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摘要: 布线是芯片设计自动化流程中至关重要也是特别耗时的一环, 直接影响最终产品的面积、成本、功耗、速度和可靠性, 研究智能布线算法对提高芯片布线效率和优化芯片布线效果具有重要意义. 芯片布线问题是一个多目标、多约束的NP困难问题. 即使已有几十年的研究历史, 目前仍存在大量未突破的问题和空间. 随着制造工艺的不断发展, 布线规则、约束和目标也持续调整和增加, 使得布线选择极其困难. 本文旨在对芯片设计自动化中自动布线的前沿研究进行全面归纳与分析, 以帮助科研人员全面了解该领域的研究进展和方向, 助力智能布线算法的研究和发展. 具体而言, 本文首先阐述芯片布线的问题背景, 然后分别介绍全局布线和详细布线的任务定义和目标、过程特点、难点和挑战、评估方法; 接着详述和分析各布线方法, 重点论述基于规划搜索的布线方法和基于机器学习的布线方法的最新研究成果、优缺点及其应用环节; 然后介绍公开数据集和开源布线工具; 最后总结现有方法在实际应用中存在的局限性, 并对自动布线未来的发展趋势和潜在研究方向进行展望.Abstract: Routing is a crucial and particularly time-consuming part of the chip design automation process, directly affecting the area, cost, power consumption, speed and reliability of the final product. It is of great significance to study intelligent routing algorithms to improve the efficiency and effectiveness of chip routing. The chip routing problem is a NP-hard problem with multiple objectives and constraints. Even with decades of research history, there are still a large number of problems and spaces for breakthrough. As manufacturing techniques evolve, design rules, constraints and objectives are continuously adjusted and added, which make wiring selection extremely difficult. This survey aims to provide a comprehensive overview and analysis of the cutting-edge research on automated routing in the chip design automation, in order to help researchers fully understand the research progresses and directions in this field, and to accelerate the research and development of intelligent routing algorithms. Specifically, this paper first describes the background of chip routing, then introduces the definitions and objectives, process characteristics, difficulties and challenges, and evaluation methods of global and detailed routing respectively, followed by a detailed description and analysis of various routing methods, focusing on the latest research results, advantages and disadvantages of planning and search-based routing methods and machine learning-based routing approaches and their application aspects, then introduces public data sets and open-source routing tools, and finally summarizes the limitations of existing methods in practical applications and provides an outlook on future trends and potential research directions for automated routing.
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Key words:
- Machine learning /
- AI planning /
- reinforcement learning /
- chip /
- routing /
- global routing /
- detailed routing
1)1 1 LEF/DEF Language Reference version 5.7,https://www.ispd.cc/contests/18/lefdefref.pdf 2)2 2 Guelph FPGA CAD Group,http://fpga.socs.uoguelph.ca/ 3)3 3 TritonRoute, UCSD Detailed Router,https://github.com/The-OpenROAD-Project/TritonRoute 4 CUGR, VLSI Global Routing Tool Developed by CUHK,https://github.com/cuhk-eda/cu-gr 5 Dr.CU, VLSI Detailed Routing Tool Developed by CUHK,https://github.com/cuhk-eda/dr-cu 6 EDA-AI,https://github.com/Thinklab-SJTU/EDA-AI 7 Verilog to Routing, Open Source CAD Flow for FPGA Research,https://github.com/verilog-to-routing/vtr-verilog-to-routing -
图 9 三维转二维全局布线流程: 投影-布线-层分配
Fig. 9 3D to 2D global routing process: projection - routing - layer assignment
表 1 智能布线方法的特点和应用阶段
Table 1 Characteristics and application phases of intelligent routing approaches
类型 布线方法 方法过程和特点 布线阶段 规划搜索类 迷宫布线 从一个引脚点出发, 采用广度优先搜索技术, 找出存在障碍的网格中另一引脚点的曼哈顿最短路径, 然后以已经连接好的路径为起点, 用同样的方法寻找下一个引脚点, 直到连接完线网的所有引脚. GR/DR 线搜索布线 首先将源和目标设置为基点, 向四个方向(两个水平和两个垂直)执行深度优先搜索, 一直延伸到芯片边界或障碍物, 生成0级线段. 然后, 将这些第$ i $级线段的每个网格点设置为新的基点, 生成第$ i+1 $级的垂直线段. 这个过程不断重复, 直到从源生成的线段与从目标生成的线段相交, 通过交叉点跟踪到源和目标来找到它们的连接路径. GR/DR 通道布线 在一个包含水平和垂直多条布线轨道的横向布线区域, 线网引脚分布在顶端和底部, 布线时构建水平约束图和垂直有向约束图, 利用贪婪算法和遗传算法等方法将不同线网的横边分配到合适的轨道上, 以减少轨道占用, 压缩通道宽度. DR A*搜索布线算法 一般以连线长度、通孔成本和违例成本为权重的曼哈顿距离作为启发式函数, 利用A*算法连接存在障碍的网格中的两个引脚点. 然后以已经连接好的路径为起点, 选择离已连线引脚的中心最近的引脚作为下一个目标点, 直到连接完线网的所有引脚. GR/DR 模式布线 对每一个双引脚线网, 只考虑L, Z, U, T, E等几种形状的连接方式, 能快速找到最短连接方案, 可用于全局布线或者详细布线的首次迭代. GR/DR 整数线性规划布线 网表中每个线网通过L型或Z型找出多个可选路径方案, 并按照成本给每个方案一个权重, 在满足每个线网只选择一个方案, 且所有线网的路径方案所使用的边不超过其容量前提下, 最小化所有方案的成本和. GR 拥塞协商 多线网布线时以协商的方式确定各线网间互联资源的分配, 迭代地进行拆线重布, 初始时所有线网都用最小代价完成布线, 逐渐加大对多个线网重复使用的互连资源或者设计规则违例区域的惩罚力度, 经过多次迭代后, 基于拥塞协商的布线能快速地分散拥塞, 避免冲突和溢出. GR/DR 多级布线 用动态规划的思想将芯片逐级划分到更小区域, 直到能够被算法处理为止, 部分线网因而被切割成多段, 待下级区域内布线完成后再向上串连各段线网, 最终输出完整的布线方案. GR/DR 查表布线 对于少于一定数量(如10个)引脚的线网, 先预先构建并存储好直线斯坦纳最小树的所有可能连接方案, 在实际布线时通过查表的方式快速确认方案的可行性; 对于大线网则通过线网拆分技术将其拆成多个小线网, 单独查表布线后再汇总连接. GR 并行布线 将布线区域进行切割或者将非重叠线网划分到不同的分组, 通过布线任务调度和多线程并行布线实现加速, 提高布线效率. GR/DR 机器学习类 拥塞与违例预测 利用卷积神经网络等深度学习框架, 基于芯片布局和引脚密度等信息生成拥塞热图, 或者基于全局布线产生的拥塞报告, 预测给定设计的详细布线所产生的设计规则违例位置, 指导布线路径优化. GR/DR 布线路径生成 利用收集的布线方案进行对抗学习, 通过生成模型生成线网的全局布线方案, 并根据预估线长和拥塞结果指导宏布局和线网排序. GR 强化学习布线 基于强化学习算法框架, 训练布线智能体完成线网排序、路径选择、违例修复等任务. GR/DR 多智能体布线 将芯片布线转化为多智能体路径规划任务, 基于多智能体深度强化学习框架训练多智能体并行布线, 利用智能体之间的异步通信来避免布线冲突. GR/DR 
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表 2 VLSI详细布线方法
Table 2 Detailed routing approaches for VLSI
布线任务 文献(年份) 方法特点 数据集 引脚连接点分析 Nieberg [69] (2011) 选择从引脚到网格点不违反设计规则的最短路径. Foundry Xu等[70] (2016) 基于引脚访问点数量来动态评估引脚可达性. OpenSparc T1 * Kahng等[72] (2020) 设计规则感知的基于动态规划的引脚连接点分析框架. ISPD18[19] 轨道分配 Zhang等[75] (2012) 基于最大加权独立集问题启发式求解的轨道分配算法. ISPD98[76]&ISPD05[77]&ISPD06[78] Wong等[79] (2016) 基于协商的轨道分配算法. DAC12[80] Liu等[81] (2019) 可布线性驱动的轨道分配算法. DAC12[80] Guo等[82] (2019) 基于离散粒子群优化、遗传操作和基于协商的精炼策略的轨道分配算法. DAC12[80] 基于网格的并行布线 Jia等[83] (2017) 基于多商品流方法的并行布线算法. Foundry&ISPD05[77]&ISPD14[85] Kahng等[86] (2018) 通过混合整数线性规划逐层进行并行布线. ISPD18[19] 基于网格的顺序布线 Sun等[87] (2018) 考虑全局指导的基于协商的并行布线方法. ISPD18[19] Kahng等[89] (2021) 基于队列的拆线重布算法以减少违例, 用全新的设计规则分析引擎准确计算路径成本. ISPD18[19]&ISPD19[20] Chen等[90] (2019) 分层并行迷宫布线方法实现总线布线. ICCAD18 ** Li等[92] (2019) 边构造边修正的路径优化并行搜索方法降低设计规则违例的数量. ISPD18[19]&ISPD19[20] Zhuang等[93] (2022) 设计规则驱动的轨道分配和违例优化方法. ISPD19[20] 无网格布线 Cong等[94] (2005) 基于多级布线框架的无网格布线器. Foundry Li等[95] (2007) 结合瓦片展开和隐式连接图的多层无网格布线器. Foundry 光刻工艺友好的布线 Du等[96] (2013) 基于符合SID (Spacer-Is-Dielectric)型自对准双重成像设计约束的图模型的拥塞协商详细布线. Foundry Ding等[97] (2015) 基于符合SIM (Spacer-Is-Metal)型自对准双重成像和自对准四重成像设计约束的图模型的拥塞协商详细布线. Generated Ou等[98] (2017) 基于DSA (Directed Self Assembly)光刻工艺友好的图模型的详细布线. OpenSparc T1 * Yu等[99] (2018) 考虑DSA光刻工艺的基于冲突和兼容性图模型的详细布线. Foundry * OpenSPARC T1, http://www.oracle.com/technetwork/systems/opensparc/index.html
** ICCAD 2018 Contest Problem B: Obstacle-Aware On-Track Bus Routing,http://iccad-contest.org/2018/problems.html
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表 3 基于元件布局优化的布线方法
Table 3 Routing approaches for placement optimization
任务类型 算法框架 文献(年份) 芯片类型 数据集 可布线性预测 SVN Chan等[124] (2017) VLSI Foundry NN Tabrizi等[125−126] (2019, 2018) VLSI ISPD15[127] CNN Yu等[128] (2019) VLSI Generated CNN Liang等[129] (2020) VLSI Foundry CNN Xie等[130]、Huang等[131] (2019) VLSI ISPD15[127] CNN Chen等[132] (2022) VLSI Foundry&DAC12[80] CNN Alhyari等[133−134] (2021, 2019) FPGA ISPD16[113]&Xilinx cGAN Alawieh等[135] (2020)、Yu等[136] (2019) FPGA ISPD16[113] LHNN Wang等[137] (2022) VLSI ISPD11[138]&DAC12[80] 布局规划优化 RL+GCN Mirhoseini等[139] (2021) VLSI Foundry&Ariane[140] 布局布线融合 RL+GNN+CNN Cheng等[141−142] (2021, 2022) VLSI ISPD05[77]
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表 5 基于详细布线优化的布线方法
Table 5 Routing approaches for detailed routing optimization
任务类型 算法框架 文献(年份) 芯片类型 数据集 违例预测与修复 RL Gandhi等[14] (2019) VLSI Generated RL Ren等[149] (2021) VLSI Foundry Random-Forest Siddiqi等[150] (2022) FPGA VTR7[151] 线网排序 RL Lin等[152] (2022), Qu等[153] (2021) VLSI ISPD18[19]&ISPD19[20] 走线选择 MCTS+RL He等[15] (2022) VLSI Generated RL Liao等[154] (2020) VLSI Foundry RL Chen等[155] (2023) VLSI Foundry 异步并行布线 MARL Ju等[156] (2021) VLSI Generated
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表 6 芯片布线常用公开数据集
Table 6 Public datasets commonly used for chip routing
类型 数据集 测试用例 方法过程和特点 方法特点 全局布线 ISPD-2007[17] 16个 8个单层和8个6~8层测试用例, 多层用例线网数量从176 715个到548 073个不等. 溢出数、总线长 ISPD-2008[18] 16个 在ISPD-2007多层用例基础上再增加8个6~8层测试用例, 线网数量从176 715个到1 647 410个不等. 溢出数、总线长、运行时长 ICCAD-2019[61] 12个 从ISPD-2018和ISPD-2019数据集中选取了6个32 nm的测试用例, 通过限制用例层数为5层, 形成额外的6个用例. 将全局布线输出的布线指导导入Dr.CU[91]并评估详细布线后的设计规则违例数、通孔数、总线长、运行时长 ICCAD-2020[67] 12个 3~16层, GCell数量最大为277×277, 线网数量从6个到332 080个不等. 零溢出、零开路、最大单元移动限制、1小时运行时长限制 ICCAD-2021[68] 10个 3~16层, GCell数量最大为277×277, 线网数量从6个到332 063个不等. 零溢出、零开路、电压区域限制、最大单元移动限制、1小时运行时长限制 详细布线 ISPD-2018[19] 10个 45 nm到32 nm, 9层, 线网数量从3 153个到182 000个. 设计规则违例数、通孔数、总线长、运行时长 ISPD-2019[20] 10个 65 nm到32 nm, 5~9层, 线网数量从3 153个到895 253个. 设计规则违例数、通孔数、总线长、运行时长 FPGA布线 VPR[151] 19个 来源于多款应用芯片, 六输入查找表数量从174到107 784. 总线长、关键路径延时 Titan[157] 23个 来源于多款应用芯片, 六输入查找表数量从24 759到805 063, 原语数量从90 778到1 859 485. 总线长、关键路径延时
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表 7 芯片智能布线方法的对比分析
Table 7 Comparison and analysis of intelligent routing approaches
线网数量 方法类型 布线方法 布线阶段 布线效率 布线质量 CPU/GPU要求 内存要求 布线规模 数据要求 单线网 规划搜索类 迷宫布线 GR/DR ○ ● ○ ○ ◑ ● 线搜索布线 GR/DR ◑ ● ◑ ◑ ◑ ● A*搜索布线算法 GR/DR ● ● ◑ ◑ ● ● 模式布线 GR/DR ● ◑ ● ● ● ● 查表布线 GR ● ● ● ● ● ● 机器学习类 布线路径生成 GR ● ○ ○ ● ○ ○ 强化学习布线 GR/DR ○ ◑ ○ ◑ ○ ◑ 多线网 规划搜索类 贪心通道布线 DR ● ◑ ● ● ○ ● 整数线性规划布线 GR ○ ● ○ ○ ◑ ● 拥塞协商 GR/DR ● ● ◑ ◑ ● ● 多级布线 GR/DR ◑ ● ○ ○ ● ● 并行布线 GR/DR ● ◑ ○ ○ ● ● 机器学习类 拥塞与违例预测 GR/DR ● ● ○ ● ◑ ○ 多智能体布线 GR/DR ◑ ◑ ○ ○ ○ ◑
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