UFO: Unified Convex Optimization Algorithms for Fixed-Outline Floorplanning Considering Pre-Placed Modules

Fixed outline floorplanning has recently attracted more attention due to its usefulness in solving real problems in industry. This paper applies two convex optimization methods, named UFO, to solve this problem, which consists of a global distribution stage followed by a local legalization phase. In the first stage, modules are transformed into circles, and a push-pull (PP) model is proposed to uniformly distribute modules over the fixed outline with consideration of their wirelength. Due to the quality of the PP model, we obtain good results after the first stage. Therefore, it is not necessary to consider wirelength in the legalization phase. In order to maintain good results of the first stage, we propose a procedure to extract the geometric relations of the modules from the results of the first stage and store it in constraint graphs. Then, the locations and shapes of the modules are determined by second-order cone programming, which penalizes overlap and obeys the boundary constraints. Finally, we extend the UFO methodology to consider pre-placed modules in a fixed outline. We have implemented two convex functions on MATLAB, and experimental results have demonstrated that UFO clearly outperforms the results reported in the literature on the GSRC and MCNC benchmarks.