A complete neural network approach to solving a class of combinatorial problems

Summary form only given. The concept of the Hopfield neural network (NN) has been generalized where discrete neurons, called quantrons (Q´trons, a shorthand for quantum neurons), are exploited. Unlike the conventional neuron in a Hopfield NN, a Q´tron may have multiple (usually more than two) output levels. A system energy, referred to as Lyapunov energy, is embedded in the NN and is shown to possess monotonically decreasing property. Therefore, a combinatorial problem can be solved using this Q´tron NN by first reformulating the problem into one which minimizes a Lyapunov energy function, on the basis of which the NN is then built. As a result, when the NN gets to settle on a stable state, the original combinatorial problem is solved. Remarkable features of this approach are: (1) a solution to the problem, if it exists, will always be reached with probability one; and (2) no false solution will ever be reported