Title: Variable Annealing Length and Parallelism in Simulated Annealing,
Abstract: 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.