Abstract
the use of genetic programming to perform automated
discovery of numerical approximation formulae. We
present results involving rediscovery of known
approximations for Harmonic numbers, discovery of
rational polynomial approximations for functions of one
or more variables, and refinement of existing
approximations through both approximation of their
error function and incorporation of the approximation
as a program tree in the initial GP population. Evolved
rational polynomial approximations are compared to Pade
approximations obtained through the Maple symbolic
mathematics package. We find that approximations
evolved by GP can be superior to Pade approximations
given certain tradeoffs between approximation cost and
accuracy, and that GP is able to evolve approximations
in circumstances where the Pade approximation technique
cannot be applied. We conclude that genetic programming
is a powerful and effective approach that complements
but does not replace existing techniques from numerical
analysis.
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