Extended Hopfield models for combinatorial optimization

The extended Hopfield neural network proposed by Abe et al. for solving combinatorial optimization problems with equality and/or inequality constraints 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 penalty energy allowing us to reduce significantly the number of neurons with intermediate level of activations. The new version of the model is validated experimentally on the set covering problem. Our results confirm the importance of instituting competitive activation mechanisms in Hopfield neural-network models.