Cost-benefit analysis of using heuristics in ACGP

Constrained Genetic Programming (CGP) is a method of searching the Genetic Programming search space non-uniformly, giving preferences to certain subspaces according to some heuristics. Adaptable CGP (ACGP) is a method for discovery of the heuristics. CGP and ACGP have previously demonstrated their capabilities using first-order heuristics: parent-child probabilities. Recently, the same advantage has been shown for second-order heuristics: parent-children probabilities. A natural question to ask is whether we can benefit from extending ACGP with deeper order heuristics. This paper attempts to answer this question by performing cost-benefit analysis while simulating the higher-order heuristics environment. We show that this method cannot be extended beyond the current second or possibly third-order heuristics without a new method to deal with the sheer number of such deeper-order heuristics.