“Optimal” neural representation for combinatorial optimization with linear cost function

Taking assignment problems as examples of combinatorial optimization problems with linear cost function, we present an “optimal” neural representation for these problems. It is proved that a vertex of this network state hypercube is asymptotically stable iff it is an optimal solution to the problem. One can always obtain an optimal solution whenever the network converges to a vertex. We can also design such “optimal” neural representations for many combinatorial optimization problems with linear cost function, as well as for assignment problems