Abstract
Neural Networks as optimizing machines have pending problems that a process of the state transition is trapped at one of local optimal solutions. Especially, local stationary of the asynchronous state transition in binary is caused by judging increase or decrease in the minimizing function value between two states at only one Hamming distance. In order to get off from such local minima, the linked state transition neural network was proposed. On the other hand, in probabilistic expectation for getting off from local minima, the Boltzmann Machine was developed in which state transitions increasing the minimizing function value are accepted in a frequency ratio. Consequently, the state transition reaching the global optimal solution is stochastic process.
In order to ignore the statistical indeterminacy, in this paper, neurons are endowed with a hysteretic input-output relation by which state transitions with increasing fluctuation of the minimizing function value within a certain range are accepted deterministically to pass over the local minima certainly, and annealed types of the Hysteresis Machines are proposed in which the hysteresis is tranquilized in a process of the state transitions to stabilize them in the global optimal solution. Moreover, the genetic algorithm is applied to acquisition of the best annealing parameters realizing the global optimal solution by trial and repeated cooling procedures of the hysteresis. It is certified in a few combinatorial optimization problems that the global optimal solution is obtained with high reliability by the hybrid annealing procedure of the Hysteresis Machine supervised by the genetic algorithm.
