Effects of the lack of selective pressure on the expected run-time distribution in genetic programming

Run-time analysis is a powerful tool to analyze algorithms. It is focused on studying the time required by an algorithm to find a solution, the expected run-time, which is one of the most relevant algorithm attributes. Previous research has associated the expected run-time in GP with the lognormal distribution. In this paper we provide additional evidence in that regard and show how the algorithm parametrization may change the resulting run-time distribution. In particular, we explore the influence of the selective pressure on the run-time distribution in tree-based GP, finding that, at least in two problem instances, the lack of selective pressure generates an expected run-time distribution well described by the Weibull probability distribution.