The recent Crossover Bias theory has shown that bloat in Genetic Programming can be caused by the proliferation of small unfit individuals in the population. Inspired by this theory, Operator Equalisation is the most recent and successful bloat control method available. In a recent work there has been an attempt to replicate the evolutionary dynamics of Operator Equalisation by joining two key ingredients found in older and newer bloat control methods. However, the obtained dynamics was very different from expected, which prompted a further investigation into the reasons that make Operator Equalisation so successful. It was revealed that, at least for complex symbolic regression problems, the distribution of program lengths enforced by Operator Equalisation is nearly flat, contrasting with the peaky and well delimited distributions of the other approaches. In this work we study the importance of having flat program length distributions for bloat control. We measure the flatness of the distributions found in previous and new Operator Equalisation variants and we correlate it with the amount of search performed by each approach. We also analyze where this search occurs and how bloat correlates to these properties. We conclude presenting a possible explanation for the unique behavior of Operator Equalisation.
|Title of host publication||Genetic Programming Theory and Practice IX|
|Editors||Riolo E R.|
|Place of Publication||Berlin|
|Publication status||Published - 1 Jan 2011|
|Name||Computer Science Collection|
Vanneschi, L. (2011). The Importance of Being Flat: Studying the Program Length Distributions of Operator Equalisation. In R. E. R. (Ed.), Genetic Programming Theory and Practice IX (pp. 211-233). (Computer Science Collection). Berlin: Springer. https://doi.org/10.1007/978-1-4614-1770-5_12