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Floorplanning of VLSI by Mixed-Variable Optimization

Jian Sun, Huabin Cheng, Jian Wu, Zhanyang Zhu, Yu Chen

TL;DR

The paper tackles VLSI floorplanning by formulating it as a mixed-variable optimization problem, where module orientations are discrete and coordinates are continuous. It introduces a dual-method framework: DEA-PPM to optimize orientations and CSA to optimize coordinates, yielding two algorithms tailored to fixed-outline (FFA-CD) and unconstrained (FA-GSS) scenarios. Empirical results on GSRC circuits show competitive performance, with FFA-CD outperforming B*-tree–based Parquet-4.5 on large instances and FA-GSS delivering strong wirelength and area trade-offs without fixed outlines. The work demonstrates low time complexity and potential for scaling to large-scale floorplanning tasks, aided by orientation exploration and robust legalization strategies.

Abstract

By formulating the floorplanning of VLSI as a mixed-variable optimization problem, this paper proposes to solve it by memetic algorithms, where the discrete orientation variables are addressed by the distribution evolutionary algorithm based on a population of probability model (DEA-PPM), and the continuous coordination variables are optimized by the conjugate sub-gradient algorithm (CSA). Accordingly, the fixed-outline floorplanning algorithm based on CSA and DEA-PPM (FFA-CD) and the floorplanning algorithm with golden section strategy (FA-GSS) are proposed for the floorplanning problems with and without fixed-outline constraint. %FF-CD is committed to optimizing wirelength targets within a fixed profile. FA-GSS uses the Golden Section strategy to optimize both wirelength and area targets. The CSA is used to solve the proposed non-smooth optimization model, and the DEA-PPM is used to explore the module rotation scheme to enhance the flexibility of the algorithm. Numerical experiments on GSRC test circuits show that the proposed algorithms are superior to some celebrated B*-tree based floorplanning algorithms, and are expected to be applied to large-scale floorplanning problems due to their low time complexity.

Floorplanning of VLSI by Mixed-Variable Optimization

TL;DR

The paper tackles VLSI floorplanning by formulating it as a mixed-variable optimization problem, where module orientations are discrete and coordinates are continuous. It introduces a dual-method framework: DEA-PPM to optimize orientations and CSA to optimize coordinates, yielding two algorithms tailored to fixed-outline (FFA-CD) and unconstrained (FA-GSS) scenarios. Empirical results on GSRC circuits show competitive performance, with FFA-CD outperforming B*-tree–based Parquet-4.5 on large instances and FA-GSS delivering strong wirelength and area trade-offs without fixed outlines. The work demonstrates low time complexity and potential for scaling to large-scale floorplanning tasks, aided by orientation exploration and robust legalization strategies.

Abstract

By formulating the floorplanning of VLSI as a mixed-variable optimization problem, this paper proposes to solve it by memetic algorithms, where the discrete orientation variables are addressed by the distribution evolutionary algorithm based on a population of probability model (DEA-PPM), and the continuous coordination variables are optimized by the conjugate sub-gradient algorithm (CSA). Accordingly, the fixed-outline floorplanning algorithm based on CSA and DEA-PPM (FFA-CD) and the floorplanning algorithm with golden section strategy (FA-GSS) are proposed for the floorplanning problems with and without fixed-outline constraint. %FF-CD is committed to optimizing wirelength targets within a fixed profile. FA-GSS uses the Golden Section strategy to optimize both wirelength and area targets. The CSA is used to solve the proposed non-smooth optimization model, and the DEA-PPM is used to explore the module rotation scheme to enhance the flexibility of the algorithm. Numerical experiments on GSRC test circuits show that the proposed algorithms are superior to some celebrated B*-tree based floorplanning algorithms, and are expected to be applied to large-scale floorplanning problems due to their low time complexity.
Paper Structure (21 sections, 29 equations, 2 tables, 8 algorithms)

This paper contains 21 sections, 29 equations, 2 tables, 8 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Statement
  4. Total Wirelength $W(\bm x,\bm y)$
  5. Sum of Overlapping Area $D(\bm x,\bm y, \bm r)$
  6. Sum of Width beyond the Fixed Outline $B(\bm x,\bm y, \bm r)$
  7. The Conjugate Sub-gradient Algorithm for Optimization of the Coordinate
  8. The Distribution Evolutionary Algorithm for Optimization of the Orientation
  9. The Fixed-outline Floorplanning Algorithm Based on CSA and DEA-PPM
  10. Framework
  11. Evolution of the Distribution Population
  12. The exploitation strategy:
  13. The disturbance strategy:
  14. Optimization of the Floorplan with a Fixed Outline
  15. Initialization of the module orientation
  16. ...and 6 more sections