A Comparison of Representations in Grammar-Guided Genetic Programming in the context of Glucose Prediction in People with Diabetes

Abstract The representation of individuals in Genetic Programming (GP) has a large impact on the evolutionary process. In this work, we investigate the evolutionary process of three Grammar-Guided GP (GGGP) methods, Context-Free Grammars GP (CFG-GP), Grammatical Evolution (GE) and Structured Grammatical Evolution (SGE), in the context of the complex, real-world problem of predicting the glucose level of people with diabetes two hours ahead of time.Our analysis differs from previous analyses by (1) comparing all three methods on a complex benchmark, (2) implementing the methods in the same framework, allowing a fairer comparison, and (3) analyzing the evolutionary process outside of performance.We conclude that representation choice is more impactful with a higher maximum depth, and that CFG-GP better explores the search space for deeper trees, achieving better results. Furthermore, we find that CFG-GP relies more on feature construction, whereas GE and SGE rely more on feature selection.Additionally, we altered the GGGP methods in two ways: using $\epsilon$-lexicase selection, which solved the overfitting problem of CFG-GP; and with a penalization of complex trees, to create more interpretable trees. Combining $\epsilon$-lexicase selection with CFG-GP performed best.Finally, we evaluated the impact of initialization methods in the quality of solutions, having found that they have no impact, even when the change of representation has.