Robust Symbolic Regression with Affine Arithmetic
Venue
Genetic and Evolutionary Computation COnference (GECCO) (2010)
Publication Year
2010
Authors
Cassio Pennachin, Moshe Looks, João A. de Vasconcelos
BibTeX
Abstract
We use affine arithmetic to improve both the performance and the robustness of
genetic programming for symbolic regression. During evolution, we use affine
arithmetic to analyze expressions generated by the genetic operators, giving an
estimate of their output range given the ranges of their inputs over the training
data. These estimated output ranges allow us to discard trees that contain
asymptotes as well as those whose output is too far from the desired output range
determined by the training instances. We also perform linear scaling of outputs
before fitness evaluation. Experiments are performed on 15 problems, comparing the
proposed system with a baseline genetic programming system with protected
operators, and with a similar system based on interval arithmetic. Results show
integrating affine arithmetic with an implementation of standard genetic
programming reduces the number of fitness evaluations during training and improves
generalization performance, minimizes overfitting, and completely avoids extreme
errors on unseen test data.
