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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

Gene Expression Programming

Gene Expression Programming was invented by myself in 1999 (Ferreira 2001), and incorporates both the simple, linear chromosomes of fixed length similar to the ones used in Genetic Algorithms and the ramified structures of different sizes and shapes similar to the parse trees of Genetic Programming. And since the ramified structures of different sizes and shapes are totally encoded in the linear chromosomes of fixed length, this is equivalent to say that, in GEP, the genotype and phenotype are finally separated from one another and the system can now benefit from all the evolutionary advantages this brings about.

Thus, the phenotype of GEP consists of the same kind of ramified structure used in GP. But the ramified structures evolved by GEP (called expression trees) are the expression of a totally autonomous genome. Therefore, with GEP, a remarkable thing happened: the second evolutionary threshold – the phenotype threshold – was crossed (Dawkins 1995). And this means that only the genome (slightly modified) is passed on to the next generation. Consequently, one no longer needs to replicate and mutate rather cumbersome structures as all the modifications take place in a simple linear structure which only later will grow into an expression tree.

The fundamental steps of Gene Expression Programming are schematically represented in Figure 5. The process begins with the random generation of the chromosomes of a certain number of individuals (the initial population). Then these chromosomes are expressed and the fitness of each individual is evaluated against a set of fitness cases (also called selection environment). The individuals are then selected according to their fitness (their performance in that particular environment) to reproduce with modification, leaving progeny with new traits. These new individuals are, in their turn, subjected to the same developmental process: expression of the genomes, confrontation of the selection environment, selection according to fitness, and reproduction with modification. The process is repeated for a certain number of generations or until a good solution has been found.

Figure 5. The flowchart of Gene Expression Programming.

So, the pivotal insight of Gene Expression Programming consisted in the invention of chromosomes capable of representing any parse tree. For that purpose a new language – Karva language – was created in order to read and express the information encoded in the chromosomes. The details of this new language are given in the next section.

Furthermore, the structure of the chromosomes was designed in order to allow the creation of multiple genes, each coding for a smaller program or sub-expression tree. It is worth emphasizing that Gene Expression Programming is the only genetic algorithm with multiple genes. Indeed, in truly functional genotype/phenotype systems, the creation of more complex individuals composed of multiple genes is a child’s play, and illustrates quite well the great versatility of the GEP system. In fact, after their inception, these systems seem to catapult themselves into higher levels of complexity such as the uni- and multicellular systems, where different cells put together different combinations of genes (Ferreira 2002a). We will see later in this chapter how the cellular system of GEP is an extremely elegant way of implementing Automatically Defined Functions that may be reused by the created programs.

The basis for all this novelty resides on the simple, yet revolutionary structure of GEP genes. This structure not only allows the encoding of any conceivable program but also allows an efficient evolution. This versatile structural organization also allows the implementation of a very powerful set of genetic operators which can then very efficiently search the solution space. As in nature, the search operators of GEP always generate valid structures and therefore are remarkably suited to creating genetic diversity.


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