The Troubling Aspects of a Building Block Hypothesis for Genetic Programming

In this paper we carefully formulate a Schema Theorem for Genetic Programming (GP) using a schema definition that accounts for the variable length and the non-homologous nature of GP's representation. In a manner similar to early GA research, we use interpretations of our GP Schema Theorem to obtain a GP Building Block definition and to state a "classical" Building Block Hypothesis (BBH): that GP searches by hierarchically combining building blocks. We report that this approach is not convincing for several reasons: it is difficult to find support for the promotion and combination of building blocks solely by rigourous interpretation of a GP Schema Theorem; even if there were such support for a BBH, it is empirically questionable whether building blocks always exist because partial solutions of consistently above average fitness and resilience to disruption are not assured; also, a BBH constitutes a narrow and imprecise account of GP search behavior