Best-so-far vs. where-you-are: New perspectives on simulated annealing for CAD

The simulated annealing (SA) algorithm [14] [5] has been applied to every di cult 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. Speci cally, 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 nite rather than in nite 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 monotonically, but are in fact either periodic or warming. (When the goal is to optimize the cost of the where-you-are solution, we con rm the traditional wisdom of cooling.) Our results open up many new research directions, particularly how to choose annealing temperatures dynamically to optimize the quality of the nite time, best-sofar solution.