Inferring and Exploiting Problem Structure with Schema Grammar

In this work we introduce a model-building algorithm that is able to infer problem structure using generative grammar induction. We define a class of grammar that can represent the structure of a problem space as a hierarchy of multivariate patterns (schemata), and a compression algorithm that can infer an instance of the grammar from a collection of sample individuals. Unlike conventional sequential grammars the rules of the grammar define unordered set-membership productions and are therefore insensitive to gene ordering or physical linkage. We show that when grammars are inferred from populations of fit individuals on shuffled nearest-neighbour NK-landscape problems, there is a correlation between the compressibility of a population and the degree of inherent problem structure. We also demonstrate how the information captured by the grammatical model from a population can aid evolutionary search. By using the lexicon of schemata inferred into a grammar to facilitate variation, we show that a population is able to incrementally learn and then exploit its own structure to find fitter regions of the search space, and ultimately locate the global optimum.