Dynamic maximum tree depth: a simple technique for avoiding bloat in tree-based GP

We present a technique, designated as dynamic maximum tree depth, for avoiding excessive growth of tree-based GP individuals during the evolutionary process. This technique introduces a dynamic tree depth limit, very similar to the Koza-style strict limit except in two aspects: it is initially set with a low value; it is increased when needed to accommodate an individual that is deeper than the limit but is better than any other individual found during the run. The results show that the dynamic maximum tree depth technique efficiently avoids the growth of trees beyond the necessary size to solve the problem, maintaining the ability to find individuals with good fitness values. When compared to lexicographic parsimony pressure, dynamic maximum tree depth proves to be significantly superior. When both techniques are coupled, the results are even better.