Dynamic Limits for Bloat Control: Variations on Size and Depth

We present two important variations on a recently successful bloat control technique, Dynamic Maximum Tree Depth, intended at further improving the results and extending the idea to non tree-based GP. Dynamic Maximum Tree Depth introduces a dynamic limit on the depth of the trees allowed into the population, initially set with a low value but increased whenever needed to accommodate a new best individual that would otherwise break the limit. The first variation to this idea is the Heavy Dynamic Limit that, unlike the original one, may fall again to a lower value after it has been raised, in case the new best individual allows it. The second variation is the Dynamic Size Limit, where size is the number of nodes, instead and regardless of depth. The variations were tested in two problems, Symbolic Regression and Parity, and the results show that the heavy limit performs generally better than the original technique, but the dynamic limit on size fails in the Parity problem. The possible reasons for success and failure are discussed.