The Importance of Being Flat–Studying the Program Length Distributions of Operator Equalisation

Abstract

The recent Crossover Bias theory has shown that bloatin Genetic Programming can be caused by theproliferation of small unfit individuals in thepopulation. Inspired by this theory, OperatorEqualisation is the most recent and successful bloatcontrol method available. In a recent work there hasbeen an attempt to replicate the evolutionary dynamicsof Operator Equalisation by joining two key ingredientsfound in older and newer bloat control methods.However, the obtained dynamics was very different fromexpected, which prompted a further investigation intothe reasons that make Operator Equalisation sosuccessful. It was revealed that, at least for complexsymbolic regression problems, the distribution ofprogram lengths enforced by Operator Equalisation isnearly flat, contrasting with the peaky and welldelimited distributions of the other approaches. Inthis work we study the importance of having flatprogram length distributions for bloat control. Wemeasure the flatness of the distributions found inprevious and new Operator Equalisation variants and wecorrelate it with the amount of search performed byeach approach. We also analyse where this search occursand how bloat correlates to these properties. Weconclude presenting a possible explanation for theunique behaviour of Operator Equalisation.