A Comprehensive Comparison of Lexicase-Based Selection Methods for Symbolic Regression Problems

Alina Geiger, Dominik Sobania, Franz Rothlauf

Abstract: Lexicase selection is a parent selection method that has been successfully used in many application domains. In recent years, several variants of lexicase selection have been proposed and analyzed. However, it is still unclear which lexicase variant performs best in the domain of symbolic regression. Therefore, we compare in this work relevant lexicase variants on a wide range of symbolic regression problems. We conduct experiments not only over a given evaluation budget but also over a given time as practitioners usually have limited time for solving their problems. Consequently, this work provides users a comprehensive guide for choosing the right selection method under different constraints in the domain of symbolic regression. Overall, we find that down-sampled \(\epsilon \)-lexicase selection outperforms other selection methods on the studied benchmark problems for the given evaluation budget and for the given time. The improvements with respect to solution quality are up to 68% using down-sampled \(\epsilon \)-lexicase selection given a time budget of 24 h.