Pulsed noise-based stochastic optimization with the Hopfield model

In this paper a new simple approach to solving combinatorial optimization problems is discussed and preliminary simulation results are presented. The pulsed noise model (PNM) introduced in the paper is based on combining the Langevin equation minimization method with the Hopfield model in a very straight forward manner. The main advantage of this approach is its conceptual simplicity without sacrificing efficiency. Unlike in previous related works (stochastic neural networks, diffusion machine), in the PNM, intensities of Gaussian noises injected to the system are independent of the neurons´ potentials. Moreover, in the PNM noises are injected to the system only at certain time instances in the opposite to continuously maintained /spl delta/-correlated noises used in previous approaches. Finally, instead of impractically long inverse logarithmic cooling schedules, linear cooling is applied. With the above strong simplifications PNM is not expected to rigorously maintain thermal equilibrium (TE). However, approximate numerical test based on the canonical Gibb-Boltzman distribution show that differences between the rigorous and estimated values are relatively low (within a few percent). In this sense PNM is said to perform quasi-termal equilibrium.