Evolvability and Redundancy in Shared Grammar Evolution

Shared grammar evolution (SGE) is a novel scheme for representing and evolving a population of variable- length programs as a shared set of grammatical productions. Productions that fail to contribute to selected solutions can be retained for several generations beyond their last use. The ensuing redundancy and its effects are assessed in this paper on two circuit design tasks associated with random number generation: finding a recurrent circuit with maximum period, and reproducing a De Bruijn counter from a set of seed/output pairs. In both instances, increasing redundancy leads to significantly higher success rates, outperforming comparable increases in population size. The results support previous studies that have shown that representational redundancy can be beneficial to evolutionary search. However, redundancy promotes an increase in further redundancy by encouraging the creation of large offspring, the evaluation of which is computationally costly. This observation should generalize to any unconstrained variable- length representation and therefore represents a notable drawback of redundancy in evolution.