Mean field annealing with continuous variables and its application to the quantification analysis problem

A mean field theory (MFT) neural network with discrete variables has been applied to many combinatorial optimization problems. The authors present mean field annealing with continuous variables and its application to the quantification analysis problem. They begin with the reformulation of the quantification analysis problem to the penalty problem. One-variable stochastic simulated annealing (SSA) is proposed based on the mean field approximation in order to overcome the difficulties in evaluating the spin average value expressed by the integral in such a network. In SSA, the perturbed state of all the spins is regarded as a solution, but in one-variable SSA the average of the perturbed state of only one spin is regarded as an equilibrium average of that spin under the field of the rest of the system. A multibody problem is thus reduced to a single-body problem. Experimental results on the quantification analysis problem show the feasibility of this approach