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C. FERREIRA Complex Systems, 13 (2): 87-129, 2001

Gene Expression Programming: A New Adaptive Algorithm for Solving Problems

Multigenic Chromosomes

GEP chromosomes are usually composed of more than one gene of equal length. For each problem or run, the number of genes, as well as the length of the head, is chosen. Each gene codes for a sub-ET and the sub-ETs interact with one another forming a more complex multisubunit ET. The details of such interactions are fully explained in section 3.4.

Consider, for example, the following chromosome with length 27, composed of three genes (the tails are shown in blue):




It has three ORFs, and each ORF codes for a sub-ET (Figure 2). Position 0 marks the start of each gene; the end of each ORF, though, is only evident upon construction of the respective sub-ET. As shown in Figure 2, the first ORF ends at position 4 (sub-ET1); the second ORF ends at position 5 (sub-ET2); and the last ORF also ends at position 5 (sub-ET3). Thus, GEP chromosomes code for one or more ORFs, each expressing a particular sub-ET. Depending on the task at hand, these sub-ETs may be selected individually according to their respective fitness (e.g., in problems with multiple outputs), or they may form a more complex, multi-subunit ET and be selected according to the fitness of the whole, multi-subunit ET. The patterns of expression and the details of selection will be discussed throughout this paper. However, keep in mind that each sub-ET is both a separate entity and a part of a more complex, hierarchical structure, and, as in all complex systems, the whole is more than the sum of its parts.

Figure 2. Expression of GEP genes as sub-ETs. (a) A three-genic chromosome with the tails shown in bold. The arrows show the termination point of each gene. (b) The sub-ETs codified by each gene.

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