  Lexicase selection is a parent selection method that considers test cases
separately, rather than in aggregate, when performing parent selection. It
performs well in discrete error spaces but not on the continuous-valued
problems that compose most system identification tasks. In this paper, we
develop a new form of lexicase selection for symbolic regression, named
epsilon-lexicase selection, that redefines the pass condition for individuals
on each test case in a more effective way. We run a series of experiments on
real-world and synthetic problems with several treatments of epsilon and
quantify how epsilon affects parent selection and model performance.
epsilon-lexicase selection is shown to be effective for regression, producing
better fit models compared to other techniques such as tournament selection and
age-fitness Pareto optimization. We demonstrate that epsilon can be adapted
automatically for individual test cases based on the population performance
distribution. Our experiments show that epsilon-lexicase selection with
automatic epsilon produces the most accurate models across tested problems with
negligible computational overhead. We show that behavioral diversity is
exceptionally high in lexicase selection treatments, and that epsilon-lexicase
selection makes use of more fitness cases when selecting parents than lexicase
selection, which helps explain the performance improvement.
