Extended hopfield models for combinatorial optimization

The extended Hopfield neural network proposed by Abe ct nl. for solving com binatorial optimization problems with equality and/or inequality constraint s has the drawback of being frequently stabilized in states with neurons of ambiguous classification as active or inactive. We introduce in the model a competitive activation mechanism and we derive a new expression of the pe nalty energy allowing us to reduce significantly the number of neurons with intermediate level of activations. The new version of the model is validat ed experimentally on the set covering problem, Our results confirm the impo rtance of instituting competitive activation mechanisms in Hopfield neural- network models.