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

Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence

The higher hierarchical organization of multigenic systems

Gene expression programming is the only genetic algorithm that deals with genes as separated entities, tied up, however, in a more complex structure – the chromosome. From the analysis of the previous section, it is clear that multigenic systems are far superior to unigenic ones. Here, we are going to make a more systematic analysis by comparing multigenic and unigenic systems with exactly the same chromosome length. The problems chosen for this analysis are exactly the same of the previous section using also the same general settings (see Tables 7.4 and 7.5).

Table 7.4
Comparing the performance of unigenic and multigenic systems on the function finding problem.

 1G 3G 5G Number of runs 100 100 100 Number of generations 50 50 50 Population size 30 30 30 Number of fitness cases 10 10 10 Function set + - * / + - * / + - * / Head length 37 12 7 Number of genes 1 3 5 Linking function -- + + Chromosome length 75 75 75 Mutation rate 0.03 0.03 0.03 One-point recombination rate 0.3 0.3 0.3 Two-point recombination rate 0.3 0.3 0.3 Gene recombination rate -- 0.1 0.1 IS transposition rate 0.1 0.1 0.1 IS elements length 1,2,3 1,2,3 1,2,3 RIS transposition rate 0.1 0.1 0.1 RIS elements length 1,2,3 1,2,3 1,2,3 Gene transposition rate -- 0.1 0.1 Selection range 25% 25% 25% Precision 0.01% 0.01% 0.01% Success rate 58% 93% 98%

For this analysis, a common chromosome length of 75 was chosen for three different chromosomal organizations: unigenic chromosomes with h = 37; three-genic chromosomes with h = 12; and five-genic chromosomes with h = 7. The performance of these systems was measured in terms of success rate and is shown in Tables 7.4 and 7.5.

Table 7.5
Comparing the performance of unigenic and multigenic systems on the sequence induction problem.

 1G 3G 5G Number of runs 100 100 100 Number of generations 100 100 100 Population size 50 50 50 Number of fitness cases 10 10 10 Function set + - * / + - * / + - * / Head length 37 12 7 Number of genes 1 3 5 Linking function -- + + Chromosome length 75 75 75 Mutation rate 0.03 0.03 0.03 One-point recombination rate 0.3 0.3 0.3 Two-point recombination rate 0.3 0.3 0.3 Gene recombination rate -- 0.1 0.1 IS transposition rate 0.1 0.1 0.1 IS elements length 1,2,3 1,2,3 1,2,3 RIS transposition rate 0.1 0.1 0.1 RIS elements length 1,2,3 1,2,3 1,2,3 Gene transposition rate -- 0.1 0.1 Selection range 25% 25% 25% Precision 0% 0% 0% Success rate 41% 79% 96%

As expected, multigenic systems are significantly more efficient than unigenic ones and should always be our first choice. There might be problems, though, for which the fractionating of the chromosome in genes is of little advantage. For instance, when we are trying to evolve a solution to a problem best modeled by a square root function of some complex expression and a multicellular system was not our first choice. But, even in those cases, the system can easily find ways of turning the unnecessary genes into neutral genes and, therefore, an efficient adaptation can still occur. But of course, in multicellular systems, the modeling of all kinds of function can benefit from multiple genes as those systems are not constrained by a particular kind of linking function.

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