Parametric Coding vs Genetic Programming: A Case Study

Created by W.Langdon from gp-bibliography.bib Revision:1.4216

  author =       "Alain Racine and Sana {Ben Hamida} and 
                 Marc Schoenauer",
  title =        "Parametric Coding vs Genetic Programming: A Case
  booktitle =    "Late-Breaking Papers of EuroGP-99",
  year =         "1999",
  editor =       "W. B. Langdon and Riccardo Poli and Peter Nordin and 
                 Terry Fogarty",
  pages =        "13--22",
  address =      "Goteborg, Sweeden",
  month =        "26-27 " # may,
  organisation = "EvoGP",
  keywords =     "genetic algorithms, genetic programming,
  URL =          "",
  URL =          "",
  abstract =     "The goal is to design the 2-dimensional profile of an
                 optical lens in order to control focalplane irradiance
                 of some laser beam. The numerical simulations of
                 irradiance of the beam through the lens, including some
                 technological constraints on the correlation radius of
                 the phase of the lens, involves two FFT (fast Fourier
                 transforms) computations, whose computational cost
                 heavily depends upon the chosen discretization.

                 A straightforward representation of a solution is that
                 of a matrix of thicknesses, based on a N by N (with N a
                 power of two) discretization of the lens. However, even
                 though some technical simplifications allow us to
                 reduce the size of the search space, its complexity
                 increased quadratically with N, making physically
                 realistic cases (e.g. N >= 256) almost untractable
                 (more than 2000 variables). An alternative
                 representation is brought by GP parse trees, searching
                 in functional space: the genotype does not depend
                 anymore on the chosen discretization.

                 The implementation of both parametric representation
                 (using ES algorithms) and functional approach (using
                 standard GP) for the lens design are described. Both
                 achieve good results compared to the sate-of-the-art
                 methods for small to medium values of the
                 discretization parameter N (up to 256). Moreover,
                 preliminary comparative results are presented between
                 the two representations, and some counter-intuitive
                 results are discussed.",
  notes =        "EuroGP'99LB part of \cite{langdon:1999:egplb}",

Genetic Programming entries for Alain Racine Sana Ben Hamida Marc Schoenauer