Abstract

The simulated annealing (SA) algorithm [14] [5] has been applied to every difficult optimization problem in VLSI CAD. Existing SA implementations use monotone decreasing, or cooling, temperature schedules motivated by the algorithm's proof of optimality as well as by an analogy with statistical thermodynamics. This paper gives strong evidence that challenges the correctness of using such schedules. Specifically, the theoretical framework under which monotone cooling schedules is proved optimal fails to capture the practical application of simulated annealing; in practice, the algorithm runs for a finite rather than infinite amount of time; and the algorithm returns the best solution visited during the entire run ("best-so-far") rather than the last solution visited ("where-you-are"). For small instances of classic VLSI CAD problems, we determine annealing schedules that are optimal in terms of the expected quality of the best-so-far solution. These optimal schedules do not decrease mo...

Citations