Covariant Parsimony Pressure for Genetic Programming

The parsimony pressure method is perhaps the simplest and most frequently used method to control bloat in genetic programming. In this paper we first reconsider the size evolution equation for genetic programming developed in [24] and rewrite it in a form that shows its direct relationship to Price’s theorem. We then use this new formulation to derive theoretical results that show how to practically and optimally set the parsimony coefficient dynamically during a run so as to achieve complete control over the growth of the programs in a population. Experimental results confirm the effectiveness of the method, as we are able to tightly control the average program size under a variety of conditions. These include such unusual cases as dynamically varying target sizes such that the mean program size is allowed to grow during some phases of a run, while being forced to shrink in others.