Structural Emergence with Order Independent Representations

This paper compares two grammar based Evolutionary Automatic Programming methods, Grammatical Evolution (GE) and Chorus. Both systems evolve sequences of derivation rules which can be used to produce computer programs, however, Chorus employs a position independent representation, while GE uses polymorphic codons, the meaning of which depends on the context in which they are used. We consider issues such as the order in which rules appear in individuals, and demonstrate that an order always emerges with Chorus, which is similar to that of GE, but more flexible. The paper also examines the final step of evolution, that is, how perfect individuals are produced, and how they differ from their immediate neighbours. We demonstrate that, although Chorus appears to be more flexible structure-wise, GE tends to produce individuals with a higher neutrality, suggesting that its representation can, in some cases, make finding the perfect solution easier.