Feature Encapsulation by Stages in the Regression Domain Using Grammatical Evolution

Feature Encapsulation by Stages (FES) is a recently proposed mechanism that can be implemented in any Evolutionary Computation (EC) metaheuristic. Encapsulation occurs via input space expansion in several stages by adding the best individual so far as an additional input. FES has been shown to perform well in training Boolean problems. This paper extends FES to the regression domain. Grammatical Evolution (GE), a branch of Genetic Programming (GP), supports the implementation of the FES approach by enabling the investigation of performance across various search guides expressed in the grammar. We conduct experiments on both synthetic and real-world symbolic regression problems, including multi-target issues. Additionally, we study several FES-based approaches utilising the best selection process for each problem, choosing between tournament, \(\epsilon \) -Lexicase, and \(\epsilon \hbox {-}\textrm{Lexi}^2\) . Statistical tests on unseen subsets’ results show that FES outperforms the standard baseline in all problems. Furthermore, we analyse individual complexity across generations, showing that populations utilising FES consist of simpler individuals, thereby reducing computational costs.