Abstract

Abstract-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 ap-proach is the determination of the starting temperature for the simu-lated 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(AC), and makes the assumption that the placement is in simulated annealing equilibrium at some temperature. The temperature of placements produced both by a simulated anneal-ing and a min-cut placement algorithm are measured, and good agree-ment with known temperatures is obtained. The P ( A C) distribution

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