A PARALLEL COMPUTATION BASED ON MEAN-FIELD THEORY FOR COMBINATORIAL OPTIMIZATION AND BOLTZMANN MACHINES

This paper proposes a parallel mean-field approximation algorithm based on the mean-field theory. In the parallel mean-field algorithm, a stable configuration at each temperature is obtained by applying the mean-field approximation to each element in the state space of a system, so that an actual state is replaced with a mean state, and by sequentially updating the mean field. This makes the convergence of a learning process faster than those in the simulated annealing algorithm and the Boltzmann machine. This paper examines Peterson's idea from the viewpoint of the mean learning algorithm and constructs a parallel learning algorithm confirming the existence of its stable distribution. To improve the processing speed of the proposed method further, this paper introduces a new temperature scheduling method (maximum entropy cooling schedule) by reexamining the temperature schedule of the Monte Carlo process and analyzing changes of the maximum entropy at a transition of a mean field of the system. Computer simulations show that the proposed method produces the same results as the conventional method but with shorter computation time, and also that the proposed maximum-entropy cooling schedule agrees with a thermodynamic analogy.