GA or ANN, and suggestions I am working to approximate, to extrapolate rather, values of a function from a few known values. Here is what I have:


*

*Less than 100 known I/O pairs.

*A monotonously positive correlation.en

*Something that is not exactly Gaussian, Poisson, or inverse binomial.


Right now I can choose between a genetic algorithm and an artificial neural network. If I use a genetic algorithm, then I will use it to approximate the relation with a polynomial or a rational function. If I use a neural network, I will simply find the first Google result for a C++ NN library (unless I am advised otherwise).
Here are my questions. Suppose I have access to a long time (1-2 week max) as well great computational might (university clusters).


*

*Would I achieve a closer approximation with a GA or an ANN?

*Which would be faster?

*For those ANN specialists out there: I am unacquainted with the world of ANN technology. If I am looking for portability, programmability, speed, and adaptability for such extrapolation, which C++ toolkit would you recommend?


Thank you.
 A: Genetic algorithms and neural networks are not really competing methods. For instance one could use a genetic algorithm to train a neural network (a field called neuroEvolution).
Genetic algorithms are used to optimise 'thing' and neural networks are 'something' to be optimised. i.e. one could optimise a neural network using backpropagation, some form of hebbian learning or a genetic algorithm.
1)
If you are going to use a genetic algorithm to optimise the weights of a polynomial function then as @alto suggests there are likely better methods.
As for neural networks, they can be universal approximators, so in theory you could achieve a very good approximation. 
2)
I couldn't find and results on typical training times. Firstly people do not often quote the training time in 'wall time'. The backpropagation world are more concerned with the final result and the genetic algorithms world compare methods using the number of evaluations to find a suitable solution. So a comparison between the two can't be made.
A: If using C++ is a must, you may take a look at Shogun. As I understand, it could be a NN, but any method that get the job done will do as well. Shogun focuses on kernel methods (SVM and GP).
As for genetic algorithms: I have no experience whatsoever with that optimization technique, but mostly because I have not come across it in the literature. It seems to me that not many people in the Machine Learning community uses it.
