An Efficient Simulated Annealing Schedule: Derivation

The popularity of simulated annealing comes from its ability to find close to optimal solutions for NP-hard combinatorial optimization problems. Unfortunately, current implementations of the method usually require massive computation time. This paper presents a general annealing schedule which speeds up simulated annealing significantly when compared with general schedules available in the literature. The annealing schedule, which lowers the temperature at every step and keeps the system in quasi-equilibrium at all times, is derived from a new quasi-equilibrium criterion. For a given move generation strategy, this schedule is shown to give the minimum final average cost among all schedules that maintain the system in quasiequilibrium. An alternate form of the schedule is derived that explicitly relates move generation to temperature decrement. This leads to a control method for the move generation strategy that further minimizes the final average cost. This research was supported by the Army Research Office under contract DAAL03-86-K-0158, by the National Science Foundation under grant ECS8314750, and by the Office of Naval Research under contracts N00014-84-K0092 and N00014-85-K-0461.