By the way, I found a neural network learning algorithms which I may be able to use. It is called Simulated Annealing. As with Genetic algorithms it is able to solve the Traveling Salesman problem. In that problem there are a group of cities and the network decides which is the best route to take. As I understand it Simulated Annealing just do it fast.
http://www.youtube.com/watch?v=kF2heJbvYcU
I am not sure it is the best way to go so I am open for all ideas.