Solving building block problems using generative grammar

Abstract

In this work we demonstrate novel applications of generative grammar to evolutionary search. We introduce a class of grammar that can represent hierarchical schema structure in a problem space, and describe an algorithm that can infer an instance of the grammar from a population of sample phenotypes. Unlike conventional sequence-based grammars this grammar represents set-membership relationships, not strings, and is therefore insensitive to gene-ordering and physical linkage. We show that these methods are capable of accurately identifying problem structure from populations of above-average-fitness individuals on simple modular and hierarchically modular test problems. We then show how these grammatical models can be used to aid evolutionary problem solving by enabling facilitated variation; specifically, by producing novel combinations of schemata observed in the sample population whilst respecting the inherent constraint structure of the problem space. This provides a robust method of building-block recombination that is linkage-invariant and not restricted to low-order schemata.