Placement Initialization via Sequential Subspace Optimization with Sphere Constraints

Abstract

State-of-the-art analytical placement algorithms for VLSI designs rely on solving nonlinear programs to minimize wirelength and cell congestion. As a consequence, the quality of solutions produced using these algorithms crucially depends on the initial cell coordinates. In this work, we reduce the problem of finding wirelength-minimal initial layouts subject to density and fixed-macro constraints to a Quadratically Constrained Quadratic Program (QCQP). We additionally propose an efficient sequential quadratic programming algorithm to recover a block-globally optimal solution and a subspace method to reduce the complexity of problem. We extend our formulation to facilitate direct minimization of the Half-Perimeter Wirelength (HPWL) by showing that a corresponding solution can be derived by solving a sequence of reweighted quadratic programs. Critically, our method is parameter-free, i.e. involves no hyperparameters to tune. We demonstrate that incorporating initial layouts produced by our algorithm with a global analytical placer results in improvements of up to 4.76% in post-detailed-placement wirelength on the ISPD'05 benchmark suite. Our code is available on github. https://github.com/choltz95/laplacian-eigenmaps-revisited.