This kind of problem doesn't sound very suitable for neural networks. Neural networks are probably most often used as classifiers with supervised learning. Typically, you have to have a training set with examples that are already classified. There are some unsupervised approaches too, most recently most notably perhaps the deep neural networks. But that is an active area of research and I doubt there are ready made tools for what you need.
You have a problem with combinatorial explosion in the parameter space. That kind of problem is often well suited for solving with evolutionary algorithms. For example genetic algorithms or simulated annealing.
With genetic algorithms the problem solving shifts to finding
- a good problem representation that allows you to do crossover and mutations,
- a suitable fitness function.
This often proves to be very difficult.
Your problem, however, seems to be very suitable for this method:
- individual solution representation: a list of parameters
i = [p_1, p_2, ..., p_n]
- crossover of
i_1
andi_2
: choose a splitting point between1
andn
and exchange the respective parts of the individuals' lists - mutation: choose a parameter and adjust it
- fitness function: rate of messages per second
It's not guaranteed that you would get an optimal solution this way but it can help you to combat the combinatorial explosion quite effectively.