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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

Incorporating Random Numerical Constants in ADFs

The incorporation of random numerical constants in Automatically Defined Functions is also easy and straightforward. As you probably guessed, the gene structure used to accomplish this includes the special domain Dc for encoding the random numerical constants, which, for the sake of simplicity and efficiency, is only implemented in the genes encoding the ADFs (one can obviously extend this organization to the homeotic genes, but nothing is gained from that except a considerable increase in computational effort). The structure of the homeotic genes remains exactly the same and they continue to control how often each ADF is called upon and how they interact with one another.

Consider, for instance, the chromosome with two conventional genes and their respective arrays of random numerical constants:







A0 = {0.664, 1.703, 1.958, 1.178, 1.258, 2.903, 2.677, 1.761, 0.923, 0.796}


A1 = {0.588, 2.114, 0.510, 2.359, 1.355, 0.186, 0.070, 2.620, 2.374, 1.710}


The genes encoding the ADFs are expressed exactly as normal genes with a Dc domain and, therefore, their respective ADFs will, most probably, include random numerical constants (Figure 10). Then these ADFs with random numerical constants are called upon as many times as necessary from any of the main programs encoded in the homeotic genes. As you can see in Figure 10, ADF0 is invoked twice in Cell0 and once in Cell1, whereas ADF1 is used just once in Cell0 and called three different times in Cell1.

Figure 10. Expression of a multicellular system with Automatically Defined Functions containing random numerical constants. a) The chromosome composed of two conventional genes and two homeotic genes (shown in bold). b) The ADFs codified by each conventional gene. c) Two different programs expressed in two different cells.


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