Rethinking the Adaptive Capability of Accretive Evolution on Hierarchically Consistent Problems

We consider how accretive evolution is able to evolve optimal solutions to hierarchical decomposable non-separable problems epitomized by hierarchically consistent test problems. We find that this feat is not as improbable as previously thought if a suitable phenotype which reflects the levels in the hierarchy is used as the object of a selection scheme which applies level directed selection pressure. An ideal selection scheme is first described and tested experimentally, followed by a meta-population model to evolve the ideal selection scheme. Experiments with the model revealed that evolution of the ideal selection scheme is not a pre-requisite to evolving optimal solutions. Optimal solutions were found even when the ideal selection scheme was not. No recombination of partial solutions is used in this paper. The findings of this paper reopen the question: what type of hierarchical structure is difficult to evolve through random mutation and selection