Markov Random Field Modelling of Royal Road Genetic Algorithms

Markov Random Fields (MRFs) [5] are a class of probabalistic models that have been applied for many years to the analysis of visual patterns or textures. In this paper, our objective is to establish MRFs as an interesting approach to modelling genetic algorithms. Our approach bears strong similarities to recent work on the Bayesian Optimisation Algorithm [9], but there are also some signi cant di erences. We establish a theoretical result that every genetic algorithm problem can be characterised in terms of a MRF model. This allows us to construct an explicit probabilistic model of the GA tness function. The model can be used to generate chromosomes, and derive a MRF tness measure for the population. We then use a speci c MRF model to analyse two Royal Road problems, relating our analysis to that of Mitchell et al. [7].