Inferring and exploiting compact models of evolutionary problem structure

Abstract

In both natural and artificial evolution, populations search a space of possibilities using the mechanisms of natural selection and random variation. However, not all variations are equally likely. The directions which variation can take are themselves a key part of the evolutionary machinery, determining the ability of evolution to create diversity whilst obeying the constraints of phenotype space. To be effective they must reflect the structure of the selective environment in which they exist. Evolutionary algorithms are often designed with a priori assumptions about this structure, but it can also be learned on the fly using “model-building” algorithms. However, there are many open questions: what information do populations contain about their selective environment? How can it be extracted from a population and represented? And how can it be exploited to facilitate more effective evolutionary search?

In this thesis, a novel type of lossless compact model called Schema Grammar is introduced. Schema Grammar overcomes the current limitations of compact models by
enabling intrinsically non-sequential data to be compressed. It offers a number of advantages over existing model-building approaches. In particular, the model is able to infer a hierarchy of genetic schemata that is consistent with the compositional structure of the selective environment, and has a strong predictive quality with respect to fitness. By using this structure to facilitate variation at many different levels of scale, instances
of well-known test problems are shown to be solvable in low-order polynomial time, matching the performance of state of the art methods.

The information-theoretic qualities of Schema Grammar also enable evolutionary information to be quantified in novel ways. Building on recent advances in information and complexity theory, the model is used to quantify mutual information between populations and their selective environment, including environments containing complex
epistatic structure. It is also used to predict the fitness of individuals by measuring their information distance to a fit population.

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Identifiers

ORCID for Richard A. Watson: orcid.org/0000-0002-2521-8255

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