Temperature Measurement and Equilibrium Dynamics of Simulated Annealing Placements

One way to reduce the computational requirements of Simulated Annealing placement algorithms is to use a faster heuristic to replace the early phase of Simulated Annealing. Such system need to know a starting temperature for the annealing phase that makes the best use of the structure provided by the heuristic, yet does an appropriate amount of improvement. This paper presents a method for measuring the temperature of an existing placement. It is based on a view of Simulated Annealing state that differs from previous work - the probability distribution of the change in cost function, as opposed to the absolute cost function. Using this view a new definition of equilibrium is given and the equilibrium temperature of a placement is defined. This also gives rise to an new view of the equilibrium dynamics of Simulated Annealing. Heat treatment. JES