Application of Genetic Programming to the Choice of a Structure of Multipoint Approximations

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

  author =       "Vassili V. Toropov and Luis F. Alvarez",
  title =        "Application of Genetic Programming to the Choice of a
                 Structure of Multipoint Approximations",
  booktitle =    "1st ISSMO/NASA Internet Conf. on Approximations and
                 Fast Reanalysis in Engineering Optimization",
  year =         "1998",
  month =        jun # " 14-27",
  organisation = "ISSMO/NASA/AIAA",
  note =         "Published on a CD ROM",
  keywords =     "genetic algorithms, genetic programming",
  URL =          "",
  size =         "9 pages",
  notes =        "ISSMO at

                 Nice www page.

                 {"}The simplified model is characterized not only by
                 its structure (to be found by the GP) but also by a set
                 of tuning parameters a to be found by model tuning,
                 i.e. the least squares fitting of the model into the
                 set of values of the original response function:{"}
                 {"}The allocation of tuning parameters a to an
                 individual tree follows the basic algebraic rules. To
                 identify the parameters of the expression by the
                 nonlinear least-squares fitting, i.e. to solve the
                 optimization problem in (1), a combination of a GA and
                 a nonlinear mathematical programming method [9] is
                 used. The output of the GA is the initial guess for the
                 subsequent derivative-based optimization method which
                 amounts to a variation of the Newton's method in which
                 the Hessian matrix is approximated by the secant
                 (quasi-Newton) updating method. Once the technique
                 comes sufficiently close to a local solution, it
                 normally converges quite rapidly. To promote
                 convergence from poor starting guesses the algorithm
                 uses the adaptive update of the Hessian and,
                 consequently, the algorithm is reduced to either a
                 Gauss-Newton or Levenberg-Marquardt method.

                 {"}Three-bar truss optimization problem{"}

                 {"}The output of the algorithm still needs some manual
                 post-processing in order to get rid of those terms in
                 the expression that give a null or tiny contribution,
                 for example when the same value is added and
                 subtracted. It is then suggested to run the problem
                 several times in order to identify, by comparison, the
                 most likely components.{"}",

Genetic Programming entries for Vassili V Toropov Luis F Alvarez