The roles of diversity preservation and mutation in preventing population collapse in multiobjective genetic programming

It has been observed previously that genetic programming populations can collapse to all single node trees when a parsimony measure (tree node count) is used in a multiobjective setting. We have investigated the circumstances under which this can occur for both the 6-parity boolean learning task and a range of benchmark machine learning problems. We conclude that mutation is an important -- and we believe a hitherto unrecognized -- factor in preventing population collapse in multiobjective genetic programming; without mutation we routinely observe population collapse. From systematic variation of the mutation operator, we conclude that a necessary condition to avoid collapse is that mutation produces, on average, an increase in tree sizes (bloating) at each generation which is then counterbalanced by the parsimony pressure applied during selection. Finally, we conclude that the use of a genotype diversity preserving mechanism is ineffective at preventing population collapse.