Estimation of Distribution Algorithm Based on PCFG-LA Mixture Model

Abstract

Estimation of distribution algorithms (EDAs) are evolutionary algorithms which substitute traditional genetic operators with distribution estimation and sampling. Recently, the application of probabilistic techniques to program and function evolution has received increasing attention, and promises to provide a strong alternative to the traditional genetic programming (GP) techniques. Although PAGE (Programming with Annotated Grammar Estimation) is a state-of-art GP-EDA based on PCFG-LA (PCFG with Latent Annotations), PAGE can not effectively estimate the distribution with multiple solutions. In this paper, we proposed extended PCFG-LA named PCFG-LAMM (PCFG-LA Mixture Model) and proposed UPAGE (Unsupervised PAGE) based on PCFG-LAMM. By applying the proposed algorithm to three computational problems, it is demonstrated that our approach requires fewer fitness evaluations. We also show that UPAGE is capable of obtaining multiple solutions in a multimodal problem.