Variable Annealing Length and Parallelism in Simulated Annealing
This work addresses a specific bottleneck in simulated annealing for optimization problems, offering an incremental improvement in parameter-free adaptive scheduling.
The paper tackles the problem of eliminating the prior knowledge requirement for annealing length in simulated annealing by proposing a restart schedule with exponentially increasing lengths and extending it to parallel implementation, achieving substantial performance gains on an NP-hard scheduling problem.
In this paper, we propose: (a) a restart schedule for an adaptive simulated annealer, and (b) parallel simulated annealing, with an adaptive and parameter-free annealing schedule. The foundation of our approach is the Modified Lam annealing schedule, which adaptively controls the temperature parameter to track a theoretically ideal rate of acceptance of neighboring states. A sequential implementation of Modified Lam simulated annealing is almost parameter-free. However, it requires prior knowledge of the annealing length. We eliminate this parameter using restarts, with an exponentially increasing schedule of annealing lengths. We then extend this restart schedule to parallel implementation, executing several Modified Lam simulated annealers in parallel, with varying initial annealing lengths, and our proposed parallel annealing length schedule. To validate our approach, we conduct experiments on an NP-Hard scheduling problem with sequence-dependent setup constraints. We compare our approach to fixed length restarts, both sequentially and in parallel. Our results show that our approach can achieve substantial performance gains, throughout the course of the run, demonstrating our approach to be an effective anytime algorithm.