keywords = "genetic algorithms, genetic programming, local search,
hill climbing",
isbn13 = "978-3-642-20406-7",
DOI = "doi:10.1007/978-3-642-20407-4_1",
abstract = "A novel heuristic technique that enhances the search
facility of the standard genetic programming (GP)
algorithm is presented. The method provides a dynamic
sniffing facility to optimise the local search in the
vicinity of the current best chromosomes that emerge
during GP iterations. Such a hybrid approach, that
combines the GP method with the sniffer technique, is
found to be very effective in the solution of inverse
problems where one is trying to construct model
dynamical equations from either finite time series data
or knowledge of an analytic solution function. As
illustrative examples, some special function ordinary
differential equations (ODEs) and integrable nonlinear
partial differential equations (PDEs) are shown to be
efficiently and exactly recovered from known solution
data. The method can also be used effectively for
solution of model equations (the direct problem) and as
a tool for generating multiple dynamical systems that
share the same solution space.",
notes = "Mathematica. Order of partial or ordinary differential
equation search in sequence starting with first order
and increasing until satisfactory match found.