Performance Models for Evolutionary Program Induction based on Problem Difficulty Indicators

Most theoretical models of evolutionary algorithms are difficult to apply to realistic situations. In this paper, two models of evolutionary program-induction algorithms (EPAs) are proposed which overcome this limitation. We test our approach with two important classes of problems — symbolic regression and Boolean function induction — and a variety of EPAs including: different versions of genetic programming, gene expression programing, stochastic iterated hill climbing in program space and one version of cartesian genetic programming. We compare the proposed models against a practical model of EPAs we previously developed and find that in most cases the new models are simpler and produce better predictions. A great deal can also be learnt about an EPA via a simple inspection of our new models. E.g., it is possible to infer which characteristics make a problem difficult or easy for the EPA.