References

Alonso and Schott1995

Laurent Alonso and Rene Schott. Random Generation of Trees. Kluwer Academic Publishers, 1995.

Koza1992

John R. Koza. Genetic Programming: On the Programming of Computers by Natural Selection. MIT Press, Cambridge, MA, USA, 1992.

Koza1995

John R. Koza. A response to the ML-95 paper entitled ``Hill climbing beats genetic search on a boolean circuit synthesis of Koza's''. Distributed 11 July 1995 at the 1995 International Machine Learning Conference in Tahoe City, California, USA, 11 July 1995.

Lang1995

Kevin J. Lang. Hill climbing beats genetic search on a boolean circuit synthesis of Koza's. In Proceedings of the Twelfth International Conference on Machine Learning, Tahoe City, California, USA, July 1995. Morgan Kaufmann.

Langdon and Poli1997

W. B. Langdon and R. Poli. Fitness causes bloat. In P. K. Chawdhry, R. Roy, and R. K. Pan, editors, Second On-line World Conference on Soft Computing in Engineering Design and Manufacturing. Springer-Verlag London, 23-27 June 1997.

Langdon and Poli1998

W. B. Langdon and R. Poli. Why ants are hard. In John R. Koza, Wolfgang Banzhaf, Kumar Chellapilla, Kalyanmoy Deb, Marco Dorigo, David B. Fogel, Max H. Garzon, David E. Goldberg, Hitoshi Iba, and Rick Riolo, editors, Genetic Programming 1998: Proceedings of the Third Annual Conference, University of Wisconsin, Madison, Wisconsin, USA, 22-25 July 1998. Morgan Kaufmann.

Rosca1997

Justinian P. Rosca. Hierarchical Learning with Procedural Abstraction Mechanisms. PhD thesis, University of Rochester, Rochester, NY 14627, February 1997.

Wolpert and Macready1997

David H. Wolpert and William G. Macready. No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1(1):67--82, April 1997.

The ramped-half-and-half method [Koza1992, page 93,] does not sample the program space uniformly. Results from the Ant problem show it samples parts of the search space with relatively few solutions. Undoubtedly at least part of this is problem specific, it simply samples too many programs which are too short to be solutions (these also fall below the size threshold discussed in the previous paragraph). However ramped-half-and-half has a shape bias, half the trees it generates are full.