Hopfield neural network applied to optimization problems: Some theoretical and simulation results

This paper is devoted to the study of continuous Hopfield-like neural networks, either in its original version [Hopfield,1984] or in its high order generalization [Samad, 1990], [Kobuchi, 1991], applied to the solution of optimization problems. Main problems affecting the practical application of these networks are brought to light: a) Incoherence between the network dynamics and the associated energy function; b) Error due to discretization of the continuous dynamical equations caused by simulation on a digital computer; c) Existence of local minima. The behavior of this kind of neural networks with respect to these problems is analyzed and simulated, indicating possible mechanisms to avoid them. The last part of the paper we shown that the integral term in the energy function is bounded, in contrast with Hopfield's statement. Using this result, a new local minima avoidance strategy is proposed with an enhanced efficiency.

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