Analysis of the effects of elitism on bloat in linear and tree-based genetic programming

Elitism, a technique which consists of copying, unchanged, one or more of the most fit individuals from one generation to the next, is widely used in generational evolutionary algorithms, including Genetic Programming (GP). Elitism ensures that the best individuals discovered in a generation (and hence in the whole run) are not lost, and, perhaps even more importantly, are made available to new generations for possible further improvements. In a recent study on the evolution of robustness in GP the average size of best of run individuals was reported to grow more slowly in the presence of elitism. This is an important finding, but no explanation was provided for why this happened nor whether this was a general effect. In this paper we model elitism mathematically and explain how, in general, elitism modulates the dynamics of the mean program size of the population, including both its positive and negative effects oil bloat. Experimental results with two GP systems and four different problems corroborate the theory