Program distribution estimation with grammar models

Abstract

This thesis studies grammar-based approaches in the application of Estimation of Distribution Algorithms (EDA) to the tree representation widely used in Genetic Programming (GP). Although EDA is becoming one of the most active fields in Evolutionary computation (EC), the solution representation in most EDA is a Genetic Algorithms (GA) style linear representation. The more complex tree representations, resembling GP, have received only limited exploration. This is unfortunate, because tree representations provide a natural and expressive way of representing solutions for many problems. This thesis aims to help fill this gap, exploring grammar-based approaches to extending EDA to GP-style tree representations.

This thesis firstly provides a comprehensive survey of current research on EDA with emphasis on EDA with GP-style tree representation. The thesis attempts to clarify the relationship between EDA with conventional linear representations and those with a GP-style tree representation, and to reveal the unique difficulties which face this research.

Secondly, the thesis identifies desirable properties of probabilistic models for EDA with GP-style tree representation, and derives the PRODIGY framework as a consequence.

Thirdly, following the PRODIGY framework, three methods are proposed. The first method is Program Evolution with Explicit Learning (PEEL). Its incremental general-to-specific grammar learning method balances the effectiveness and efficiency of the grammar learning. The second method is Grammar Model-based Program Evolution (GMPE). GMPE realises the PRODIGY framework by introducing elegant inference methods from the formal grammar field. GMPE provides good performance on some problems, but also provides a means to better understand some aspects of conventional GP, especially the building block hypothesis. The third method is Swift GMPE (sGMPE), which is an extension of GMPE, aiming at reducing the computational cost.

Fourthly, a more accurate Minimum Message Length metric for grammar learning in PRODIGY is derived in this thesis. This metric leads to improved performance in the GMPE system, but may also be useful in grammar learning in general. It is also relevant to the learning of other probabilistic graphical models.