Several key problems previously analyzed by simulated annealing are well described by a simple two-state statistical mechanical model, equivalent to the one-dimensional Ising model, in conjunction with an Arrhenius type rate equation. With this model we develop an analytic solution for the optimal cooling strategy which computationally is much faster than the previously developed adaptive algorithm. In the long time limit the analytic solution reduces to the one cooling schedule which is sure to reach the ground state. Our model predictions are in good agreement with earlier numerical simulation results for optimal cooling schedules as well as for stationary and dynamic properties of system energy, heat capacity, and relaxation time.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Mathematical Physics