  Epsilon-lexicase selection is a parent selection method in genetic
programming that has been successfully applied to symbolic regression problems.
Recently, the combination of random subsampling with lexicase selection
significantly improved performance in other genetic programming domains such as
program synthesis. However, the influence of subsampling on the solution
quality of real-world symbolic regression problems has not yet been studied. In
this paper, we propose down-sampled epsilon-lexicase selection which combines
epsilon-lexicase selection with random subsampling to improve the performance
in the domain of symbolic regression. Therefore, we compare down-sampled
epsilon-lexicase with traditional selection methods on common real-world
symbolic regression problems and analyze its influence on the properties of the
population over a genetic programming run. We find that the diversity is
reduced by using down-sampled epsilon-lexicase selection compared to standard
epsilon-lexicase selection. This comes along with high hyperselection rates we
observe for down-sampled epsilon-lexicase selection. Further, we find that
down-sampled epsilon-lexicase selection outperforms the traditional selection
methods on all studied problems. Overall, with down-sampled epsilon-lexicase
selection we observe an improvement of the solution quality of up to 85% in
comparison to standard epsilon-lexicase selection.
