Abstract
In the asynchronous state transition of the Hopfield's type of neural networks with binary states, the state transition of neurons is trapped at one of local optima in a neighbourhood with radius of one Hamming distance, because all the transition occurs between two states at a distance of a single bit. In this paper, we present a neural network whose states transit directly through the Hamming distance of several bits and get off from such a local optimum in order to reach deterministicly the global optimum.
Concretely, the only when the states are trapped at a local optimum in the asynchronous transition mode, the mode is changed into the linked transition mode in which some of the neurons change the states cooperatively and simultaneously according to threshold rule for total inputs value concerned with the linked neurons. The simulation results for unconstrained types of 0-1 combinatorial optimization problems with a quadratic function demonstrate the fundamentals of the proposed linked state transition.
