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@TechReport{burgess:1999:faasdeGP, 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 equations", URL = "http://203.36.224.190/cgi-bin/dsto/extract.pl?DSTO-TR-0838", URL = "http://www.dsto.defence.gov.au/corporate/reports/DSTO-TR-0838.pdf", 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