Lexi ²

Bloat, a well-known phenomenon in Evolutionary Computation, often slows down evolution and complicates the task of interpreting the results. We propose Lexi 2 , a new selection and bloat-control method, which extends the popular lexicase selection method, by including a tie-breaking step which considers attributes related to the size of the individuals. This new step applies lexicographic parsimony pressure during the selection process and is able to reduce the number of random choices performed by lexicase selection (which happen when more than a single individual correctly solve the selected training cases). Furthermore, we propose a new Grammatical Evolution-specific, low-cost diversity metric based on the grammar mapping modulus operations remainders, which we then utilise with Lexi 2 . We address four distinct problems, and the results show that Lexi 2 is able to reduce significantly the length, the number of nodes and the depth for all problems, to maintain a high level of diversity in three of them, and to significantly improve the fitness score in two of them. In no case does it adversely impact the fitness.