Authors: Gabriel Kronberger, Fabricio Olivetti de Franca, Deaglan J. Bartlett, Harry Desmond, Pedro G. Ferreira
Organizations: Heuristic and Evolutionary Algorithms Laboratory University of Applied Sciences Upper Austria Softwarepark 11, 4232 Hagenberg, Austria · Center of Mathematics, Computing and Cognition Federal University of ABC Av. dos Estados 5001, Santo Andre, 09280-560, SP, Brazil · Astrophysics, University of Oxford Denys Wilkinson Building, Keble Road, Oxford, OX1 3RH, UK · Institute of Cosmology & Gravitation, University of Portsmouth Dennis Sciama Building, Portsmouth, PO1 3FX, UK
Symbolic regression with genetic programming (GPSR) may suffer from overfitting and structural bloat, especially when noise is present. In this paper we evaluate description length (DL) and fractional Bayes factor (FBF) criteria as principled, data-efficient alternatives to heuristics for selecting compact expressions that generalise well. We implement DL using a Fisher-information-based parameter encoding and compare it to AIC and BIC across multiple datasets, including noisy synthetic benchmarks and real-world regression problems. We study three search/selection strategies: (i) multi-objective search for accuracy and program length followed by DL/FBF selection; (ii) multi-objective search using DL directly as an objective; and (iii) single-objective optimisation with DL/FBF as the fitness. Across datasets we find that DL/FBF post-selection improves test performance compared to AIC/BIC baseline and that BIC in combination with the same function complexity penalty from DL/FBF produces similar results. In contrast, using DL/FBF directly as a fitness function in single-objective GPSR frequently induces premature convergence to overly simple models. We conclude with practical guidance for using DL/FBF as robust model-selection tools in genetic programming workflows.