Empirical and theoretical studies of the simulated evolution method applied to standard cell placement

The authors present a quantitative analysis of the simulated evolution (SE) technique based on a variety of parameters. The measurement results and their relevance to practical implementations are discussed. A mathematical formulation of the SE algorithm is introduced. The associated Markov chain model is thoroughly analyzed. It is shown that the algorithm will hit a global minimum with probability one. The theoretical analysis suggests some modifications to a previously published SE-based method that was applied to cell placement problems. In order to compensate for additional computation times required by the new technique, the authors also introduce a novel hierarchical placement method. It has inherent advantages over the flat method in both CPU time requirements and result quality. It is also shown how a windowing method can be used to significantly reduce computation times