WO2021253744A1 - 基于离散粒子群优化的轨道规划方法 - Google Patents

基于离散粒子群优化的轨道规划方法 Download PDF

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WO2021253744A1
WO2021253744A1 PCT/CN2020/134412 CN2020134412W WO2021253744A1 WO 2021253744 A1 WO2021253744 A1 WO 2021253744A1 CN 2020134412 W CN2020134412 W CN 2020134412W WO 2021253744 A1 WO2021253744 A1 WO 2021253744A1
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particles
swarm optimization
particle swarm
track
discrete particle
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French (fr)
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刘耿耿
陈晓华
兰翔钧
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
    • G06F30/394—Routing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]

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  • the invention relates to the field of ultra-large-scale integrated circuit design, in particular to an orbit planning method based on discrete particle swarm optimization.
  • the wiring problem is generally composed of two stages: overall wiring and detailed wiring.
  • the overall wiring stage divides the wiring area into a set of global cells, and determines which cells each wire net needs to be placed in.
  • the detailed wiring stage uses the information obtained from the overall wiring to refine the wiring to realize the wire net.
  • the connection between the pin and the line segment Because the overall wiring often ignores a lot of specific information, such as pin connections, local network connections, etc., there is a large degree of mismatch between the overall wiring and the detailed wiring, and the result is very poor routing. Wiring scheme. Therefore, the stage of track planning is added between the overall wiring and the detailed wiring, and the wiring problem is divided into three stages.
  • the track planning stage stipulates that one line segment overlaps another line segment or the line segment and obstacles are blocked are regarded as violations.
  • the work of track planning is to plan each segment to be routed on a corresponding track, thereby reducing the number of violations, that is, reducing the occurrence of overlapping and blocking phenomena, and then generating a track planning plan, and passing this plan information to the detailed At the wiring stage, improve the wiringability of integrated circuit design.
  • the current research methods for trajectory planning are either easy to miss some line segments or fall into local extremes.
  • the particle swarm optimization technology is a search technology based on swarm intelligence, which is easy to implement, has fewer parameters, and has stronger global optimization capabilities.
  • the purpose of the present invention is to provide a trajectory planning method based on discrete particle swarm optimization, which effectively solves the problem of mismatch between overall wiring and detailed wiring.
  • An orbit planning method based on discrete particle swarm optimization including the following steps:
  • Step S1 Extract line segments from the global network and local network at the same time according to the results obtained from the overall wiring, and create a track;
  • Step S2 According to the obtained trajectory, consider the line length cost, overlap cost and obstacle cost, and use the improved discrete particle swarm optimization algorithm to find the preliminary trajectory planning plan;
  • Step S3 Use the wire removal-rewind technology to further optimize the preliminary track planning scheme to obtain the optimal track planning scheme.
  • step S1 is specifically:
  • Two Steiner trees are constructed for each local network, which are a single vertical main Steiner tree and a single horizontal main Steiner tree;
  • panel is a collection of all G-cells in a row or column of a wiring layer
  • G-cell is the overall wiring stage, which divides the wiring area into a group of sub-wiring areas.
  • step S2 is specifically:
  • each bit of the particle code represents the orbit number of the corresponding line segment, that is, the code of the i-th bit of the particle is j, which represents the The line segment i on the panel is allocated on track j;
  • ⁇ is the inertia weight, which determines the probability of mutation
  • c 1 and c 2 are acceleration factors, which determine the probability of particle crossover
  • N 1 is the self-mutation operation
  • N 2 and N 3 are crossover operations
  • the preliminary trajectory planning scheme is obtained.
  • ⁇ represents the probability of mutation
  • rand() is a random number between [0,1]
  • c 1 represents the probability of crossing with its own optimal particle
  • c 2 represents the probability of crossing with excellent particles in the population.
  • the improved discrete particle swarm optimization algorithm adopts a new social learning method, an oscillation parameter strategy and an adaptive inertia weight.
  • the new social learning method is specifically as follows: in the social learning stage, each particle learns from a particle with a better fitness value than its own particle according to the size of the fitness value.
  • the oscillating parameter strategy is specifically: dividing the maximum number of iterations max_iter into an iterative process with each stage being SI times, so that the global exploration and local search alternately change mod (max_iter, SI) times during the entire iterative process.
  • mod (max_iter, SI) mod (max_iter, SI) times during the entire iterative process.
  • ⁇ init and ⁇ end are the initial value and the end value of the inertia weight ⁇ respectively
  • c init and c end are the initial value and the end value of the acceleration factor c respectively (ie, both c 1 and c 2 use formula (8))
  • t is the current number of iterations
  • SI is the maximum number of iterations in each stage.
  • the adaptive inertia weight is specifically: calculating the average fitness value of the current population, and dividing all particles into two levels according to the size of the fitness value of each particle, and selecting different inertia factor formulas according to the levels.
  • the steps for adjusting the inertia factor of particles in the sub-evolution iteration process are as follows:
  • the present invention has the following beneficial effects:
  • the invention reduces line length cost, overlap cost and obstacle cost, and effectively solves the problem of mismatch between overall wiring and detailed wiring.
  • Fig. 1 is a schematic diagram of particle encoding in an embodiment of the present invention
  • Figure 2 is a pseudo code of a mutation operation in an embodiment of the present invention
  • Figure 3 is a pseudo code of the interleaving operation in an embodiment of the present invention.
  • Figure 4 is a schematic diagram of a mutation operation in an embodiment of the present invention.
  • Fig. 5 is a schematic diagram of the interleaving operation in an embodiment of the present invention.
  • the present invention provides a trajectory planning method based on discrete particle swarm optimization, which includes the following steps:
  • Step S1 Extract line segments from the global network and local network at the same time according to the results obtained from the overall wiring, and create a track;
  • each local network is constructed with two Steiner trees, which are a single vertical main Steiner tree and a single horizontal main Steiner tree;
  • the track directions of all panels on each layer are the same, and the track directions of adjacent layers are inconsistent; that is, the track direction of the odd-numbered layer is horizontal, and the track direction of the even-numbered layer is the vertical direction;
  • panel is a collection of all G-cells in a row or column of a wiring layer
  • G-cell is the overall wiring stage, which divides the wiring area into a group of sub-wiring areas.
  • Step S2 According to the obtained trajectory, consider the line length cost, overlap cost and obstacle cost, and use the improved discrete particle swarm optimization algorithm to find the preliminary trajectory planning plan;
  • the line length cost is the sum of the line lengths used to connect each component in each line network
  • Overlapping cost Each line segment corresponds to an interval. If two line segments are allocated on the same track and the intervals overlap, the overlap length is called overlap cost. If the wireless segments overlap, the overlap cost is zero;
  • Obstacle cost If a line segment is partly or completely overlapped with one or several obstacle areas in the interval on one of the tracks, then the obstacle cost of this line segment is equal to the overlap length between each related obstacle sum.
  • a one-dimensional real number coding method is used to encode the track planning problem.
  • a particle represents a trajectory planning scheme, and each bit of the particle code represents the orbit number of the corresponding line segment, that is, the code of the i-th bit of the particle is j, which means that the line segment i on the panel is allocated on the track j.
  • different allocation sequences are used for trajectory planning to generate the initial population, so that the initial population has a smaller line length cost.
  • the fitness function of formula (1) to find a trajectory planning scheme with smaller line length cost, overlap cost and obstacle cost.
  • ⁇ is a custom parameter, set to 100000, to ensure that obstacle costs are controlled in the iterative process.
  • the update formula of particles is redefined by introducing mutation operators and crossover operators (see Figure 2 and Figure 3 for pseudo codes for mutation and crossover operations, respectively), so that the particle swarm optimization algorithm can better solve the problem of trajectory planning .
  • the update formula is as follows:
  • ⁇ is the weight of inertia, which determines the probability of mutation
  • c 1 and c 2 are acceleration factors, which determine the probability of particle crossing
  • N 1 is a self-mutation operation
  • N 2 and N 3 are crossover operations.
  • the inertia retention part of the particle is the inertia retention part of the particle:
  • ⁇ represents the probability of mutation
  • rand() is a random number between [0,1].
  • Figure 4 The schematic diagram of the mutation operation is shown in Figure 4.
  • c 1 represents the probability of crossing with its own optimal particle
  • rand() is a random number between [0,1].
  • c 2 represents the probability of crossing with excellent particles in the population
  • rand() is a random number between [0,1].
  • Figure 5 The schematic diagram of the crossover operation is shown in Figure 5.
  • the improved discrete particle swarm optimization algorithm adopts a new social learning method, an oscillation parameter strategy and an adaptive inertia weight.
  • the new social learning method is specifically as follows: in the iterative process, the particles in the population with a lower fitness value than the current particle are called excellent particles, denoted as kbest, and each particle is in the social learning stage according to its fitness value. Particle learning with better particle fitness. In particular, if the particle is the best particle in the current population, social learning is not performed.
  • the oscillating parameter strategy is specifically as follows: divide the maximum number of iterations max_iter into an iterative process with SI times for each stage, so that the global exploration and local search alternately change mod (max_iter, SI) times during the entire iterative process.
  • Each stage uses the following Parameter formula:
  • ⁇ init and ⁇ end are the initial value and the end value of the inertia weight ⁇ respectively
  • c init and c end are the initial value and the end value of the acceleration factor c respectively (ie, both c 1 and c 2 use formula (8))
  • t is the current number of iterations
  • SI is the maximum number of iterations in each stage.
  • the adaptive inertia weight is specifically: Calculate the average fitness value of the current population, and divide all particles into two levels according to the fitness value of each particle, and select different inertia factor formulas according to the level. In each evolutionary iteration process The steps for adjusting the inertia factor of particles are as follows:
  • Step S3 Use the wire removal-rewind technology to further optimize the preliminary track planning scheme, focusing on optimizing the overlap cost, and obtain the optimal track planning scheme.
  • step S2 what is obtained is a result of low line length cost, low barrier cost and suboptimal overlap cost.
  • the present embodiment adopts the unwound-rewind technology to optimize the trajectory planning scheme of step S2.
  • the total overlap cost is gradually reduced by continuously removing the line segments with larger costs and re-planning them on a track with the least cost.
  • the overlap cost and historical cost of each line segment are considered; in the rewinding phase, the present invention considers the line length cost, overlap cost, obstacle cost, and historical cost of each line segment. This can effectively improve the quality of the solution.
  • the historical cost of a line segment is defined as the total historical cost of each unit interval occupied by the line segment on its track.
  • the initial value of the historical cost of each unit interval is set to 0. After each re-planning, if it overlaps with another line segment, the historical cost of this overlapping interval will increase by 1.
  • the method of the present invention has an average optimization rate of 8.92% in terms of the online cost.
  • each test case is optimized by 76.10% on average, while the barrier cost remains unchanged, and the overall optimization effect is significant.
  • the method of the present invention reduces the overlap cost by 1.91% on average when the online length cost and the barrier cost are almost unchanged.

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Abstract

一种基于离散粒子群优化的轨道规划方法，包括以下步骤：步骤S1：根据总体布线得到的结果中,同时从全局线网和局部线网中提取线段，并创建轨道；步骤S2：根据得到的轨道，考虑线长成本、重叠成本和障碍成本，并采用改进的离散粒子群优化算法寻找，得到初步的轨道规划方案；步骤S3：采用拆线-重绕技术，进一步优化初步的轨道规划方案，得到最优的轨道规划方案。该方法有效解决总体布线和详细布线之间不匹配的问题。

Description

基于离散粒子群优化的轨道规划方法 技术领域
本发明涉及超大规模集成电路设计领域，具体涉及一种基于离散粒子群优化的轨道规划方法。
背景技术
在现代超大规模集成电路设计流程中，布线是其中一个重要环节，布线问题一般由两个阶段组成：总体布线和详细布线。总体布线阶段将布线的区域划分为一组全局单元格，并确定每个线网需要放置在哪些单元格内，详细布线阶段将总体布线所得到的信息，进行细化布线，实现了线网中引脚和线段之间的连接。由于总体布线往往会忽略很多具体的信息，如引脚连接，局部线网的连接等问题，使得总体布线和详细布线之间存在很大程度的不匹配，从而得到的是可布线性很差的布线方案。所以总体布线与详细布线之间加进了轨道规划这一阶段，将布线问题划分为三个阶段。轨道规划阶段规定，一条线段和另一条线段重叠或者线段和障碍物发生阻塞都被视为违规。轨道规划的工作就是将每一条待布线段都规划在一个相应的轨道上，从而减少违规的数量，即降低重叠和阻塞现象的发生，然后生成一个轨道规划方案，并将这个方案信息传递给详细布线阶段，提高集成电路设计的可布线性。
技术问题
目前针对轨道规划问题的研究方法或是容易遗漏部分的线段，或是容易陷入局部极值。而粒子群优化技术是一种基于群体智能的搜索技术，实现起来容易，参数较少，并有更强的全局优化能力等特点。
技术解决方案
有鉴于此，本发明的目的在于提供一种基于离散粒子群优化的轨道规划方法，有效解决总体布线和详细布线之间不匹配的问题。
为实现上述目的，本发明采用如下技术方案：
一种基于离散粒子群优化的轨道规划方法，包括以下步骤：
步骤S1:根据总体布线得到的结果中,同时从全局线网和局部线网中提取线段，并创建轨道；
步骤S2：根据得到的轨道，考虑线长成本、重叠成本和障碍成本，并采用改进的离散粒子群优化算法寻找，得到初步的轨道规划方案；
步骤S3:采用拆线-重绕技术，进一步优化初步的轨道规划方案，得到最优的轨道规划方案。
进一步的，所述步骤S1具体为：
(1)每个局部线网均构建两棵斯坦纳树，分别为单株垂直主干斯坦纳树和单株水平主干斯坦纳树；
(2)通过计算它们的长度，选择二者中长度较小的树主干作为该局部线网的线段；
(3)为每个panel创建轨道，每一层上的所有panels的轨道方向是一致的，相邻层的轨道方向不一致；即奇数层的轨道方向为水平方向，偶数层的轨道方向为垂直方向
其中，panel为一个布线层的行或列中所有G-cell的集合，G-cell为总体布线阶段将布线区域划分成一组子布线区域。
进一步的，所述步骤S2具体为：
(1)采用一维实数编码方式来编码轨道规划问题,一个粒子表一个轨道规划方案，粒子编码的每一位代表了对应线段所在的轨道序号，即粒子第i位的编码为j，代表该panel上的线段i被分配在轨道j上；
(2)通过不同的分配顺序进行轨道规划，以产生初始种群；
(3)构建适应值函数
Figure PCTCN2020134412-appb-000001
其中，
Figure PCTCN2020134412-appb-000002
是每个panel的适应值函数，OverlapCost是粒子的重叠成本，BlockCost是粒子的障碍成本。β为自定义参数；
(4)引入变异算子和交叉算子来重新定义粒子的更新公式
Figure PCTCN2020134412-appb-000003
其中ω是惯性权重，决定了变异的概率，c 1和c 2是加速因子，决定了粒子交叉的概率；N 1是自身变异操作，N 2和N 3是交叉操作；
(5)根据改进离散粒子群优化算法寻找，得到初步的轨道规划方案。
进一步的，所述更新公式具体分为：
(1)粒子的惯性保持部分：
Figure PCTCN2020134412-appb-000004
其中，ω表示发生变异的概率，rand()是[0,1]之间的随机数；
(2)粒子的个体学习部分：
Figure PCTCN2020134412-appb-000005
其中，c 1表示与自身最优粒子交叉的概率；
(3)粒子的社会学习部分：
Figure PCTCN2020134412-appb-000006
其中，c 2表示与种群中优秀粒子交叉的概率。
进一步的，所述改进的离散粒子群优化算法采用新的社会学习方式，震荡参数策略和自适应的惯性权重。
进一步的，所述新的社会学习方式具体为：每个粒子在社会学习阶段，根据适应值的大小，向比自身粒子适应值更优的粒子学习。
进一步的，所述震荡参数策略具体为：将最大迭代次数max_iter划分为每个阶段为SI次的迭代过程，使全局勘探和局部搜索在整个迭代过程中交替变化mod(max_iter,SI)次，每个阶段使用如下的参数公式：
Figure PCTCN2020134412-appb-000007
Figure PCTCN2020134412-appb-000008
Figure PCTCN2020134412-appb-000009
其中，ω init和ω end分别为惯性权重ω的初始值和结束值，c init和c end分别为加速因子c的初始值和结束值(即c 1和c 2均使用公式(8))，t为当前迭代次数，SI为每个阶段的最大迭代次数。
进一步的，所述自适应的惯性权重具体为：计算当前种群的平均适应值，并依照每个粒子适应值的大小把全部粒子分为两个级别，依照级别选取不同的惯性因子的公式，每次进化迭代过程中粒子的惯性因子调整的步骤如下：
(1)计算种群的平均适应值，记为f avg；
(2)适应值比f avg差或者相等的粒子采取公式(6)；
(3)适应值优于f avg的粒子采取公式(7)。
有益效果
本发明与现有技术相比具有以下有益效果：
本发明减少线长成本、重叠成本和障碍成本，有效解决总体布线和详细布线之间不匹配的问题。
附图说明
图1是本发明一实施例中粒子编码的示意图；
图2是本发明一实施例中变异操作的伪代码；
图3是本发明一实施例中交叉操作的伪代码；
图4是本发明一实施例中变异操作的示意图；
图5是本发明一实施例中交叉操作的示意图。
本发明的实施方式
下面结合附图及实施例对本发明做进一步说明。
本发明提供一种基于离散粒子群优化的轨道规划方法，包括以下步骤：
步骤S1:根据总体布线得到的结果中,同时从全局线网和局部线网中提取线段，并创建轨道；
优选的，在本实施例中，每个局部线网均构建两棵斯坦纳树，分别为单株垂直主干斯坦纳树和单株水平主干斯坦纳树；
通过计算它们的长度，选择二者中长度较小的树主干作为该局部线网的线段；
为每个panel创建轨道，每一层上的所有panels的轨道方向是一致的，相邻层的轨道方向不一致；即奇数层的轨道方向为水平方向，偶数层的轨道方向为垂直方向；
其中，panel为一个布线层的行或列中所有G-cell的集合，G-cell为总体布线阶段将布线区域划分成一组子布线区域。
步骤S2：根据得到的轨道，考虑线长成本、重叠成本和障碍成本，并采用改进的离散粒子群优化算法寻找，得到初步的轨道规划方案；
在本实施例中，所述线长成本为每个线网中的每个组件都要产生连接，连接所用的线长的总和；
重叠成本：每条线段对应一个区间，如果两条线段被分配在同一个轨道上，且区间具有重叠，则重叠长度称为重叠成本，若无线段重叠，重叠成本为零；
障碍成本：若一条线段在其中一条轨道上的区间，恰好和一个或者几个障碍物区间有部分或全部重叠，则这条线段的障碍成本是和每个相关的障碍物之间的重叠长度的总和。
在本实施例中，如图1所示，采用了一维实数编码方式来编码轨道规划问题。一个粒子代表一个轨道规划方案，粒子编码的每一位代表了对应线段所在的轨道序号，即粒子第i位的编码为j，代表该panel上的线段i被分配在轨道j上。
在本实施例中，使用不同的分配顺序进行轨道规划，以产生初始种群，以使得初始种群具有较小的线长成本。并设计了公式(1)的适应值函数，以寻找一个具有较小线长成本、重叠成本和障碍成本的轨道规划方案。
Figure PCTCN2020134412-appb-000010
其中，
Figure PCTCN2020134412-appb-000011
是每个panel的适应值函数，OverlapCost是粒子的重叠成本，BlockCost是粒子的障碍成本。β为自定义参数，设置为100000，以保证在迭代过程中控制障碍成本。
本实施例中，通过引入变异算子和交叉算子来重新定义粒子的更新公式(变异和交叉操作的伪代码分别见图2和图3)，使得粒子群优化算法更好地解决轨道规划问题。更新公式如下：
Figure PCTCN2020134412-appb-000012
其中ω是惯性权重，决定了变异的概率，c 1和c 2是加速因子，决定了粒子交叉的概率。N 1是自身变异操作，N 2和N 3是交叉操作。依据轨道规划问题，将粒子更新公式分为如下三个具体的部分：
粒子的惯性保持部分：
Figure PCTCN2020134412-appb-000013
其中，ω表示发生变异的概率，rand()是[0,1]之间的随机数。变异操作的示意图如图4所示。
粒子的个体学习部分：
Figure PCTCN2020134412-appb-000014
其中，c 1表示与自身最优粒子交叉的概率，rand()是[0,1]之间的随机数。
粒子的社会学习部分：
Figure PCTCN2020134412-appb-000015
其中，c 2表示与种群中优秀粒子交叉的概率，rand()是[0,1]之间的随机数。交叉操作的示意图如图5所示。
在本实施例中，优选的，改进的离散粒子群优化算法采用新的社会学习方式，震荡参数策略和自适应的惯性权重。
新的社会学习方式具体为：在迭代过程中，将种群里比当前粒子适应值低的粒子称为优秀粒子，记为kbest，每个粒子在社会学习阶段，根据适应值的大小，向比自身粒子适应值更优的粒子学习。特殊地，如果粒子是当前种群里最优的粒子，便不进行社会学习。
震荡参数策略具体为：将最大迭代次数max_iter划分为每个阶段为SI次的迭代过程，使全局勘探和局部搜索在整个迭代过程中交替变化mod(max_iter,SI)次，每个阶段使用如下的参数公式：
Figure PCTCN2020134412-appb-000016
Figure PCTCN2020134412-appb-000017
Figure PCTCN2020134412-appb-000018
其中，ω init和ω end分别为惯性权重ω的初始值和结束值，c init和c end分别为加速因子c的初始值和结束值(即c 1和c 2均使用公式(8))，t为当前迭代次数，SI为每个阶段的最大迭代次数。
自适应的惯性权重具体为：计算当前种群的平均适应值，并依照每个粒子适应值的大小把全部粒子分为两个级别，依照级别选取不同的惯性因子的公式，每次进化迭代过程中粒子的惯性因子调整的步骤如下：
(1)计算种群的平均适应值，记为f avg；
(2)适应值比f avg差或者相等的粒子采取公式(6)；
(3)适应值优于f avg的粒子采取公式(7)。
步骤S3:采用拆线-重绕技术，进一步优化初步的轨道规划方案，重点优化重叠成本，得到最优的轨道规划方案。
在本实施例中，经过步骤S2，得到的是一个低线长成本，低障碍成本和次优重叠成本的结果。为了进一步降低重叠成本，本实施例采用了拆线-重绕技术来优化步骤S2的轨道规划方案。在这一步骤中，通过不断地移除具有较大成本的线段，并将其重新规划到一个成本最小的轨道上，来逐渐降低总的重叠成本。在拆线阶段，考虑了每条线段的重叠成本和历史成本；在重绕阶段，本发明考虑了每条线段的线长成本、重叠成本、障碍成本和历史成本。如此能够有效提升解方案的质量。
其中，一条线段的历史成本定义为该线段在其轨道上占据的每个单位区间的历史成本总和。而每个单位区间的历史成本初值设置为0，在经过每次重新规划后，若与另一条线段产生重叠，则这个重叠区间的历史成本将增加1。
在本实施例中，为了验证在求解轨道规划问题中的有效性，在基准测试电路上进行了仿真实验，对比了本发明方法与现有的两种优秀的轨道规划方法在线长成本(WL)、重叠成本(OC)和障碍成本(BC)上的优化能力。表1为本发明方法与加权二分匹配方法(WBM)的比较结果，表2为本发明方法与基于协商的轨道规划方法(NTA)的比较结果。
表1 本发明方法与WBM的比较
Figure PCTCN2020134412-appb-000019
Figure PCTCN2020134412-appb-000020
表2 本发明方法与NTA的比较
Figure PCTCN2020134412-appb-000021
从表1的实验数据可以看出，相对WBM方法，本发明方法在线长成本上，平均优化率为8.92％。在重叠成本上，平均每个测试用例优化了76.10％，同时障碍成本不变，总体优化效果显著。在表2中，本发明方法与NTA方法相比，在线长成本和障碍成本几乎不变的情况下，平均减少了1.91％的重叠成本。上述实验结果证明了本 发明方法在轨道规划问题上的有效性，并且也体现了本发明方法在重叠成本这一最重要的指标上具有显著的优化效果。
以上所述仅为本发明的较佳实施例，凡依本发明申请专利范围所做的均等变化与修饰，皆应属本发明的涵盖范围。

Claims (8)

  1. 一种基于离散粒子群优化的轨道规划方法，其特征在于，包括以下步骤：
    步骤S1:根据总体布线得到的结果中,同时从全局线网和局部线网中提取线段，并创建轨道；
    步骤S2：根据得到的轨道，考虑线长成本、重叠成本和障碍成本，并采用改进的离散粒子群优化算法寻找，得到初步的轨道规划方案；
    步骤S3:采用拆线-重绕技术，进一步优化初步的轨道规划方案，得到最优的轨道规划方案。
  2. 根据权利要求1所述的基于离散粒子群优化的轨道规划方法，其特征在于：所述步骤S1具体为：
    (1)每个局部线网均构建两棵斯坦纳树，分别为单株垂直主干斯坦纳树和单株水平主干斯坦纳树；
    (2)通过计算它们的长度，选择二者中长度较小的树主干作为该局部线网的线段；
    (3)为每个panel创建轨道，每一层上的所有panels的轨道方向是一致的，相邻层的轨道方向不一致；即奇数层的轨道方向为水平方向，偶数层的轨道方向为垂直方向
    其中，panel为一个布线层的行或列中所有G-cell的集合，G-cell为总体布线阶段将布线区域划分成一组子布线区域。
  3. 根据权利要求1所述的基于离散粒子群优化的轨道规划方法，其特征在于，所述步骤S2具体为：
    (1)采用一维实数编码方式来编码轨道规划问题,一个粒子代表一个轨道规划方案，粒子编码的每一位代表了对应线段所在的轨道序号，即粒子第i位的编码为j，代表该panel上的线段i被分配在轨道j上；
    (2)通过不同的分配顺序进行轨道规划，以产生初始种群；
    (3)构建适应值函数
    Figure PCTCN2020134412-appb-100001
    其中，
    Figure PCTCN2020134412-appb-100002
    是每个panel的适应值函数，OverlapCost是粒子的重叠成本，BlockCost是粒子的障碍成本。β为自定义参数；
    (4)引入变异算子和交叉算子来重新定义粒子的更新公式
    Figure PCTCN2020134412-appb-100003
    其中ω是惯性权重，决定了变异的概率，c 1和c 2是加速因子，决定了粒子交叉的概率；N 1是自身变异操作，N 2和N 3是交叉操作；
    (5)根据改进离散粒子群优化算法寻找，得到初步的轨道规划方案。
  4. 根据权利要求3所述的基于离散粒子群优化的轨道规划方法，其特征在于，所述更新公式具体分为：
    (1)粒子的惯性保持部分：
    Figure PCTCN2020134412-appb-100004
    其中，ω表示发生变异的概率，rand()是[0,1]之间的随机数；
    (2)粒子的个体学习部分：
    Figure PCTCN2020134412-appb-100005
    其中，c 1表示与自身最优粒子交叉的概率；
    (3)粒子的社会学习部分：
    Figure PCTCN2020134412-appb-100006
    其中，c 2表示与种群中优秀粒子交叉的概率。
  5. 根据权利要求1所述的基于离散粒子群优化的轨道规划方法，其特征在于，所述改进的离散粒子群优化算法采用新的社会学习方式，震荡参数策略和自适应的惯性权重。
  6. 根据权利要求5所述的基于离散粒子群优化的轨道规划方法，其特征在于，所述新的社会学习方式具体为：每个粒子在社会学习阶段，根据适应值的大小，向比自身粒子适应值更优的粒子学习。
  7. 根据权利要求5所述的基于离散粒子群优化的轨道规划方法，其特征在于，所述震荡参数策略具体为：将最大迭代次数max_iter划分为每个阶段为SI次的迭代过程，使全局勘探和局部搜索在整个迭代过程中交替变化mod(max_iter,SI)次，每个阶段使用如下的参数公式：
    Figure PCTCN2020134412-appb-100007
    Figure PCTCN2020134412-appb-100008
    Figure PCTCN2020134412-appb-100009
    其中，ω init和ω end分别为惯性权重ω的初始值和结束值，c init和c end分别为加速因子c的初始值和结束值，t为当前迭代次数，SI为每个阶段的最大迭代次数。
  8. 根据权利要求7所述的基于离散粒子群优化的轨道规划方法，其特征在于，所述自适应的惯性权重具体为：计算当前种群的平均适应值，并依照每个粒子适应值的大小把全部粒子分为两个级别，依照级别选取不同的惯性因子的公式，每次进化迭代过程中粒子的惯性因子调整的步骤如下：
    (1)计算种群的平均适应值，记为f avg；
    (2)适应值比f avg差或者相等的粒子采取公式(6)；
    (3)适应值优于f avg的粒子采取公式(7)。
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