Probabilistic model building in genetic programming: a critical review

Probabilistic model-building algorithms (PMBA), a subset of evolutionary algorithms, have been successful in solving complex problems, in addition providing analytical information about the distribution of fit individuals. Most PMBA work has concentrated on the string representation used in typical genetic algorithms. A smaller body of work has aimed to apply the useful concepts of PMBA to genetic programming (GP), mostly concentrating on tree representation. Unfortunately, the latter research has been sporadically carried out, and reported in several different research streams, limiting substantial communication and discussion. In this paper, we aim to provide a critical review of previous applications of PMBA and related methods in GP research, to facilitate more vital communication. We illustrate the current state of research in applying PMBA to GP, noting important perspectives. We use these to categorise practical PMBA models for GP, and describe the main varieties on this basis.