Mixed Integer Programming based Placement Refinement by RSMT Model with Movable Pins

Placement is a critical step in the physical design for digital application specific integrated circuits (ASICs), as it can directly affect the design qualities such as wirelength and timing. For many domain specific designs, the demands for high performance parallel computing result in repetitive hardware instances, such as the processing elements in the neural network accelerators. As these instances can dominate the area of the designs, the runtime of the complete design’s placement can be traded for optimizing and reusing one instance’s placement to achieve higher quality. Therefore, this work proposes a mixed integer programming (MIP)-based placement refinement algorithm for the repetitive instances. By efficiently modeling the rectilinear steiner tree wirelength, the placement can be precisely refined for better quality. Besides, the MIP formulations for timing-driven placement are proposed. A theoretical proof is then provided to show the correctness of the proposed wirelength model. For the instances in various popular fields, the experiments show that given the placement from the commercial placers, the proposed algorithm can perform further placement refinement to reduce 3.76%/3.64% detailed routing wirelength and 1.68%/2.42% critical path delay under wirelength/timing-driven mode, respectively, and also outperforms the state-of-the-art previous work.