A Study on the Dynamics and Effectiveness of the Deflate Geometric Semantic Mutation

Geometric Semantic Genetic Programming (GSGP) is a variant of Genetic Programming (GP) that induces an error surface without local minima for supervised learning tasks. However, GSGP is limited by the fact that its operators produce increasingly large individuals, leading to overly complex models. The slim addresses this issue by introducing a deflate geometric semantic mutation capable of producing offspring smaller than their parents. Preliminary studies show that slim can maintain accuracy comparable to traditional GSGP while generating much smaller models. However, a thorough analysis of this mutation remains lacking. This work fills that gap by conducting a detailed study of the deflate mutation, focusing on its behavior and practical value. Our results show that, when applied at the right stage of evolution, deflate mutation mitigates overfitting and yields compact, accurate models. This is also the first study to explore the timing and interaction of inflate and deflate mutations in slim, demonstrating how deflation enhances generalization and reduces overfitting. We support our conclusions with a comprehensive experimental approach, including comparisons between exclusive use of inflate mutation and alternating it with deflation. We also evaluate numerical indicators such as improvement rate and training effectiveness. The consistency across these methods reinforces our findings and highlights the deflate mutation as a robust regularization strategy. Finally, when compared to established non-evolutionary machine learning methods, SLIM shows competitive performance. Overall, this study confirms SLIM as a promising direction for GP and lays the foundation for future research.