A Performance Analysis of Lexicase-Based and Traditional Selection Methods in GP for Symbolic Regression

In recent years, several new lexicase-based selection variants have emerged due to the success of standard lexicase selection in various application domains. For symbolic regression problems, variants that use an \(\epsilon\) -threshold or batches of training cases, among others, have led to performance improvements. Lately, especially variants that combine lexicase selection and down-sampling strategies have received a lot of attention. This article evaluates the most relevant lexicase-based selection methods as well as traditional selection methods in combination with different down-sampling strategies on a wide range of symbolic regression problems. In contrast to most work, we not only compare the methods over a given evaluation budget, but also over a given time budget as time is usually limited in practice. We find that for a given evaluation budget, \(\epsilon\) -lexicase selection in combination with a down-sampling strategy outperforms all other methods. If the given running time is very short, lexicase variants using batches of training cases perform best. Further, we find that the combination of tournament selection with informed down-sampling performs well in all studied settings.