Modified Hopfield-Tank Neural Networks Applied to the “Unitized” Maximum Flow Problem

Two new approaches called “graph unitization” are proposed to apply neural networks similar to the Hopfield-Tank models to determine optimal solutions for the maximum flow problem. They are: (1) n-vertex and n2-edge neurons on a unitized graph; (2) m-edge neurons on a unitized graph. Graph unitization is to make the flow capacity of every edge equal to 1 by placing additional vertices or edges between existing vertices. In our experiments, solutions converged most of the time, and the converged solutions were always optimal, rather than near optimal.