  The Hopfield network has been applied to solve optimization problems over
decades. However, it still has many limitations in accomplishing this task.
Most of them are inherited from the optimization algorithms it implements. The
computation of a Hopfield network, defined by a set of difference equations,
can easily be trapped into one local optimum or another, sensitive to initial
conditions, perturbations, and neuron update orders. It doesn't know how long
it will take to converge, as well as if the final solution is a global optimum,
or not. In this paper, we present a Hopfield network with a new set of
difference equations to fix those problems. The difference equations directly
implement a new powerful optimization algorithm.
