Error-free parallel implementation of simulated annealing

Abstract

Simulated Annealing is a powerful optimization method which has been applied to a number of industrial problems; however, it often requires large computation times. One way to overcome this drawback is the design of finely tuned cooling schedules, which may ensure a fast convergence of the sequential algorithm towards near-optimal solutions. Another way of decreasing the computation time is the use of parallel implementations. Obviously, both approaches can be combined; however, this is possible only if the parallel implementation of the algorithm exhibits the same convergence behaviour as the sequential one. In the present paper, we show that the previously proposed parallel algorithms deviate from the sequential simulated annealing algorithm, and we suggest a problem-independent parallel implementation which is guaranteed to exhibit the same convergence behaviour as the sequential one. We introduce various modes of parallelization, depending on the value of the acceptance rate, and we derive statistical models which can predict the speedup for any problem, as a function of the acceptance rate, of the number of processes and of the time caracteristics of the annealing. The performances are evaluated on a simple placement problem with a Transputer-based network, and the analytical models are compared to experiments.