An experimental study on fitness distributions of tree shapes in GP with one-point crossover

Abstract

In Genetic Programming (GP), One-Point Crossover is an alternative to the destructive properties and poor performance of Standard Crossover. One-Point Crossover acts in two phases, first making the population converge to a common tree shape, then looking for the best individual within that shape. So, we understand that One-Point Crossover is making an implicit evolution of tree shapes. We want to know if making this evolution explicit could lead to any improvement in the search power of GP. But we first need to define how this evolution could be performed. In this work we made an exhaustive study of fitness distributions of tree shapes for 6 different GP problems. We were able to identify common properties on distributions, and we propose a method to explicitly evaluate tree shapes. Based on this method, in the future, we want to implement a new genetic operator and a novel representation system for GP.