A Probabilistic Model of Size Drift

Abstract

Drift towards growing size of genotypes is one outstanding and constantly disputed invariant in an overwhelming number of applications of evolutionary algorithms with variable-size structures. In contrast to previous work to reveal its fundamentals, we probabilistically analyze genotype growth by building on the idea of a “representation-less” model by Banzhaf and Langdon. Our model, called the fitness-size model, corresponds to a simple evolutionary algorithm using overproduction selection and mutation working on abstract objects retaining only fitness and size information.

The probalistic analysis offer some surprises counterr to present credence. The analysis predicts that average effective and noneffective lengths (and thus overall size) tend to be invariant over time. The same is true for the variance of the effective length. In contrast, the variance of the noneffective size features increases linearly in time, and its variation shows the trademark of a difussion process.Drift to increasing size manifest s if search biases favor boundary conditions. We present experimental results with both the implementation of the theoretical model and a standard genetic programming algorithm. Statistical results with the two implementations are similar and fit the theoretical predictions.