Neural networks for NP-complete problems

combinatorial optimization is an active field of research in Neural Networks. Since the first attempts to solve the travelling salesman problem with Hopfield nets several progresses have been made, I will present some Neural Network approximate solutions for NP-complete problems that have a sound mathematical foundation and that, beside their theoretical interest, are also numerically encouraging. These algorithms easily deal with problems with thousands of instances taking Neural Network approaches out of the "toy-problem" era.