Comparing methods to creating constants in grammatical evolution

Abstract

This chapter evaluates the performance of various methods to constant creation in Grammatical Evolution (GE), and validates the results by comparing against those from a reasonably standard Genetic Programming (GP) setup. Specifically, the chapter compares a standard GE method to constant creation termed digit concatenation with what this chapter calls compact methods to constant creation. Constant creation in GE is an important issue due to the disruptive nature of ripple crossover, which can radically remap multiple terminals in an individual, and we investigate if more compact methods, which are more similar to the GP style of constant creation (Ephemeral Random Constants (ERCs), perform better. The results are surprising. Against common wisdom, a standard GE approach of digit concatenation does not produce individuals that are any larger than those from methods which are designed to use less genetic material. In fact, while GP characteristically evolves increasingly larger individuals, GE-after an initial growth or drop in sizes-tends to keep individual sizes stable despite no explicit mechanisms to control size growth. Furthermore, various GE setups perform acceptably well on unseen test data and typically outperform GP. Overall, these results encourage a belief that standard GE methods to symbolic regression are relatively resistant to pathogenic evolutionary tendencies of code bloat and overfitting.