Inbreeding Properties of Geometric Crossover and Non-geometric Recombinations

Created by W.Langdon from gp-bibliography.bib Revision:1.4524

  author =       "Alberto Moraglio and Riccardo Poli",
  title =        "Inbreeding Properties of Geometric Crossover and
                 Non-geometric Recombinations",
  year =         "2007",
  booktitle =    "Foundations of Genetic Algorithms",
  editor =       "Christopher R. Stephens and Marc Toussaint and 
                 Darrell Whitley and Peter F. Stadler",
  volume =       "4436",
  series =       "LNCS",
  pages =        "1--14",
  address =      "Mexico City",
  month =        jan # " 8-11",
  organisation = "ACM SigEvo",
  publisher =    "Springer",
  note =         "Revised Selected Papers",
  keywords =     "genetic algorithms, genetic programming",
  isbn13 =       "978-3-540-73482-6",
  URL =          "",
  DOI =          "doi:10.1007/978-3-540-73482-6_1",
  abstract =     "Geometric crossover is a representation-independent
                 generalization of traditional crossover for binary
                 strings. It is defined in a simple geometric way by
                 using the distance associated with the search space.
                 Many interesting recombination operators for the most
                 frequently used representations are geometric
                 crossovers under some suitable distance. Showing that a
                 given recombination operator is a geometric crossover
                 requires finding a distance for which offspring are in
                 the metric segment between parents. However, proving
                 that a recombination operator is not a geometric
                 crossover requires excluding that one such distance
                 exists. It is, therefore, very difficult to draw a
                 clear-cut line between geometric crossovers and
                 non-geometric crossovers. In this paper we develop some
                 theoretical tools to solve this problem and we prove
                 that some well-known operators are not geometric.
                 Finally, we discuss the implications of these
  notes =        "Notes based on pre-publication slides

                 p21 No distance metric is possible for GP using only
                 Koza style sub-tree crossover. Hence no fitness
                 landscape for GP?????

                 p7 Metric for Homologous GP crossover

Genetic Programming entries for Alberto Moraglio Riccardo Poli