Robust symbolic regression with affine arithmetic

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, estimating 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 that 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 of unseen test data.