  Genetic programming systems often use large training sets to evaluate the
quality of candidate solutions for selection, which is often computationally
expensive. Down-sampling training sets has long been used to decrease the
computational cost of evaluation in a wide range of application domains. More
specifically, recent studies have shown that both random and informed
down-sampling can substantially improve problem-solving success for GP systems
that use the lexicase parent selection algorithm. We test whether these
down-sampling techniques can also improve problem-solving success in the
context of three other commonly used selection methods, fitness-proportionate,
tournament, implicit fitness sharing plus tournament selection, across six
program synthesis GP problems. We verified that down-sampling can significantly
improve the problem-solving success for all three of these other selection
schemes, demonstrating its general efficacy. We discern that the selection
pressure imposed by the selection scheme does not interact with the
down-sampling method. However, we find that informed down-sampling can improve
problem solving success significantly over random down-sampling when the
selection scheme has a mechanism for diversity maintenance like lexicase or
implicit fitness sharing. Overall, our results suggest that down-sampling
should be considered more often when solving test-based problems, regardless of
the selection scheme in use.
