We propose a transistor placement algorithm to generate standard cell layout in a two-dimensional placement style. The algorithm optimizes the one-dimensional placement in the first stage, folds the large transistors in the second stage, and optimizes the two-dimensional placement in the final stage. We also propose "cost function" based on wiring length, which closely match the cell optimization. This transistor placement algorithm has been applied to several standard cells, and demonstrated the capability to generate a two-dimensional placement that is comparable to manually designed placement.

Another high performance simulated annealing is proposed which we call widely stepping simulated annealing (WSSA). It flies from a starting high temperature to a finishing low temperature staying at only twenty or so temperatures to approach thermal equilibriums. We survey the phase transition in simulated annealing process and estimate the major cost variation (dEc) at the critical temperature. The WSSA uses a function (H(t)) that represents the probability for a hill-climbing with the dEc of cost increase to be accepted in Metropolis' Monte Carlo simulation at temperature t. We have applied the first version of WSSA to one dimensional transistor placement optimizations for several industrial standard cells, and compared its performance with simulated annealing with a geometrically scheduled cooling. The solutions by the WSSA are as good as, and sometimes much better than, the solutions by the simulated annealing, while the time consumption by the WSSA is properly under one 30th of that by the simulated annealing.