Pruning of Genetic Programming Trees Using Permutation Tests

We present a novel approach based on statistical permutation tests for pruning redundant subtrees from genetic programming (GP) trees. We observe that over a range of regression problems, median tree sizes are reduced by around 20% largely independent of test function, and that while some large subtrees are removed, the median pruned subtree comprises just three nodes; most take the form of an exact algebraic simplification. Our statistically-based pruning technique has allowed us to explore the hypothesis that a given subtree can be replaced with a constant if this substitution results in no statistical change to the behaviour of the parent tree—what we term approximate simplification. In the eventuality, we infer that &95% of the pruned subtrees are the result of algebraic simplifications, which provides some practical insight into the scope of removing redundancies in GP trees.