Temperature measurement and equilibrium dynamics of simulated annealing placements

One way to alleviate the heavy computation required by simulated annealing placement algorithms is to replace a significant fraction of the higher or middle temperatures with a faster heuristic, and then follow it with simulated annealing. A crucial issue in this approach is the determination of the starting temperature for the simulated annealing phase-a temperature should be chosen that causes an appropriate amount of optimization to he done, but makes good use of the structure provided by the heuristic. This paper presents a method for measuring the temperature of an existing placement. The approach is based on the measurement of the probability distribution of the change in cost function, P ( A C ) , and makes the assumption that the placement is in simulated annealing equilibrium at some temperature. The temperature of placements produced both by a simulated annealing and a min-cut placement algorithm are measured, and good agreement with known temperatures is obtained. The P( A C ) distribution is also used to give an interesting view of the equilibrium dynamics of simulated annealing.