WO2021169468A1 - 考虑电压转换速率的X结构Steiner树构造方法 - Google Patents

考虑电压转换速率的X结构Steiner树构造方法 Download PDF

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WO2021169468A1
WO2021169468A1 PCT/CN2020/134415 CN2020134415W WO2021169468A1 WO 2021169468 A1 WO2021169468 A1 WO 2021169468A1 CN 2020134415 W CN2020134415 W CN 2020134415W WO 2021169468 A1 WO2021169468 A1 WO 2021169468A1
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steiner tree
particle
obstacle
wiring
steiner
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PCT/CN2020/134415
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French (fr)
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刘耿耿
黄逸飞
郭文忠
陈国龙
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福州大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/39—Circuit design at the physical level
    • G06F30/392—Floor-planning or layout, e.g. partitioning or placement

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  • the invention belongs to the technical field of integrated circuit computer-aided design, and in particular relates to a method for constructing a Steiner tree with an X structure considering the voltage conversion rate.
  • the problem of Steiner tree structure is a basic problem in the physical design of large-scale integrated circuits.
  • the Steiner tree can be used to construct the initial topology of the line network in the wiring phase.
  • the line network bus length, congestion and delay value can be estimated, and it can also be used for the wiring of some important line networks, such as power supply ( VDD) and ground (GND) wiring.
  • VDD power supply
  • GND ground
  • the Steiner tree construction problem is an NP-complete problem, so the optimal solution cannot be constructed in polynomial time.
  • wiring obstacles in the wiring area, such as: pre-wired nets, macro cells, and intellectual property protection modules.
  • the inside of the obstacles is not strictly forbidden to pass through.
  • Reasonable use of the wiring resources inside the obstacles can greatly Shorten the line length and improve the chip performance.
  • the purpose of the present invention is to provide an X-structure Steiner tree construction method considering the voltage slew rate, which is beneficial to optimize the wiring line length while satisfying the voltage slew rate constraint.
  • the technical solution adopted by the present invention is: a Steiner tree construction method of X structure considering voltage slew rate, including the following steps:
  • Pre-processing pre-process and memorize the information between the pin and the obstacle to save time for judging whether the wiring passes through the obstacle and calculating the node voltage conversion rate in the later stage;
  • Hybrid correction Select a better correction strategy through the hybrid correction strategy including the comparison of the barrier adjustment strategy and the overall adjustment strategy, and adjust the part that violates the constraints in the Steiner tree structure, so that the Steiner tree meets the voltage conversion rate constraint, and obtain The final Steiner tree structure.
  • step S1 is as follows: firstly encode the edges of the Steiner tree with pin pairing, and encode each edge of the tree with three digits, and the first two digits represent the two connected pins. Serial number, the third digit indicates the wiring selection between the two pins, and the fitness value is used to evaluate the quality of the entire wiring solution; then the Prim algorithm is used to generate the initial Steiner tree structure to reduce the convergence time of the next stage, and finally the particle swarm population is initialized , And set relevant parameters.
  • the specific method of the step S2 is: pre-processing the information between the pin and the obstacle, and generating two pre-check tables: the obstacle judgment table and the obstacle information record table.
  • the obstacle judgment table records whether the wiring is After the obstacle, the obstacle information record table records information between the wiring that has passed the obstacle and the obstacle that has passed.
  • step S3 PSO is an algorithm based on a population, each particle of the population is a potential solution of the optimization problem, and each particle has a speed and evaluation that determines its own flight direction and distance The fitness value of its own position.
  • the update includes three parts: speed update, individual experience perception, and global experience perception.
  • the particle position update formula is as follows:
  • ⁇ is the inertia weight, which means the probability of the particle performing mutation operation
  • c 1 , c 2 are acceleration factors, which means the probability of the particle performing crossover operation
  • F 1 is the individual experience perception
  • F 2 is the global experience perception
  • V is the speed update
  • the speed update is used to prevent the discrete particle swarm optimization algorithm from falling into local optimal convergence.
  • the specific formula is as follows:
  • r 3 is a random number in the interval (0,1);
  • the line length is used as the fitness value of the discrete particle swarm optimization algorithm. For wiring that passes through obstacles but does not meet the constraints, a certain penalty is applied to reduce the generation of this type of wiring.
  • the penalty function formula is:
  • P(T) represents the penalty function of the Steiner tree
  • (i,j) represents the pin pair
  • T represents a specific Steiner tree
  • k represents the penalty factor
  • X Dis(i,j) represents the pin pair (i ,j) the actual length of the wiring
  • the larger inertial weight w, larger c 1 and smaller c 2 are used in the early stage of the search, and the smaller inertial weight w and smaller c 1 are used in the later stage of the search.
  • the larger c 2 the parameter update formula is:
  • w new , w start , and w end respectively represent the current value, start value, and end value of the inertia weight w
  • C denote the current value of the acceleration factor of 1
  • the eval represents the current iteration
  • evals represents the total number of iterations.
  • step S4 is: consider each pin in the Steiner tree structure as the root node of a local Steiner tree, and consider the adjacent pins of the pin as the leaf nodes of the local Steiner tree, and pass Traverse the root node of the local Steiner tree and the wiring selection combination of different leaf nodes, select the local Steiner tree structure with the shortest global line length, in order to achieve the goal of global optimization by optimizing the local structure of the Steiner tree.
  • step S5 adjusting the part of the Steiner tree structure that violates the constraints through a hybrid correction strategy.
  • the hybrid correction strategy includes an edge-obstacle adjustment strategy and an overall adjustment strategy.
  • the barrier adjustment strategy performs obstacle circumvention processing along the obstacle where it is located, and the overall adjustment strategy selects the corner point closest to the line formed by the two endpoints to be connected from the corner points of the obstacle passed by the wiring as the pseudo Steiner Point connection to bypass the obstacle; set the judgment condition, adopt the adjustment strategy along the obstacle for the wiring that meets the judgment condition, and use the overall adjustment strategy to adjust the wiring that does not meet the judgment condition; the judgment function used for judgment is:
  • 0 represents the adjustment strategy along the barrier
  • 1 represents the overall adjustment strategy
  • len 1 and len 2 are the two set reference values
  • the calculation method is:
  • len 2
  • i is the serial number of the obstacle
  • l i represents the length of the segment within the obstacle i
  • x i1 and y i1 represent the abscissa and ordinate of the upper left corner of the rectangular barrier
  • x i2 and y i2 represent the left and right lower corners of the rectangular barrier.
  • the abscissa and ordinate, set represents the set of all obstacles passed by the wiring
  • set(o i ) represents the set of obstacles passed by the wiring.
  • the present invention has the following beneficial effects: a method for constructing an X-structure Steiner tree considering the constraints of voltage slew rate is proposed.
  • the discrete particle swarm optimization algorithm optimizes the Steiner tree structure.
  • a better Steiner tree structure is obtained under a certain number of iterations, and then through local optimization, the wiring length of the Steiner tree is further reduced, and finally modified by mixing
  • the strategy is to adjust the part of the Steiner tree structure that violates the constraints, so as to effectively meet the voltage slew rate constraint, while optimizing the wiring line length, which has strong practicability and broad application prospects.
  • Fig. 1 is a schematic diagram of a Steiner tree with a three-pin X structure in an embodiment of the present invention.
  • Fig. 2 is a schematic diagram of a resistance-capacitance combination model in an embodiment of the present invention.
  • Fig. 3 is a schematic diagram of an internal tree modeled as a capacitor resistor circuit in an embodiment of the present invention.
  • Fig. 4 is a schematic diagram of a hybrid correction strategy in an embodiment of the present invention.
  • Fig. 5 is a schematic diagram of a mutation operation in an embodiment of the present invention.
  • Fig. 6 is a schematic diagram of the interleaving operation in the embodiment of the present invention.
  • Fig. 7 is a schematic diagram of three-node local Steiner tree optimization in an embodiment of the present invention.
  • Fig. 8 is a flowchart of a method implementation of an embodiment of the present invention.
  • a buffer is placed in front of the drive node of the internal tree, and a buffer is placed after each receiving node, and the interconnection lines and buffers in the wiring are modeled as resistance-capacitance circuits, as shown in Figure 2.
  • Figure 2(a) is the modeling of the capacitance and resistance circuit of the interconnection line
  • Figure 2(b) is the modeling of the capacitance and resistance circuit of the buffer.
  • Figure 3(a) is an internal tree with three nodes
  • Figure 3(b) is to model the internal tree in Figure 3(a) as a capacitor-resistance circuit, and calculate the voltage slew rate of each receiving node point by point.
  • the specific voltage conversion rate calculation formula is as follows:
  • K b is the inherent voltage slew rate of the buffer
  • R b is the voltage slew rate impedance of the buffer
  • c is the unit capacitance
  • D p is the Elmore delay
  • C is the sum of capacitances of subsequent nodes.
  • Pin P 1 is the signal source, other pins are sink points, the pins are not located inside the barriers and the barriers do not overlap.
  • an initial internal tree will be formed in each obstacle. Satisfying the voltage slew rate constraint means that the voltage slew rate of each node that finally forms the internal tree in each obstacle is not higher than the specified valve. value.
  • the X-structure Steiner tree construction method of the present invention takes into account the voltage slew rate constraint and combines the global convergence discrete particle swarm algorithm to minimize the line length, thereby obtaining a high-quality X considering the voltage slew rate constraint. Structure Steiner tree.
  • the X-structure Steiner tree construction method that considers the voltage slew rate proposed by the present invention, as shown in FIG. 8, includes the following steps:
  • Pre-processing pre-process and memorize the information between the pin and the obstacle to save time for judging whether the wiring passes through the obstacle and calculating the node voltage conversion rate in the later stage.
  • the present invention pre-processes the information between the pins and the obstacles, and generates two pre-check tables: the failure judgment table and the obstacle information record table, which are used to guide the subsequent wiring.
  • the obstacle judgment table records whether the wiring has passed an obstacle
  • the obstacle information record table records information between the wiring that has passed the obstacle and the obstacle that has passed.
  • PSO is an algorithm based on a population. Each particle in the population is a potential solution to the optimization problem. Each particle has a speed that determines its own flight direction and distance and an fitness value to evaluate its own position.
  • the particle position update includes three parts: speed update, individual experience perception and global experience perception.
  • the particle position update formula is as follows:
  • ⁇ is the inertia weight, which means the probability of the particle performing mutation operation
  • c 1 , c 2 are acceleration factors, which means the probability of the particle performing crossover operation
  • F 1 is the individual experience perception
  • F 2 is the global experience perception
  • V is the speed update.
  • Speed update is used to effectively prevent the discrete particle swarm optimization algorithm from falling into local optimal convergence.
  • the specific formula is as follows:
  • r 3 is a random number in the interval (0,1).
  • the mutation operation is to randomly select an edge from n-1 edges in the Steiner tree with n nodes to delete, and divide the Steiner tree into two subtrees, and randomly select them from the two subtrees. Two nodes are selected for connection, so that the constituted Steiner tree remains connected and has no ring edges.
  • the use of the union search set to record points avoids selecting two nodes from the same subtree, thereby causing the Steiner tree to be disconnected.
  • the mutation operator greatly improves the global search ability of the particle swarm algorithm.
  • the crossover operation is to divide all edges into two edge sets from two Steiner trees with the same point set but different edge sets.
  • the same edge is divided into the set S 1
  • the remaining edges are divided into the set S 2 .
  • the crossover operation acts on the individual perception and global perception of the particle swarm, which is the process of concretizing the concept of perception of the Steiner tree as a particle in the present invention.
  • the line length is the most important indicator of particle quality, so the line length is used as the fitness value of the discrete particle swarm optimization algorithm.
  • the penalty function formula is:
  • P(T) represents the penalty function of the Steiner tree
  • (i,j) represents the pin pair
  • T represents a specific Steiner tree
  • k represents the penalty factor
  • X Dis(i,j) represents the pin pair (i , The actual length of the wiring of j)
  • X Dis generally refers to the pin pair that violates the constraint in the Steiner tree.
  • the larger inertial weight w, larger c 1 and smaller c 2 are used in the early stage of the search, and the smaller inertial weight w and smaller c 1 are used in the later stage of the search.
  • a larger c 2 not only ensures strong global search ability in the early stage and not easy to converge prematurely, but also ensures faster convergence in the later stage and does not diverge in meaningless searches.
  • the parameter update formula is:
  • w new , w start , and w end respectively represent the current value, start value, and end value of the inertia weight w
  • C denote the current value of the acceleration factor of 1
  • the eval represents the current iteration
  • evals represents the total number of iterations.
  • pin A is the root node of the tree
  • pins B and C are leaf nodes
  • Hybrid correction Select a better correction strategy through the hybrid correction strategy including the comparison of the barrier adjustment strategy and the overall adjustment strategy, and adjust the part that violates the constraints in the Steiner tree structure, so that the Steiner tree meets the voltage conversion rate constraint, and obtain The final Steiner tree structure.
  • the purpose of the correction is to solve the situation that some structures in the Steiner tree may violate constraints, and to further reduce the line length and improve the quality of wiring.
  • the hybrid correction strategy includes an obstacle adjustment strategy and an overall adjustment strategy.
  • the barrier adjustment strategy is used to circumvent obstacles along the obstacles where they are located, and the overall adjustment strategy selects appropriate points from the end points of the barriers that the wiring passes through as pseudo Steiner points to connect and circumvent the barriers.
  • Figure 4(a) shows the wiring between pins p and q.
  • the barrier adjustment strategy is for the segments that violate constraints in the wiring, and the barriers are bypassed along the barriers to obtain the voltage slew rate as shown in Figure 4(b).
  • the constraint is zero and the routing based on the edge barrier adjustment strategy.
  • the overall adjustment strategy selects the corner point closest to the line formed by the two endpoints to be connected from the corner points of the obstacles that each wiring passes through as the pseudo Steiner point to connect the obstacles, and obtain Figure 4 ( c) Wiring based on the overall adjustment strategy under the voltage slew rate constraint shown as 0.
  • the edge barrier adjustment strategy has certain advantages.
  • Figure 4(d) shows the wiring based on the edge barrier adjustment strategy under the larger voltage slew rate constraint.
  • the judgment function used for judgment is:
  • 0 represents the adjustment strategy along the barrier
  • 1 represents the overall adjustment strategy
  • len 1 and len 2 are the two set reference values
  • the calculation method is:
  • len 2
  • i is the number of the barrier
  • l i represents the length of the segment in the barrier i
  • x i1 and y i1 represent the abscissa and ordinate of the upper left corner of the rectangular barrier
  • x i2 and y i2 represent the lower right corner of the rectangular barrier
  • the abscissa and ordinate, set represents the set of all obstacles passed by the wiring
  • set(o i ) represents the set of obstacles passed by the wiring.

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Abstract

一种考虑电压转换速率的X结构Steiner树构造方法，包括以下步骤：生成初始的Steiner树结构（S1）；预先处理及记忆引脚与障碍之间的信息（S2）；采用离散粒子群优化算法优化Steiner树结构，通过包括速度更新、自我感知及群体感知的粒子更新过程，得到优化的Steiner树结构（S3）；对Steiner树结构进行局部优化，使其局部结构达到最优，以进一步缩短布线线长（S4）；通过混合修正策略，对Steiner树结构中违反约束的部分进行调整，使Steiner树满足电压转换速率约束，得到最终的Steiner树结构（S5）。该方法有利于在满足电压转换速率约束的同时，优化布线线长。

Description

考虑电压转换速率的X结构Steiner树构造方法 技术领域
本发明属于集成电路计算机辅助设计技术领域，具体涉及一种考虑电压转换速率的X结构Steiner树构造方法。
背景技术
Steiner树构造问题是大规模集成电路物理设计中的一个基本问题。Steiner树在布线阶段可用于构造线网的初始拓扑，在布图规划和布局阶段，可以估算线网总线长、拥挤度和时延值，也可以用于一些重要线网的布线，如电源(VDD)和地线(GND)布线。
技术问题
Steiner树构造问题是一个NP-完全问题，因此无法在多项式时间内构造出最优解。而且在实际布线中，布线区域内存在大量布线障碍，如：预布线的线网、宏单元、以及知识产权保护模块，障碍内部并不严格禁止布线穿过，合理利用障碍内布线资源，可以大大缩短线长，提高芯片性能。
技术解决方案
本发明的目的在于提供一种考虑电压转换速率的X结构Steiner树构造方法，该方法有利于在满足电压转换速率约束的同时，优化布线线长。
为实现上述目的，本发明采用的技术方案是：一种考虑电压转换速率的X结构Steiner树构造方法，包括以下步骤：
S1)初始化：生成初始的Steiner树结构；
S2)预处理：预先处理及记忆引脚与障碍之间的信息，以为后面阶段中判断布线是否穿过障碍及计算节点电压转换速率节约时间；
S3)PSO搜索：采用离散粒子群优化算法优化Steiner树结构，在设定的迭代次数下，通过包括速度更新、自我感知及群体感知的粒子更新过程，得到优化的Steiner树结构；
S4)局部优化：对优化后的Steiner树结构进行局部优化，使Steiner树的局部结构达到最优，以进一步缩短布线线长，达到全局线长优化；
S5)混合修正：通过包括比较沿障调整策略和总体调整策略的混合修正策略，选择较佳的修正策略，对Steiner树结构中违反约束的部分进行调整，使Steiner树满足电压转换速率约束，得到最终的Steiner树结构。
进一步地，所述步骤S1的具体方法为：首先将Steiner树的边用引脚对方式进行编码， 将树的每条边用三位数进行编码，前两位数表示连接的两个引脚序号，第三位表示两引脚间的布线选择，对于整个布线解用适应值评估质量；然后采用Prim算法生成初始的Steiner树结构，以减小下一阶段的收敛时间，最后初始化粒子群种群，并设置相关参数。
进一步地，所述步骤S2的具体方法为：预先处理引脚与障碍之间的信息，并生成两张预查表：经障判断表与障碍信息记录表，所述经障判断表记录布线是否经过障碍，所述障碍信息记录表记录经过障碍的布线与所经过的障碍之间的信息。
进一步地，所述步骤S3的具体方法为：PSO是基于种群的一种算法，种群的每个粒子都是优化问题的潜在解，每个粒子都有决定自身飞行的方向和距离的速度和评定自身位置优劣的适应值，粒子通过两个最优粒子来更新自己：一个是当前迭代中自身搜索到的个体最优粒子，另一个是当前迭代中种群搜索到的全局最优粒子；粒子位置更新包括三个部分：速度更新、个体经验感知和全局经验感知，所述粒子位置更新公式如下所示：
Figure PCTCN2020134415-appb-000001
其中，
Figure PCTCN2020134415-appb-000002
表示第i个粒子进行第t次位置更新，ω是惯性权重，表示粒子进行变异操作的概率，c 1、c 2是加速因子，表示粒子进行交叉操作的概率，F 1为个体经验感知，F 2为全局经验感知，V为速度更新；
速度更新用于防止离散粒子群优化算法陷入局部最优收敛，具体公式如下所示：
Figure PCTCN2020134415-appb-000003
其中，
Figure PCTCN2020134415-appb-000004
表示第i个粒子进行第t次速度更新，M表示变异操作，r 1为区间(0,1)内的随机数；
个体经验感知是粒子与粒子历史最佳位置进行学习的过程，具体公式如下所示：
Figure PCTCN2020134415-appb-000005
其中，
Figure PCTCN2020134415-appb-000006
表示第i个粒子进行第t次个体感知，C表示交叉操作，r 2为区间(0,1)内的随机数；
全局经验感知是粒子与种群当前最佳位置进行学习的过程，具体公式如下所示：
Figure PCTCN2020134415-appb-000007
其中，r 3为区间(0,1)内的随机数；
将线长作为离散粒子群优化算法的适应值，对于穿过障碍但不满足约束的布线，进行一定惩罚以减少该类型布线产生，惩罚函数公式为：
Figure PCTCN2020134415-appb-000008
其中，P(T)表示Steiner树的惩罚函数，(i,j)表示引脚对，T表示一棵具体的Steiner树，k表示惩罚因子，X Dis(i,j)表示引脚对(i,j)的布线的实际长度；
对于离散粒子群优化算法的参数设定，在搜索前期采用较大的惯性权重w、较大的c 1及较小的c 2而在搜索后期采用较小的惯性权重w、较小的c 1及较大的c 2，参数更新公式为：
Figure PCTCN2020134415-appb-000009
Figure PCTCN2020134415-appb-000010
Figure PCTCN2020134415-appb-000011
其中，w new、w start、w end分别表示惯性权重w的当前值、开始值、结束值，
Figure PCTCN2020134415-appb-000012
Figure PCTCN2020134415-appb-000013
分别表示加速因子c 1的当前值、开始值、结束值以及加速因子c 2的当前值，eval表示当前迭代次数，evals表示总迭代次数。
进一步地，所述步骤S4的具体方法为：将Steiner树结构中每个引脚看做一个局部Steiner树的根节点，将该引脚的相邻引脚看做局部Steiner树的叶子节点，通过遍历局部Steiner树的根节点与不同叶子节点的布线选择组合搭配，选择对于全局线长最短的局部Steiner树结构，以通过使Steiner树的局部结构达到最优实现全局优化目的。
进一步地，所述步骤S5的具体方法为：通过混合修正策略对Steiner树结构中违反约束的部分进行调整，所述混合修正策略包括沿障调整策略与总体调整策略，对于布线中违反约束的片段，所述沿障调整策略沿着所在的障碍进行绕障处理，所述总体调整策略则从布线经过的障碍的角点中选择距离两个待连接端点构成的连线最近的角点作为伪Steiner点进行连接绕障；设定判断条件，对于满足判断条件的布线采用沿障调整策略进行调整，不满足的采用总体调整策略进行调整；用于判断的判断函数为：
Figure PCTCN2020134415-appb-000014
其中0表示沿障调整策略，1表示总体调整策略；len 1和len 2为设定的两个参考值，其计 算方法为：
Figure PCTCN2020134415-appb-000015
len 2＝|max(set(x i1))-min(set(x i2))|+|max(set(y i1))-min(set(y i2))|
其中，i为障碍的序号，l i表示片段在障碍i内的长度，x i1、y i1表示矩形障碍左上角角点的横坐标与纵坐标，x i2、y i2表示矩形障碍左右下角角点的横坐标与纵坐标，set表示布线经过的所有障碍的集合，set(o i)表示布线经过的障碍的集合。
有益效果
相较于现有技术，本发明具有以下有益效果：提出了一种考虑电压转换速率约束的X结构Steiner树构造方法，该方法首先通过预处理，避免了频繁的电压转换速率的计算，再采用离散粒子群优化算法优化Steiner树结构，通过设置惩罚机制，在一定的迭代次数下，得到一个较优的Steiner树结构，然后通过局部优化，使Steiner树的布线长度进一步得到减少，最后通过混合修正策略，对Steiner树结构中违反约束的部分进行调整，从而在有效满足电压转换速率约束的同时，优化了布线线长，具有很强的实用性和广阔的应用前景。
附图说明
图1是本发明实施例中三引脚X结构Steiner树示意图。
图2是本发明实施例中电阻电容组合模型示意图。
图3是本发明实施例中内部树建模为电容电阻电路示意图。
图4是本发明实施例中混合修正策略示意图。
图5是本发明实施例中变异操作示意图。
图6是本发明实施例中交叉操作示意图。
图7是本发明实施例中三节点局部Steiner树优化示意图。
图8是本发明实施例的方法实现流程图。
本发明的实施方式
下面结合附图及具体实施例对本发明作进一步说明。
Steiner树构建模型：
超大规模集成电路物理设计布线阶段中，在Steiner树布线区域中，给定一个布线图G＝(P,O),P i＝{P 1,P 2,...,P n,i＝1,2,...,n}为线网上待连接的一组引脚,，O i＝{O 1,O 2,...,O k,i＝1,2,...,k}为线网上的一组矩形障碍，其中每个引脚P i对应一个二维坐标(x,y)分别表示引脚的横坐标和纵坐标，其中每个障碍O i对应两个二维坐标(x 1,y 1)，(x 2,y 2)分别表示障碍两个对 角端点的横坐标和纵坐标，在不违反电压转换速率条件下，构建一棵连接集合P i中的所有引脚的Steiner最小树。如图1所示为一棵三引脚的Steiner树，其中P＝{1,2,3},O＝{A,B,C}。
电压转换速率计算：
在电压转换速率模型下，在内部树的驱动节点前放置缓冲器，而在每个接收节点后放置缓冲器，并将布线中的互连线及缓冲器建模成电阻电容电路，如图2所示(其中，图2(a)为互连线的电容电阻电路建模，图2(b)为缓冲器的电容电阻电路建模)。图3(a)为一棵带三个节点的内部树，图3(b)为将图3(a)中内部树建模为电容电阻电路，并逐点计算各个接收节点的电压转换速率，具体电压转换速率计算公式如下所示：
Figure PCTCN2020134415-appb-000016
Figure PCTCN2020134415-appb-000017
s step(v i,v j)＝α×D p(v i,v j),α＝ln9
Figure PCTCN2020134415-appb-000018
其中，K b为缓冲器的固有电压转换速率，R b为缓冲器电压转换速率阻抗，c为单位电容，D p为Elmore时延,C表示后继节点的电容和。
Steiner树构造目标：
考虑电压转换速率约束的X结构Steiner最小树构造问题可以描述为：在布线区域上，给定一组引脚P i＝{P 1,P 2,...,P n}以及一组矩形障碍O i＝{O 1,O 2,...,O k}。引脚P 1为信号源，其他引脚为宿点，引脚不位于障碍内部且障碍之间不重叠。
在确定Steiner树的初始拓扑后，每个障碍中会形成初始的内部树，满足电压转换速率约束是指各个障碍中的最终形成内部树的每个节点的电压转换速率都不高于规定的阀值。
在满足约束条件下，线长是Steiner树构造问题下最重要的优化目标。因此，本发明的X结构Steiner树构造方法在考虑电压转换速率约束条件下，结合全局收敛的离散粒子群算法，以最小化线长为目标，从而得到一个高质量的考虑电压转换速率约束的X结构Steiner树。
本发明提出的考虑电压转换速率的X结构Steiner树构造方法，如图8所示，包括以下步骤：
S1)初始化：生成初始的Steiner树结构。
首先将Steiner树的边用引脚对方式进行编码，将树的每条边用三位数进行编码，前两位数表示连接的两个引脚序号，第三位表示两引脚间的布线选择，对于整个布线解用适应值评 估质量；然后采用Prim算法生成初始的Steiner树结构，以减小下一阶段的收敛时间，最后初始化粒子群种群，并设置相关参数。
S2)预处理：预先处理及记忆引脚与障碍之间的信息，以为后面阶段中判断布线是否穿过障碍及计算节点电压转换速率节约时间。
在电压转换速率约束模型下Steiner树的构造需要频繁计算电压转换速率，而电压转换速率的计算与线长紧密相关。因此预先处理并记录下引脚与障碍之间的布线信息，能够对PSO搜寻过程以及之后步骤的执行节约大量判断与计算时间。出于该目的，本发明预先处理引脚与障碍之间的信息，并生成两张预查表：经障判断表与障碍信息记录表，用于指导后面的布线。所述经障判断表记录布线是否经过障碍，所述障碍信息记录表记录经过障碍的布线与所经过的障碍之间的信息。
S3)PSO搜索：采用离散粒子群优化算法优化Steiner树结构，在设定的迭代次数下，通过包括速度更新、自我感知及群体感知的粒子更新过程，得到优化的Steiner树结构。
PSO是基于种群的一种算法，种群的每个粒子都是优化问题的潜在解，每个粒子都有决定自身飞行的方向和距离的速度和评定自身位置优劣的适应值。粒子通过两个最优粒子来更新自己：一个是当前迭代中自身搜索到的个体最优粒子，另一个是当前迭代中种群搜索到的全局最优粒子。粒子位置更新包括三个部分：速度更新、个体经验感知和全局经验感知，所述粒子位置更新公式如下所示：
Figure PCTCN2020134415-appb-000019
其中，
Figure PCTCN2020134415-appb-000020
表示第i个粒子进行第t次位置更新，ω是惯性权重，表示粒子进行变异操作的概率，c 1、c 2是加速因子，表示粒子进行交叉操作的概率，F 1为个体经验感知，F 2为全局经验感知，V为速度更新。
速度更新用于有效防止离散粒子群优化算法陷入局部最优收敛，具体公式如下所示：
Figure PCTCN2020134415-appb-000021
其中，
Figure PCTCN2020134415-appb-000022
表示第i个粒子进行第t次速度更新，M表示变异操作，r 1为区间(0,1)内的随机数。
个体经验感知是粒子与粒子历史最佳位置进行学习的过程，具体公式如下所示：
Figure PCTCN2020134415-appb-000023
其中，
Figure PCTCN2020134415-appb-000024
表示第i个粒子进行第t次个体感知，C表示交叉操作，r 2为区间(0,1)内的随机数。
全局经验感知是粒子与种群当前最佳位置进行学习的过程，具体公式如下所示：
Figure PCTCN2020134415-appb-000025
其中，r 3为区间(0,1)内的随机数。
变异操作：
如图5所示，变异操作是在n个节点的Steiner树中，随机从n-1条边中选择一条边删除，将Steiner树分割为两颗子树，并分别随机从两颗子树中选择出两个节点进行连接，使得构成Steiner树保持连接且无环边。本发明中运用并查集来记录点的情况，避免从同一颗子树选择出两个节点，从而导致Steiner树不连接的情况发生。变异算子大大提高了粒子群算法的全局搜索能力。
交叉操作：
如图6所示，交叉操作是从两棵点集相同但边集不同的Steiner树中，将所有的边划分成两个边集。在两棵树中，存在相同的边划分进集合S 1，其余的边划分进集合S 2。以集合S 1中的边作为新树的基本架构，再随机从集合S 2中选择合适的边，构成新的连接且无环边Steiner树，并用并查集记录点的连接情况。交叉操作作用于粒子群的个体感知及全局感知部分，是本发明中对Steiner树作为粒子在感知这一概念具体化的过程。
为了评估粒子的质量，线长作为粒子质量最重要的指标，因此将线长作为离散粒子群优化算法的适应值。对于穿过障碍但不满足约束的布线，因为需要花费更大的布线代价进行修复，所以对该类型布线进行一定惩罚以减少该类型布线产生，惩罚函数公式为：
Figure PCTCN2020134415-appb-000026
其中，P(T)表示Steiner树的惩罚函数，(i,j)表示引脚对，T表示一棵具体的Steiner树，k表示惩罚因子，X Dis(i,j)表示引脚对(i,j)的布线的实际长度，X Dis泛指中Steiner树存在违反约束的引脚对。
对于离散粒子群优化算法的参数设定，在搜索前期采用较大的惯性权重w、较大的c 1及较小的c 2而在搜索后期采用较小的惯性权重w、较小的c 1及较大的c 2，既保证在前期有较强的全局搜索能力，不易过早的收敛，又保证了在后期能够较快的收敛，不发散于无意义的搜索中，参数更新公式为：
Figure PCTCN2020134415-appb-000027
Figure PCTCN2020134415-appb-000028
Figure PCTCN2020134415-appb-000029
其中，w new、w start、w end分别表示惯性权重w的当前值、开始值、结束值，
Figure PCTCN2020134415-appb-000030
Figure PCTCN2020134415-appb-000031
分别表示加速因子c 1的当前值、开始值、结束值以及加速因子c 2的当前值，eval表示当前迭代次数，evals表示总迭代次数。
S4)局部优化：对优化后的Steiner树结构进行局部优化，使Steiner树的局部结构达到最优，以进一步缩短布线线长，达到全局线长优化。
将Steiner树结构中每个引脚看做一个局部Steiner树的根节点，将该引脚的相邻引脚看做局部Steiner树的叶子节点，通过遍历局部Steiner树的根节点与不同叶子节点的布线选择组合搭配，选择对于全局线长最短的局部Steiner树结构，以通过使Steiner树的局部结构达到最优实现全局优化目的。
如图7所示，引脚数为3的局部Steiner树中，引脚A为树的根节点，引脚B、C为叶节点，局部Steiner树中存在共4 3-1种潜在结构，可以发现图7(i)中，局部Steiner树的结构的线长达到了最短，故选择该结构作为优化的布线结构。
S5)混合修正：通过包括比较沿障调整策略和总体调整策略的混合修正策略，选择较佳的修正策略，对Steiner树结构中违反约束的部分进行调整，使Steiner树满足电压转换速率约束，得到最终的Steiner树结构。
修正的目的是为了解决Steiner树中可能存在部分结构违反约束的情况，并进一步减少线长，提高布线的质量。
对于Steiner树中违反约束的片段，本发明提出一种混合修正策略来进行调整。所述混合修正策略包括沿障调整策略与总体调整策略。对于布线中违反约束的片段，所述沿障调整策略沿着所在的障碍进行绕障处理，所述总体调整策略则从布线经过的障碍的端点中选择合适的点作为伪Steiner点进行连接绕障。图4(a)表示引脚p、q间的布线，沿障调整策略对于布线中存在违反约束的片段，沿着所在的障碍进行绕障处理，得到如图4(b)所示电压转换速率约束为0下基于沿障调整策略的布线。在该策略中需要判断接收节点与驱动节点所处的障碍边，以及节点间沿障碍的最短路径。但该策略在多片段布线中，存在由于布线经过障碍的数量与位置，而引起过多不必要绕障，从而导致线长代价的浪费。针对这种情况，所述总体调 整策略从每个布线经过的障碍的角点中选择距离两个待连接端点构成的连线最近的角点作为伪Steiner点进行连接绕障，得到如图4(c)所示电压转换速率约束为0下基于总体调整策略的布线。在电压转换速率约束阈值较大时，沿障调整策略有一定优势，如图4(d)所示为电压转换速率约束较大下基于沿障调整策略的布线。
设定判断条件，对于满足判断条件的布线采用沿障调整策略进行调整，不满足的采用总体调整策略进行调整。用于判断的判断函数为：
Figure PCTCN2020134415-appb-000032
其中0表示沿障调整策略，1表示总体调整策略；len 1和len 2为设定的两个参考值，其计算方法为：
Figure PCTCN2020134415-appb-000033
len 2＝|max(set(x i1))-min(set(x i2))|+|max(set(y i1))-min(set(y i2))|
其中，i为障碍的序号，l i表示片段在障碍i内的长度，x i1、y i1表示矩形障碍左上角角点的横坐标与纵坐标，x i2、y i2表示矩形障碍右下角角点的横坐标与纵坐标，set表示布线经过的所有障碍的集合，set(o i)表示布线经过的障碍的集合。
以上是本发明的较佳实施例，凡依本发明技术方案所作的改变，所产生的功能作用未超出本发明技术方案的范围时，均属于本发明的保护范围。

Claims (6)

  1. 一种考虑电压转换速率的X结构Steiner树构造方法，其特征在于，包括以下步骤：
    S1)初始化：生成初始的Steiner树结构；
    S2)预处理：预先处理及记忆引脚与障碍之间的信息，以为后面阶段中判断布线是否穿过障碍及计算节点电压转换速率节约时间；
    S3)PSO搜索：采用离散粒子群优化算法优化Steiner树结构，在设定的迭代次数下，通过包括速度更新、自我感知及群体感知的粒子更新过程，得到优化的Steiner树结构；
    S4)局部优化：对优化后的Steiner树结构进行局部优化，使Steiner树的局部结构达到最优，以进一步缩短布线线长，达到全局线长优化；
    S5)混合修正：通过包括比较沿障调整策略和总体调整策略的混合修正策略，选择较佳的修正策略，对Steiner树结构中违反约束的部分进行调整，使Steiner树满足电压转换速率约束，得到最终的Steiner树结构。
  2. 根据权利要求1所述的考虑电压转换速率的X结构Steiner树构造方法，其特征在于，所述步骤S1的具体方法为：首先将Steiner树的边用引脚对方式进行编码，将树的每条边用三位数进行编码，前两位数表示连接的两个引脚序号，第三位表示两引脚间的布线选择，对于整个布线解用适应值评估质量；然后采用Prim算法生成初始的Steiner树结构，以减小下一阶段的收敛时间，最后初始化粒子群种群，并设置相关参数。
  3. 根据权利要求1所述的考虑电压转换速率的X结构Steiner树构造方法，其特征在于，所述步骤S2的具体方法为：预先处理引脚与障碍之间的信息，并生成两张预查表：经障判断表与障碍信息记录表，所述经障判断表记录布线是否经过障碍，所述障碍信息记录表记录经过障碍的布线与所经过的障碍之间的信息。
  4. 根据权利要求1所述的考虑电压转换速率的X结构Steiner树构造方法，其特征在于，所述步骤S3的具体方法为：PSO是基于种群的一种算法，种群的每个粒子都是优化问题的潜在解，每个粒子都有决定自身飞行的方向和距离的速度和评定自身位置优劣的适应值，粒子通过两个最优粒子来更新自己：一个是当前迭代中自身搜索到的个体最优粒子，另一个是当前迭代中种群搜索到的全局最优粒 子；粒子位置更新包括三个部分：速度更新、个体经验感知和全局经验感知，所述粒子位置更新公式如下所示：
    Figure PCTCN2020134415-appb-100001
    其中，
    Figure PCTCN2020134415-appb-100002
    表示第i个粒子进行第t次位置更新，ω是惯性权重，表示粒子进行变异操作的概率，c 1、c 2是加速因子，表示粒子进行交叉操作的概率，F 1为个体经验感知，F 2为全局经验感知，V为速度更新；
    速度更新用于防止离散粒子群优化算法陷入局部最优收敛，具体公式如下所示：
    Figure PCTCN2020134415-appb-100003
    其中，
    Figure PCTCN2020134415-appb-100004
    表示第i个粒子进行第t次速度更新，M表示变异操作，r 1为区间(0,1)内的随机数；
    个体经验感知是粒子与粒子历史最佳位置进行学习的过程，具体公式如下所示：
    Figure PCTCN2020134415-appb-100005
    其中，
    Figure PCTCN2020134415-appb-100006
    表示第i个粒子进行第t次进行个体感知，C表示交叉操作，r2为区间(0,1)内的随机数；
    全局经验感知是粒子与种群当前最佳位置进行学习的过程，具体公式如下所示：
    Figure PCTCN2020134415-appb-100007
    其中，r3为区间(0,1)内的随机数；
    将线长作为离散粒子群优化算法的适应值，对于穿过障碍但不满足约束的布线，进行一定惩罚以减少该类型布线产生，惩罚函数公式为：
    Figure PCTCN2020134415-appb-100008
    其中，P(T)表示Steiner树的惩罚函数，(i,j)表示引脚对，T表示一棵具体的Steiner树，k表示惩罚因子，X Dis(i,j)表示引脚对(i,j)布线的实际长度；
    对于离散粒子群优化算法的参数设定，在搜索前期采用较大的惯性权重w、较大的c1及较小的c2而在搜索后期采用较小的惯性权重w、较小的c1及较大的c2，参数更新公式为：
    Figure PCTCN2020134415-appb-100009
    Figure PCTCN2020134415-appb-100010
    Figure PCTCN2020134415-appb-100011
    其中，w new、w start、w end分别表示惯性权重w的当前值、开始值、结束值，
    Figure PCTCN2020134415-appb-100012
    分别表示加速因子c1的当前值、开始值、结束值以及加速因子c2的当前值，eval表示当前迭代次数，evals表示总迭代次数。
  5. 根据权利要求1所述的考虑电压转换速率的X结构Steiner树构造方法，其特征在于，所述步骤S4的具体方法为：将Steiner树结构中每个引脚看做一个局部Steiner树的根节点，将该引脚的相邻引脚看做局部Steiner树的叶子节点，通过遍历局部Steiner树的根节点与不同叶子节点的布线选择组合搭配，选择对于全局线长最短的局部Steiner树结构，以通过使Steiner树的局部结构达到最优实现全局优化目的。
  6. 根据权利要求1所述的考虑电压转换速率的X结构Steiner树构造方法，其特征在于，所述步骤S5的具体方法为：通过混合修正策略对Steiner树结构中违反约束的部分进行调整，所述混合修正策略包括沿障调整策略与总体调整策略，对于布线中违反约束的片段，所述沿障调整策略沿着所在的障碍进行绕障处理，所述总体调整策略则从布线经过的障碍的角点中选择距离两个待连接端点构成的连线最近的角点作为伪Steiner点进行连接绕障；设定判断条件，对于满足判断条件的布线采用沿障调整策略进行调整，不满足的采用总体调整策略进行调整；用于判断的判断函数为：
    Figure PCTCN2020134415-appb-100013
    其中0表示沿障调整策略，1表示总体调整策略；len1和len2为设定的两个参考值，其计算方法为：
    Figure PCTCN2020134415-appb-100014
    len 2＝|max(set(x i1))-min(set(x i2))|
    +|max(set(y i1))-min(set(y i2))|
    其中，i为障碍的序号，li表示片段在障碍i内的长度，xi1、yi1表示矩形障碍左上角角点的横坐标与纵坐标，xi2、yi2表示矩形障碍右下角角点的横坐标与纵坐标，set表示布线经过的所有障碍的集合，set(oi)表示布线经过的障碍的集合。
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