Cooperative Problem Decomposition in Pareto Competitive Classifier Models of Coevolution

Abstract

Pareto competitive models of coevolution have the potential to provide a number of distinct advantages over the canonical approach to training under the Genetic Programming (GP) classifier domain. Recent work has specifically focused on the reformulation of training as a two-population competition, that is learners versus training exemplars. Such a scheme affords, for example, the capacity to decouple the fitness evaluation overhead from the data set size through sub sampling while naturally encouraging ‘teams’ or composite solutions as opposed to solutions based on a single individual alone. One outstanding question with respect to the latter characteristic is with regards to the nature of the team (archive) behavior in terms of pattern coverage. That is to say, which models are used when, and what are the implications for solution modularity as it relates, for example, to the assignment of exemplars to solution participants. The current work investigates two Pareto competitive approaches to classification under GP, with one configured to employ an explicitly cooperative multi-objective cost function based and the other employing the classical (error-based) cost function. We empirically demonstrate a critical distinction between the two with regards to problem decomposition, with the capacity to provide a decomposition into unique behaviors being much more prevalent when co-operative mechanisms are explicitly supported.