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C. FERREIRA In N. Nedjah, L. de M. Mourelle, A. Abraham, eds., Genetic Systems Programming: Theory and Experiences, Studies in Computational Intelligence, Vol. 13, pp. 21-56, Springer-Verlag, 2006.

Automatically Defined Functions in Gene Expression Programming


Comparatively to Genetic Programming, the implementation of Automatically Defined Functions in Gene Expression Programming is very simple because it stands on the shoulders of the multigenic system with static linking and, therefore, requires just a small addition to make it work. And because the cellular system of GEP with ADFs, like all GEP systems, continues to be totally encoded in a simple linear genome, it poses no constraints whatsoever to the action of the genetic operators and, therefore, these systems can also evolve efficiently (indeed, all the genetic operators of GEP were easily extended to the homeotic genes). As a comparison, the implementation of ADFs in GP adds additional constraints to the already constrained genetic operators in order to ensure the integrity of the different structural branches of the parse tree. Furthermore, due to its mammothness, the implementation of multiple main programs in Genetic Programming is prohibitive, whereas in Gene Expression Programming the creation of a multicellular system encoding multiple main programs is a child's play.

Indeed, another advantage of the cellular system of GEP, is that it can easily grow into a multicellular one, encoding not just one but multiple cells or main programs, each using a different set of ADFs. These multicellular systems have multiple applications, some of which were already illustrated in this work, but their real potential resides in solving problems with multiple outputs where each cell encodes a program involved in the identification of a certain class or pattern. Indeed, the high performance exhibited by the multicellular system in this work gives hope that this system can be fruitfully explored to solve much more complex problems. In fact, in this work, not only the multicellular but also the unicellular and the multigenic system with static linking, were all far from stretched to their limits as the small population sizes of just 50 individuals used in all the experiments of this work indicate. As a comparison, to solve this same problem, the GP system with ADFs uses already populations of 4,000 individuals.

And yet another advantage of the ADFs of Gene Expression Programming, is that they are free to become functions of one or several arguments, being this totally decided by evolution itself. Again, in GP, the number of arguments each ADF takes must be a priori decided and cannot be changed during the course of evolution lest invalid structures are created.

And finally, the cellular system (and multicellular also) encoding ADFs with random numerical constants was for the first time described in this work. Although their performance was also compared to other systems, the main goal was to show that ADFs with random numerical constants can also evolve efficiently, extending not only their appeal but also the range of their potential applications.

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