- author = "Riccardo Poli and William B. Langdon and Stephen Dignum",
- title = "On the Limiting Distribution of Program Sizes in Tree-based Genetic Programming",
- editor = "Marc Ebner and Michael O'Neill and Anik\'o Ek\'art and Leonardo Vanneschi and Anna Isabel Esparcia-Alc\'azar",
- booktitle = "Proceedings of the 10th European Conference on Genetic Programming",
- publisher = "Springer",
- series = "Lecture Notes in Computer Science",
- volume = "4445",
- year = "2007",
- address = "Valencia, Spain",
- month = "11-13 " # apr,
- pages = "193--204",
- note = "Best paper award",
- keywords = "genetic algorithms, genetic programming, Internal Node, Tree Size, Catalan Number, Tree Shape",
- ISBN = "3-540-71602-5",
- isbn13 = "978-3-540-71602-0",
-
URL = "
http://cswww.essex.ac.uk/staff/poli/papers/PoliLangdonDignumEuroGP2007.pdf",
-
DOI = "
doi:10.1007/978-3-540-71605-1_18",
-
abstract = "We provide strong theoretical and experimental
evidence that standard sub-tree crossover with uniform
selection of crossover points pushes a population of
a-ary GP trees towards a distribution of tree sizes of
the form:
Pr{n} = (1 - ap)C_n^{an + 1}(1-p)^{(a-1)n+1} p^n
where n is the number of internal nodes in a tree and p is a constant. This result generalises the result previously reported in \cite{poli:2001:EuroGP_exact}, \cite{mcphee:2001:astamsbgplr}, \cite{Rowe01}, \cite{poli03:ECJ_gener_schem_part_I}, \cite{poli03:ECJ_gener_schem_part_II} for the case a = 1.",
-
notes = "Part of \cite{ebner:2007:GP} EuroGP'2007 held in
conjunction with EvoCOP2007, EvoBIO2007 and
EvoWorkshops2007
See also \cite{poli:2006:CSM464}",
