Meta-Genetic Programming: Co-evolving the Operators of Variation - Bruce Edmonds

5. MGP as a framework for a set of techniques

The relation of "Population A acting as operators on population B" can be represented diagrammatically by an arrow. In figure 13, I illustrate traditional GP and basic MGP setups, with evolving population represented by ellipses and fixed populations by rectangles.

Figure 13: GP and MGP setups

There is no a priori reason why many different setups should not be investigated. For example figure 14 shows a simple enhancement of GP where just the proportions of the operators is changed, implementing a similar technique as invented by for GAs, and figure 15 illustrates the possibility of combining a fixed and evolving population of operators.

Figure 14: GP with the proportion of operators evolving

Figure 15: A setup with a mixture of fixed and evolving operators

Finally there is no reason why populations of operators should not operate recursively. One can even imagine situations in which the interpretation (i.e. fitness) of the base population and operator population was done consistently enough such that you only had one population acting on itself in a self-organising loop, as in figure 16. In this case care would need to be taken in the allocation of fitness values, maybe by some mechanism as the bucket-brigade algorithm [6] or similar. Such a structure may allow the implicit decision of the best structure and allow for previously unimaginable hybrid operator-base genes *1. It does seem unlikely, however, that the same population of operators would be optimal for evolving the operators as the base population, due to their different functions.

Figure 16: A recursively evolving MGP setup

Further, if the language of the operators described above could be extended with the addition of nodes like "if-then-else", "equal", "and" and "root-is-implies" nodes, then operators like Modus Ponens (the logical rule that says from and you can infer ) could be encoded (see figure 17). This would mean that such an operator would produce child genes which were the logical inferences of those in previous generations. Such an operator would produces deductions on the genes. In a similar way one could allow for a techniques which allow different mixes of inferential and evolutionary learning techniques.

Figure 17: A Modus Ponens operator

In this way the differences between approaches become less marked, allowing a range of mixed learning approaches to tried. It also provides a rudimentary framework for them to be compared.

Meta-Genetic Programming: Co-evolving the Operators of Variation - Bruce Edmonds - 28 JAN 98

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