Continuous functions can be approximated by ANN effectively, which is proved both in theory and practice, as well as the discrete version of these continuous functions.
However, there is a kind of discrete functions in the field of discrete event systems(DES), where the min/max algebra can be applied. Min/max operations are the basic operations in these functions. These functions are common in production scheduling, resource allocation and so on.
Many articles treat DESs as black-boxes, and train ANNs with their input and output data directly. But do ANNs have the ability to approximate these functions with min/max operations?
I've just conducted several groups of experiments, in which the NEH heuristics is approximated by an RBF NN. Results turn out to be with the opinion, and the errors are very low.
However, could anyone show me some theoretical supports?
The Cybenko theorem clearly states that ANNs have the ability to learn any function, including discrete ones.
Whether ANNs are the most efficient way of doing this is a different matter entirely.
Dear Nejati,
I've noticed that the theorem has been proved for continuous functions, as Cybenko in 1989, as well as Kurt Hornik in 1991.
( http://en.wikipedia.org/wiki/Universal_approximation_theorem )
For more details refer the article: "Simplified neural networks algorithm for function approximation on discrete input spaces in high dimension-limited sample applications" by Hyder & Zheng in Neuro computing Journal.
Dear Ramesh,
Thank you so much for your valuable recommendation. It helps a lot.
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