Meta-controlled Boltzmann machine: Its convergence and application to power system

In this paper, meta controlled Boltzmann machine; the double-layered Boltzmann machine consisting of upper (Hopfield network) and lower (Boltzmann network) layers, is built and the double-layered Boltzmann machine is proved to converge the optimal solution, after then, is efficiently applied to solve the investment problem to power system where the problem is understood as mean-variance problem using mathematical programming with two objectives: the minimization of risk and the maximization of expected return. The proposed method is applied both diffusion processes and simulated annealing. The convergence proof of the proposed method is showed in this paper. Meta-controlled Boltzmann machine shows an ability to solve combinatorial optimization problems better than either Hopfield networks or Boltzmann machines.