Electrostatic placers are a type of non-linear placers that gained popularity due to their high quality of results. Obtaining an accurate placement solution is crucial in Field-Programmable Gate Arrays (FPGAs), where routing resources are limited and post-placement improvements, such as buffer insertions, are not possible. This paper investigates the electrostatic placer in the open-source place&route framework nextpnr. Driven by the vast interest in machine learning, new gradient direction algorithms emerged. We revisit the choice of gradient direction algorithm and compare Nesterov’s method used in ePlace and elfPlace against RMSProp, Adam, Adan, and an adaptive restarting scheme. Further, we add optional initial bi-partitioning and tune the hyper-parameters for two schemes to update the Lagrange multipliers. Initial experiments show that adaptively restarting Nesterov’s method can be beneficial and emphasize Adam as a promising candidate besides Nesterov’s method due to its high-quality results and fast convergence.

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Revisiting Gradient Direction Algorithms in Electrostatic Placers

  • Meinhard Kissich,
  • Marcel Baunach

摘要

Electrostatic placers are a type of non-linear placers that gained popularity due to their high quality of results. Obtaining an accurate placement solution is crucial in Field-Programmable Gate Arrays (FPGAs), where routing resources are limited and post-placement improvements, such as buffer insertions, are not possible. This paper investigates the electrostatic placer in the open-source place&route framework nextpnr. Driven by the vast interest in machine learning, new gradient direction algorithms emerged. We revisit the choice of gradient direction algorithm and compare Nesterov’s method used in ePlace and elfPlace against RMSProp, Adam, Adan, and an adaptive restarting scheme. Further, we add optional initial bi-partitioning and tune the hyper-parameters for two schemes to update the Lagrange multipliers. Initial experiments show that adaptively restarting Nesterov’s method can be beneficial and emphasize Adam as a promising candidate besides Nesterov’s method due to its high-quality results and fast convergence.