- author = "Alain Racine and Sana {Ben Hamida} and Marc Schoenauer",
- title = "Parametric Coding vs Genetic Programming: A Case Study",
- 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, evolutionstrategies",
-
URL = "
http://www.cs.ucl.ac.uk/staff/W.Langdon/eebic/eurogp99/eurogp99_lbp.html",
-
URL = "
ftp://ftp.cwi.nl/pub/CWIreports/SEN/SEN-R9913.pdf",
-
URL = "
ftp://ftp.cwi.nl/pub/CWIreports/SEN/SEN-R9913.ps.Z",
-
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}",
