  A feedback neural network approach to communication routing problems is
developed with emphasis on Multiple Shortest Path problems, with several
requests for transmissions between distinct start- and endnodes. The basic
ingredients are a set of Potts neurons for each request, with interactions
designed to minimize path lengths and to prevent overloading of network arcs.
The topological nature of the problem is conveniently handled using a
propagator matrix approach. Although the constraints are global, the
algorithmic steps are based entirely on local information, facilitating
distributed implementations. In the polynomially solvable single-request case
the approach reduces to a fuzzy version of the Bellman-Ford algorithm. The
approach is evaluated for synthetic problems of varying sizes and load levels,
by comparing with exact solutions from a branch-and-bound method. With very few
exceptions, the Potts approach gives legal solutions of very high quality. The
computational demand scales merely as the product of the numbers of requests,
nodes, and arcs.
