Communication network routing using neural nets-numerical aspects and alternative approaches

The authors discuss various approaches of using Hopfield networks in routing problems in computer communication networks. It is shown that the classical approach using the original Hopfield network leads to evident numerical problems, and hence is not practicable. The heuristic choice of the Lagrange parameters, as presented in the literature, can result in incorrect solutions for variable dimensions, or is very time consuming, in order to search the correct parameter sets. The modified method using eigenvalue analysis using predetermined parameters yields recognizable improvements. On the other hand, it is not able to produce correct solutions for different topologies with higher dimensions. From a numerical viewpoint, determining the eigenvalues of the connection matrix involves severe problems, such as stiffness, and shows evident instability of the simulated differential equations. The authors present possible alternative approaches such as the self-organizing feature map and modifications of the Hopfield net, e.g. mean field annealing, and the Pottglas model