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C. FERREIRA, 2002 (Terms of Use) ISBN: 9729589054

Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence

Other levels of complexity
 
As we have seen in the examples above, although a very simple system, gene expression programming exhibits already a complex development. The most complex individuals evolved by GEP contain, besides the head and the tail, extra domains encoding one-element sub-ETs. These one-element sub-ETs interact with the main sub-ET encoded in the head/tail domain, forming a more complex entity with a complex network of interactions.

One such architecture was developed to manipulate random numerical constants in symbolic regression (Ferreira 2001). For instance, the following chromosome:

01234567890123456789012

+*?+?*+a??aaa??09081345

(2.28)

contains an extra domain Dc (shown in blue) encoding random numerical constants. Its translation is shown in Figure 2.14. In section 4.2 we will learn how these sub-ETs interact with one another so that the individual is fully developed.


Figure 2.14. Translation of chromosomes with multiple domains. a) A multi-domain chromosome composed of a conventional head/tail domain and an extra domain (Dc) encoding random numerical constants (shown in bold). b) The sub-ETs codified by each gene. The one-element sub-ETs encoded in Dc are placed together apart. ? represents the random numerical constants encoded in the numerals of Dc. How all these sub-ETs interact will be shown in section 4.2.


Multiple domains are also used to design neural networks totally encoded in a linear genome (see chapter 5). These neural networks are one of the most complex kind of individual evolved by GEP. In this case, the network architecture is encoded in a conventional head/tail domain whereas the weights and thresholds are encoded in two extra domains, Dw and Dt, each composed of one-element genes. The chromosome below contains two extra domains encoding the weights and the thresholds (the domains are shown in different colors):

012345678901234567890123456789012345

DUbUTdaedbfaabad42998409791482467584

(2.29)

Its translation is shown in Figure 2.15. In chapter 5 we will learn the rules of their complete development and how populations of these complex individuals evolve, finding solutions to problems in the form of a GEP encoded neural network.


Figure 2.15. Translation of chromosomes with multiple domains. a) A multi-domain chromosome composed of a conventional head/tail domain encoding the neural network architecture, and two extra domains one encoding the weights (Dw) of the neural network and another the thresholds (Dt). Dw and Dt are shown in different shades. b) The sub-ETs codified by each gene. The one-element sub-ETs encoded in Dw and Dt are placed together apart. U, D, and T represent, respectively, functions with connectivity one, two, and three. How all these sub-ETs interact will be shown in chapter 5.

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