Probabilistically Guided Prefix Gene Expression Programming

Abstract

Over the years there has been an increasing interest in probabilistically oriented Evolutionary Algorithms (EAs), but it has not been until recently that these innovative methods have been collectively recognized and achieved an independent status. By eliminating the traditionally employed genetic operators, these probabilistic EAs have been forced to adopt an alternative approach, and in the case of Estimation of Distribution Algorithms (EDAs), probabilistic graphical models have become the favored substitute. In this paper, we propose to utilize a previously overlooked probabilistic model known as Hidden Markov Models (HMMs). But preferring not to completely abandon the biologically inspired genetic operations, we largely ignore the classical learning algorithms used to train HMMs, and instead use Differential Evolution (DE) to evolve the underlying numerical parameters of the chosen probabilistic model. The evolved HMMs are then used to generate Prefix Gene Expression Programming (PGEP) chromosomes which encode candidate solutions, and thus provide feedback to guide this proposed evolutionary search process. Finally, benchmarking on a set of symbolic function regression problems has been conducted in order to compare this novel approach to the existing PGEP method.