A Grammatical Genetic Programming Approach to Modularity in Genetic Algorithms

The ability of Genetic Programming to scale to problems of increasing difficulty operates on the premise that it is possible to capture regularities that exist in a problem environment by decomposition of the problem into a hierarchy of modules. As computer scientists and more generally as humans we tend to adopt a similar divide-and-conquer strategy in our problem solving. In this paper we consider the adoption of such a strategy for Genetic Algorithms. By adopting a modular representation in a Genetic Algorithm we can make efficiency gains that enable superior scaling characteristics to problems of increasing size. We present a comparison of two modular Genetic Algorithms, one of which is a Grammatical Genetic Programming algorithm, the meta-Grammar Genetic Algorithm (mGGA), which generates binary string sentences instead of traditional GP trees. A number of problems instances are tackled which extend the Checkerboard problem by introducing different kinds of regularity and noise. The results demonstrate some limitations of the modular GA (MGA) representation and how the mGGA can overcome these. The mGGA shows improved scaling when compared the MGA.