Mathematics prevents bloat [genetic programming]

This paper provides an explanation for recent results that displayed a tendency for variable length genomes to shrink when random selection is used. This shrinking effect is also observed under a form of "null selection" that allows every member of the population to reproduce in every generation. It is theoretically and empirically shown that the presence of an absorbing boundary contributes to this shrinking effect. The analysis is performed in a representation and problem independent manner and is thus applicable to any form of crossover-based evolutionary algorithm that uses variable length encodings