Lexicase selection promotes effective search and behavioural diversity of solutions in Linear Genetic Programming

Linear Genetic Programming (LGP) is an evolutionary algorithm aimed at solving computational problems, most common problem types being symbolic regression and classification. The standard method for selecting the parent individuals that get to undergo modification at each generation of the algorithm is tournament selection, which operates based on an aggregate fitness value computed on the whole training dataset. Lexicase selection, a novel parent selection method introduced by Lee Spector and his research group, works differently by randomly ordering the samples in the training dataset and using each of them in turn to eliminate parent candidates from consideration. As a result it allows for selecting specialist individuals, which perform well on some samples but badly on others, instead of generalist individuals whose average performance on all of the samples is good. Lexicase selection has previously been tested on tree-GP and PushGP, but not on LGP. In this study, we use three different benchmark problems to compare its performance to tournament selection, investigating the mean best fitness values of the test runs at each generation, as well as the effect of the parent selection operator on behavioural diversity. We conclude that lexicase selection drives the search towards good solutions more effectively than tournament selection, and that this effect correlates with improved behavioural diversity in most cases.