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

The simulated annealing (SA) algorithm has been applied to every difficult optimization problem in VLSI (very large scale integration) 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, the authors 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, they confirm the traditional wisdom of cooling.) The results open up many new research directions, particularly how to choose annealing temperatures dynamically to optimize the quality of the finite time, best-so-far solution.<>