Finding Approximate Analytic Solutions To Differential Equations Using Genetic Programming

Created by W.Langdon from gp-bibliography.bib Revision:1.4208

  author =       "Glenn Burgess",
  title =        "Finding Approximate Analytic Solutions To Differential
                 Equations Using Genetic Programming",
  institution =  "Surveillance Systems Division, Defence Science and
                 Technology Organisation, Australia",
  month =        Feb,
  year =         "1999",
  type =         "Technical Report",
  number =       "DSTO-TR-0838",
  address =      "Salisbury, SA, 5108, Austrlia",
  notes =        "Based on author's 1997 Dept. Phys. Honours Thesis,
                 Flinders University of South Australia",
  keywords =     "genetic algorithms, genetic programming, differential
  URL =          "",
  URL =          "",
  abstract =     "The computational optimisation technique, genetic
                 programming, is applied to the analytic solution of
                 general differential equations. The approach generates
                 a mathematical expression that is an approximate or
                 exact solution to the particular equation under
                 consideration. The technique is applied to a number of
                 differential equations of increasing complexity in one
                 and two dimensions. Comparative results are given for
                 varying several parameters of the algorithm such as the
                 size of the calculation stack and the variety of
                 available mathematical operators. Several novel
                 approaches gave negative results. Angeline's module
                 acquisition (MA) and Koza's automatically defined
                 functions (ADF) are considered and the results of some
                 modifications are presented. One result of significant
                 theoretical interest is that the syntax-preserving
                 crossover used in Genetic Programming may be
                 generalised to allow the exchange of n-argument
                 functions without adverse effects.

                 The results show that Genetic Programming is an
                 effective technique that can give reasonable results,
                 given plenty of computing resources. The technique used
                 here can be applied to higher dimensions; although in
                 practice the algorithmic complexity may be too high.",
  size =         "73 pages",

Genetic Programming entries for Glenn Burgess