Temperature schedules for simulated annealing

It is well known that the behaviour of the simulated annealing approach to optimization is crucially dependent on the choice of temperature schedule. In this paper, a dynamic programming approach is used to find the temperature schedule which is optimal for a simple minimization problem. The optimal schedule is compared with certain standard non-optimal choices. These generally perform well provided the first and last temperatures are suitably selected. Indeed, these temperatures can be chosen in such a way as to make the performance of the logarithmic schedule almost optimal. This optimal performance is fairly robust to the choice of the first temperature. The dynamic programming approach cannot be applied directly to problems of more realistic size, such as those arising in statistical image reconstruction. Nevertheless, some simulation experiments suggest that the general conclusions from the simple minimization problem do carry over to larger problems. Various families of schedules can be made to perform well with suitable choice of the first and last temperatures, and the logarithmic schedule combines good performance with reasonable robustness to the choice of the first temperature.