “Finding needles in haystacks is not hard with neutrality,” in Genetic Programming, Proceedings of the 5th European Conference, J.A. Foster et al. (eds.), EuroGP 2002, vol. 2278 of LNCS, Springer-Verlag: Kinsale, Ireland, 3–5 April 2002, pp. 13–25.

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Acknowledgments

For their invaluable contributions during my work, my gratitude to: Richard Carter, Jacques Fleuriot, Michelle Galea, John Levine, Julian Miller, Dave Robertson and Henrik Westerberg. Sincere thanks are also due to the reviewers

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    M. Collins

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Collins, M. Finding needles in haystacks is harder with neutrality. Genet Program Evolvable Mach 7, 131–144 (2006). https://doi.org/10.1007/s10710-006-9001-y

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  • DOI: https://doi.org/10.1007/s10710-006-9001-y

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