Abstract: This paper presents two generalized updating rules based on Hopfield-type neural networks (with delay or without delay) for optimization problems. These rules are characterized by dynamic thresholds of the updating sequence. Convergence theorems of discrete Hopfield-type neural networks with delay are obtained, which extend the exsiting convergence results. Also obtained is a sufficient and necessary condition for the relation between the stable states of neural networks and the points of local maximum value of energy function. Decomposed strategy is given in order to apply the Hopfield-type neural networks with delay to optimization problems effectively. Finally, the experimental results demonstrate that the given algorithm improves the convergence rate and decreases the updating time when compared with Hopfield-type neural network without delay.