A comparison of tournament and lexicase selection paradigms in regression problems: error-based fitness versus correlation fitness

Lexicase parent selection considers training cases separately, postulating that aggregated fitness reduces the information about the behavior of individuals. Originally lexicase was proposed in the context of program synthesis, characterized by uncompromising problems that require qualitatively different actions for different inputs, but it has since been extended to regression problems. To facilitate valley-crossing a relaxation parameter μ was added broadening the pass condition at a given training case. Although μ-lexicase has demonstrated superior effectiveness, it was compared against selection methods that aggregated squared (or absolute) errors. Recent contributions, however, demonstrate that correlation fitness functions can lead to significant performance gains over the root mean square error (RMSE) in tournament-guided evolution for symbolic regression. Here we compare μ-lexicase (with and without down-sampling) against tournament selection using both error- and correlation-based fitness to guide Genetic Programming (GP). We also assess batch μ-lexicase selection as an intermediate condition. Finally, we explore different selection pressures to assess the exploration-exploitation trade-off. We analyze the experimental results using different metrics, including code redundancy, sharpness-awareness and selection impact. Our results demonstrate that tournament selection with correlation fitness function significantly outperforms μ-lexicase on regression problems and that its batch variant also benefits from correlation-based aggregation.