Article thumbnail
Location of Repository

On the limiting distribution of program sizes in tree-based genetic programming

By Stephen Dignum


Recent research [1] has found that standard sub-tree crossover with uniform selection of crossover points, in the absence of fitness pressure, pushes a population of GP trees towards a Lagrange distribution of tree sizes. However, the result applied to the case of single arity function plus leaf node combinations, e.g., unary, binary, ternary, etc trees only. In this paper we extend those findings and show that the same distribution is also applicable to the more general case where the function set includes functions of mixed arities. We also provide empirical evidence that strongly corroborates this generalisation. Both predicted and observed results show a distinct bias towards the sampling of shorter programs irrespective of the mix of function arities used. Practical applications and implications of this knowledge are investigated with regard to search efficiency and program bloat. Work is also presented regarding the applicability of the theory to the traditional 90%-function 10%terminal crossover node selection policy

Topics: I.2.2 [Artificial Intelligence, Automatic Programming General Terms Algorithms, Performance Keywords Genetic Programming, Crossover Bias, Program Size Distribution, Bloat, Initialisation
Publisher: Forthcoming
Year: 2007
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX

Suggested articles

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.