An Adverse Interaction between the Crossover Operator and a Restriction on Tree Depth

The Crossover operator is common to most implementations of Genetic Programming (GP). Another, usually unavoidable, factor is some form of restriction on the size of trees in the GP population. This paper concentrates on the interaction between the Crossover operator and a restriction on tree depth demonstrated by the MAX problem , which involves returning the largest possible value for given function and terminal sets. Some characteristics and inadequacies of Crossover in`normal' use are highlighted and discussed. Subtree discovery and movement takes place mostly near the leaf nodes, with nodes near the root left untouched. Diversity drops quickly to zero near the root node in the tree population. GP is then unable to creatè`tter' trees via the crossover operator, leaving a Mutation operator as the only common, but ineeective, route to discovery of``tter' trees.