On the Acceleration of Simulated Annealing

Abstract

The simulated annealing algorithm has been very successful in the field of VLSI design automation. The main drawback to the algorithm is its sometimes prohibitive computational cost. This dissertation examines two methods for accelerating the algorithm. The first method is a uni-processor approach called two-stage simulated annealing. The second method is a multi-processor approach called population-oriented simulated annealing. In a traditional homogeneous two-stage simulated annealing system, the paradigm's early temperatures are replaced by a faster heuristic method. The main problem in the design of a two-stage simulated annealing system is the determination of the new starting temperature such that solution quality is maintained while acceleration is maximized. Most of the early work in this area avoided the problem of formalizing a general method of starting temperature determination by finding a reasonable ad hoc constant starting temperature for the low temperature simulated annealing phase. This dissertation instead presents a more formal method for approximating the starting temperature for traditional homogeneous two-stage simulated annealing systems that is both computationally inexpensive and accurate in practice. The proposed method is tested on three NP-hard combinatorial problems using two disparate homogeneous cooling schedules in an attempt to show applicability to different homogeneous simulated annealing formulations. Other robustness issues are also explored in addition to a new parameterized stop criterion for the classic cooling schedule. Parallelization is another approach to the problem of accelerating the simulated annealing algorithm. However, an efficient application-independent parallelization has yet to be presented. Instead, this dissertation examines an alternative thermodynamic/genetic hybrid approach to parallelization, inspired by the genetic algorithm. The proposed thermodynamic/genetic hybrid algorithm, called population-oriented simulated annealing, combines the advantages of the genetic algorithm's efficient parallelization with simulated annealing's superior convergence control. Both sequential and distributed results are presented for two NP-hard combinatorial problems. The sequential versions are empirically shown to compare favorably with other effective heuristic methods in terms of solution quality given equal amounts of computation time. Both distributed versions experimentally illustrate the algorithm's efficient parallelization as both are seen to exhibit continued speedup up to 10 processors, indicating the possibility of further scaling of the algorithm to larger numbers of processors.