Modelling Genetic Programming as a Simple Sampling Algorithm

Abstract

This chapter proposes a new model of tree-based Genetic Programming (GP) as a simple sampling algorithm that samples minimal schemata (subsets of the solution space) described by a single concrete node at a single position in the expression tree. We show that GP explores these schemata in the same way across three benchmarks, rapidly converging the population to a specific function at each position throughout the upper layers of the expression tree. This convergence is driven by covariance between membership of a simple schema and rank fitness. We model this process using Prices theorem \cite{price:nature} and provide empirical evidence to support our model. The chapter closes with an outline of a modification of the standard GP algorithm that reinforces this bias by converging populations to fit schemata in an accelerated way.