When solving combinatorial optimization problems with a binary Hopfield-type neural network, the updating process in neural network is an important step in achieving a solution. In this letter, we propose a new updating procedure in binary Hopfield-type neural network for efficiently solving combinatorial optimization problems. In the new updating procedure, once the neuron is in excitatory state, then its input potential is in positive saturation where the input potential can only be reduced but cannot be increased, and once the neuron is in inhibitory state, then its input potential is in negative saturation where the input potential can only be increased but cannot be reduced. The new updating procedure is evaluated and compared with the original procedure and other improved methods through simulations based on N-Queens problem. The results show that the new updating procedure improves the searching capability of neural networks with shorter computation time. Particularly, the simulation results show that the performance of proposed method surpasses the exiting methods for N-queens problem in synchronous parallel computation model.

By adding some functions to memories, highly parallel computation may be realized. We have proposed memory-based parallel computation models, which uses a new functional memory as a SIMD type parallel computation engine. In this paper, we consider models with communication between the words of the functional memory. The memory-based parallel computation model consists of a random access machine and a functional memory. On the functional memory, it is possible to access multiple words in parallel according to the partial match with their memory addresses. The cube-FRAM model, which we propose in this paper, has a hypercube network on the functional memory. We prove that PSPACE is accelerated to polynomial time on the model. We think that the operations on each word of the functional memory are, in a sense, the essential ones for SIMD type parallel computation to realize the computational power.