On Fitness Proportionate Selection and the Schema Theorem in the Presence of Stochastic Effects

Created by W.Langdon from gp-bibliography.bib Revision:1.3872

@TechReport{Poli00-2,
  author =       "Riccardo Poli",
  title =        "On Fitness Proportionate Selection and the Schema
                 Theorem in the Presence of Stochastic Effects",
  institution =  "University of Birmingham, School of Computer Science",
  number =       "CSRP-00-2",
  month =        feb,
  year =         "2000",
  keywords =     "genetic algorithms, genetic programming",
  email =        "R.Poli@cs.bham.ac.uk",
  file =         "/2000/CSRP-00-02.ps.gz",
  URL =          "ftp://ftp.cs.bham.ac.uk/pub/tech-reports/2000/CSRP-00-02.ps.gz",
  abstract =     "Holland's schema theorem has been criticised in (Fogel
                 and Ghozeil 1997, Fogel and Ghozeil 1998, Fogel and
                 Ghozeil 1999) for not being able to estimate correctly
                 the expected proportion of a schema in the population
                 when fitness proportionate selection is used in the
                 presence of noise or other stochastic effects. This is
                 incorrect for two reasons. Firstly, the theorem in its
                 original form is not applicable to this case. As
                 clarified in the paper, if the quantities involved in
                 schema theorems are random variables, the theorems must
                 be interpreted as conditional statements. Secondly, the
                 conditional versions of Holland and other researchers'
                 schema theorems are indeed very useful to model the
                 sampling of schemata in the presence of stochasticity.
                 In the paper I show how one can calculate the correct
                 expected proportion of a schema in the presence of
                 stochastic effects when selection only is present,
                 using a conditional interpretation of Holland's schema
                 theorem. In addition, I generalise this result (again
                 using schema theorems) to the case in which crossover,
                 mutation, and selection with replacement are used. This
                 can be considered as an exact schema theorem applicable
                 both in the presence and in the absence of stochastic
                 effects.",
}

Genetic Programming entries for Riccardo Poli

Citations