Abstract
When a mutually connected neural network (Hopfield net) is applied to the minimization problem, the process may fall in a local minimum and not converge to the global minimum. To remedy this problem, several means have been proposed such as Boltzmann machine; however, this and other proposals take too much time.
This paper proposes a neural net that permits multitransition (transition between states with two or more Hamming distances). It is shown that convergence to the global minimum can be realized escaping from the local minimum. It is shown first that the decrement of the energy when more than one element simultaneously changes can be calculated by simple additionβsubtractions of the weight factors for the inputs to the element and the coupling factors among elements. A probabilistic minimum search algorithm is presented based on the multitransition. The optimization problem for 100 elements was solved by a personal computer, and the process converged to the minimum within an hour in 398 trials of 400. The average convergence time is 10 min, and the convergence is achieved in 20 s in the fastest case. The computation time increases with the increase of elements with a much slower rate than in the case of allβsearch.