Exact Schema Theorems for GP with One-Point and Standard Crossover Operating on Linear Structures and their Application to the Study of the Evolution of Size

Created by W.Langdon from gp-bibliography.bib Revision:1.2715

@InProceedings{poli:2001:EuroGP_exact,
  author =       "Riccardo Poli and Nicholas Freitag McPhee",
  title =        "Exact Schema Theorems for {GP} with One-Point and
                 Standard Crossover Operating on Linear Structures and
                 their Application to the Study of the Evolution of
                 Size",
  booktitle =    "Genetic Programming, Proceedings of EuroGP'2001",
  year =         "2001",
  editor =       "Julian F. Miller and Marco Tomassini and 
                 Pier Luca Lanzi and Conor Ryan and Andrea G. B. Tettamanzi and 
                 William B. Langdon",
  volume =       "2038",
  series =       "LNCS",
  pages =        "126--142",
  address =      "Lake Como, Italy",
  publisher_address = "Berlin",
  month =        "18-20 " # apr,
  organisation = "EvoNET",
  publisher =    "Springer-Verlag",
  keywords =     "genetic algorithms, genetic programming, Schema
                 theory, Crossover, Crossover bias, Standard Crossover,
                 Fixed points, Variable-length Genetic Algorithms,",
  ISBN =         "3-540-41899-7",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0302-9743&volume=2038&spage=126",
  doi =          "doi:10.1007/3-540-45355-5_11",
  size =         "17 pages",
  abstract =     "In this paper, firstly we specialise the exact GP
                 schema theorem for one-point crossover to the case of
                 linear structures of variable length, for example
                 binary strings or programs with arity-1 primitives
                 only. Secondly, we extend this to an exact schema
                 theorem for GP with standard crossover applicable to
                 the case of linear structures. Then we study, both
                 mathematically and numerically, the schema equations
                 and their fixed points for infinite populations for
                 both a constant and a length-related fitness function.
                 This allows us to characterise the bias induced by
                 standard crossover. This is very peculiar. In the case
                 of a constant fitness function, at the fixed-point,
                 structures of any length are present with non-zero
                 probability. However, shorter structures are sampled
                 exponentially much more frequently than longer ones.",
  notes =        "EuroGP'2001, part of \cite{miller:2001:gp}",
}

Genetic Programming entries for Riccardo Poli Nicholas Freitag McPhee