基于分枝搜索的带缓冲集束型设备调度与性能分析

针对带缓冲与驻留约束的集束型设备调度问题,本文提出了一种基于分枝的搜索调度方法.首先,构造问题域的数学模型,在此基础上提出了一种全局搜索算法;然后,通过数学分析证明引出必要的引理,提出一个基于分枝搜索的算法;最后,进行了仿真实验和分析,结果表明本文提出的算法是有效且可行的,同时还表明了带缓冲模块的集束型设备在一定程度上能提高集束型设备的产能.     

有滞留时间约束的集束型装备在线调度问题研究

针对半导体制造中有滞留时间约束的集束型装备,研究了临时晶网到达时的在线调度问题,描述了调度问题域.建立了问题的数学模型,并根据模型提出了两层调度方法.外层算法通过粒子群优化过程求解临时晶网的加工顺序;内层算法在给定加工顺序的基础上,采用前向和后向递推方法获得口,行解窄问,并从可行解窄问获得最优完工时间.从理论上证明了算...     

基于Petri网的组合设备建模与调度综述

组合设备是半导体晶圆制造的核心装备,其调度与控制优化是半导体制造领域极具挑战性的课题. Petri网因其强大的建模能力和简约的图形化表达优势,被广泛地应用于组合设备的建模与调度.对基于Petri网的组合设备建模与调度方法进行综述,归纳总结了组合设备的结构类型、晶圆流模式、调度策略及Petri网建模方法,并系统阐述组合设备的7类典型调度问题,包括驻留时间约束、作业时间波动、晶圆重入加工、多品种晶圆加工、加工模块(Process module, PM)故障、PM清洗和组合设备群.最后,讨论了当前组合设备调度存在的挑战及后续可能的研究方向.     

面向单臂组合设备中紧急订单的调度

随着晶圆制造模式向多品种、小批量的转变，在实际生产过程中频繁出现紧急订单插入的情况，不合理的调度策略将降低组合设备生产效率。为了提高组合设备的生产柔性，研究了在考虑晶圆逗留时间约束条件下，单臂组合设备面对紧急插单时的调度问题。首先，对紧急插单的加工过程进行分析，提出针对单臂组合设备的机械手调度规则，实现了加工过程的可调度性。其次，对于因加工参数不同产生的两种加工状态，分别推导出可调度性判断条件，然后给出用于求解机械手等待时间的数学解析式。最后，提出组合设备面对紧急插单时的最优调度算法，并通过实例验证和对比分析的方法验证了该调度方法的有效性。     

组合窗口约束(m,k)＾的实时系统分析与研究

在研究基于窗口约束(m,k)模型的实时系统的基础上,提出一种基于非重叠组合窗口约束的实时系统.通过对该实时系统的可调度性条件的研究,提出一种新的组合窗口约束(m,k)＾的调度算法,该算法充分利用组合约束的特点,考虑本次调度对该窗口的可调度的影响来确定任务的优先级,并以此来提高任务的可调度性、减少组合窗口限制违例.仿真试验表明该算法在组合窗口约束的调度上,优于传统的独立比较两个约束确定优先级的调度算法.     

组合窗口约束（m，k）^∧〈h，k〉的实时系统分析与研究

在研究基于窗口约束（m,k）模型的实时系统的基础上,提出一种基于非重叠组合窗口约束的实时系统.通过对该实时系统的可调度性条件的研究,提出一种新的组合窗口约束（m,k）^∧〈h,k〉的调度算法,该算法充分利用组合约束的特点,考虑本次调度对该窗口的可调度的影响来确定任务的优先级,并以此来提高任务的可调度性、减少组合窗口限制违例.仿真试验表明该算法在组合窗口约束的调度上,优于传统的独立比较两个约束确定优先级的调度算法.     

工序间存在零等待约束的复杂产品调度研究

针对实际装配生产中工序之间存在零等待约束的复杂产品的调度问题, 提出了一种把存在零等待约束的工序虚拟成一个工序的方法. 该方法在提出复杂产品、标准工序、虚拟工序、零等待和扩展加工工艺树的概念基础上, 对扩展加工工艺树中的标准工序采用拟关键路径法和最佳适应调度的车间调度算法进行调度, 对虚拟工序采用移动交换算法在相应设备上分离调度, 将存在零等待约束的调度问题转化为存在虚拟工序的无零等待约束的调度问题. 实例表明, 所提出的调度算法能够较好地解决具有实际意义的工序间存在零等待约束的复杂产品的调度问题, 且易于实现.     

稳态调度下单臂组合设备时间延迟分析与优化

在半导体晶圆制造过程中,驻留时间延迟过长对晶圆质量具有消极影响.本文研究单臂组合设备稳态调度中如何合理地分配机械手等待时间,抵消驻留时间延迟的问题.首先,采用Petri网模型描述晶圆制造过程,分析了单臂组合设备稳态调度的时间特性,获得了稳态下工序驻留时间延迟计算表达式.其次,通过解构机械手等待时间对驻留时间延迟的影响机理,提出了一种机械手等待时间分配优先级规则.进一步,将虚拟瓶颈工序用于辅助分配机械手等待时间,结合优先级规则,提出了一种单臂组合设备稳态调度启发式算法.最后,通过例子验证了算法的可行性与有效性.与传统拉式策略和尽早加工策略对比,该算法能有效地减少单臂组合设备稳态调度下的驻留时间延迟并能满足晶圆制造的严格要求.     

具有清洗工艺的单臂组合设备终止暂态调度

随着多品种小批量生产模式的普及,导致了组合设备频繁的暂态加工过程.为了提高组合设备的生产柔性,同时考虑晶圆驻留时间约束和腔室清洗时间约束,研究了单臂组合设备的终止暂态调度问题.首先,提出了 1-周期清洗工艺的暂态调度规则,并采用了面向资源的Petri网对单臂组合设备的终止暂态过程进行建模,引入避免死锁的变迁触发规则;其次,根据系统的终止暂态时间特性并考虑不同的调度情形,建立了终止暂态调度的线性规划模型;最后,通过实例验证了该方法的可行性.实验结果表明,与运用改进拉式策略的虚拟晶圆方案相比,该调度方案可有效地减少组合设备终止暂态的完工时间,并满足晶圆制造的工艺要求.     

基于安全性约束和协同禁忌优化算法的云计算工作流调度

针对现有的云计算工作流调度方法侧重于节能和可靠性等方面进行研究,忽略了安全性约束的要求,设计了一种基于协同禁忌算法的具有安全型约束的能实现云计算工作流高效调度的方法;首先,定义了云计算工作流调度的DAG图,对安全性约束进行了形式化描述,并建立了云计算工作流调度的数学模型;然后,在经典的协同禁忌算法的基础上,通过设计解的编码方式、适应度函数、变邻域结构和双禁忌表,实现对经典的协同禁忌算法进行改进;最后,定义了基于改协同禁忌算法实现对云计算工作流调度的具体算法;在云计算的仿真环境Cloud-Sim下进行实验,实验结果证明了文中方法不仅具有较快的收敛速度,而且能寻求到比其它方法更优的调度方案,能满足安全性约束要求,是一种可行实用的调度方法.     

Optimal Integrated Schedule of Entire Process of Dual-blade Multi-cluster Tools From Start-up to Close-down

Multi-cluster tools are widely used in majority of wafer fabrication processes in semiconductor industry. Smaller lot production, thinner circuit width in wafers, larger wafer size, and maintenance have resulted in a large quantity of their start-up and close-down transient periods. Yet, most of existing efforts have been concentrated on scheduling their steady states. Different from such efforts, this work schedules their transient and steady-state periods subject to wafer residency constraints. It gives the schedulability conditions for the steady-state scheduling of dual-blade robotic multi-cluster tools and a corresponding algorithm for finding an optimal schedule. Based on the robot synchronization conditions, a linear program is proposed to figure out an optimal schedule for a start-up period, which ensures a tool to enter the desired optimal steady state. Another linear program is proposed to find an optimal schedule for a close-down period that evolves from the steady state period. Finally, industrial cases are presented to illustrate how the provided method outperforms the existing approach in terms of system throughput improvement.      

Optimal <Emphasis Type="Italic">K</Emphasis>-unit cycle scheduling of two-cluster tools with residency constraints and general robot moving times

The semiconductor manufacturing industry is significantly expensive both in equipment and materials. Cluster tools, a type of automated manufacturing system integrating processing modules and transport modules, are commonly used in this industry. Nowadays, multi-cluster tools, which are composed of several cluster tools connected by joint buffer modules, are often used for wafer production. This paper deals with K-unit cycle scheduling problems in single-armed two-cluster tools for processing identical wafers in deterministic settings. In a K-unit cycle, K wafers are exactly inserted into the two-cluster tool, and K completed wafers leave the two-cluster tool, usually not the same K wafers. Residency constraints and general moving times by the robot are both considered. The objective is to obtain optimal K-unit cycle schedules, which minimize cycle times. To analyze this scheduling problem in detail, a mixed integer linear programming (MILP) model is formulated and solved. Numerical examples are used to explain how the solution can be obtained from the MILP model in a K-unit cycle.     

虚拟计算环境中的多机群协同调度算法

基于虚拟计算环境的核心机理,提出由自主调度单元、域调度共同体、元调度执行体为核心的多机群协同系统框架.剖析多机群任务并发运行性能模型,设计了多机群协同调度算法框架,提出最大空闲节点优先、最小网络拥塞优先、最小异构因子优先与最小异构空闲节点优先4种启发式资源选择策略.实验验证了协同调度模型与算法在任务集完成时间与系统平均利用率的测度上的有效性.     

具有多品种晶圆混合加工的单臂组合设备调度

为了提高晶圆制造中组合设备的生产效率,在考虑晶圆驻留时间约束条件下,研究没有共享加工模块的多品种晶圆混合加工的单臂组合设备调度问题.首先,采用面向资源的Petri网模型描述多种晶圆产品的混合加工过程,引入控制变迁避免模型的死锁,采用赋时库所和赋时变迁模拟系统资源的活动时间.其次,通过虚拟加工的方法平衡工序的负载,基于系统Petri网模型和拉式调度策略,推导出单臂组合设备在多品种晶圆混合加工情形下的可调度性判定条件,并以解析形式描述.最后,提出了系统稳态调度求解算法并以实例验证了算法的有效性和可行性.     

Steady-State Throughput and Scheduling Analysis of Multicluster Tools: A Decomposition Approach

Cluster tools are widely used as semiconductor manufacturing equipment. While throughput analysis and scheduling of single-cluster tools have been well-studied, research work on multicluster tools is still at an early stage. In this paper, we analyze steady-state throughput and scheduling of multicluster tools. We consider the case where all wafers follow the same visit flow within a multicluster tool. We propose a decomposition method that reduces a multicluster tool problem to multiple independent single-cluster tool problems. We then apply the existing and extended results of throughput and scheduling analysis for each single-cluster tool. Computation of lower-bound cycle time (fundamental period) is presented. Optimality conditions and robot schedules that realize such lower-bound values are then provided using ldquopullrdquo and ldquoswaprdquo strategies for single-blade and double-blade robots, respectively. For an -cluster tool, we present lower-bound cycle time computation and robot scheduling algorithms. The impact of buffer/process modules on throughput and robot schedules is also studied. A chemical vapor deposition tool is used as an example of multicluster tools to illustrate the decomposition method and algorithms. The numerical and experimental results demonstrate that the proposed decomposition approach provides a powerful method to analyze the throughput and robot schedules of multicluster tools.     

Scheduling online mixed-parallel workflows of rigid tasks in heterogeneous multi-cluster environments

Workflow scheduling on parallel systems has long been known to be a NP-complete problem. As modern grid and cloud computing platforms emerge, it becomes indispensable to schedule mixed-parallel workflows in an online manner in a speed-heterogeneous multi-cluster environment. However, most existing scheduling algorithms were not developed for online mixed-parallel workflows of rigid data-parallel tasks and multi-cluster environments, therefore they cannot handle the problem efficiently. In this paper, we propose a scheduling framework, named Mixed-Parallel Online Workflow Scheduling (MOWS), which divides the entire scheduling process into four phases: task prioritizing, waiting queue scheduling, task rearrangement, and task allocation. Based on this framework, we developed four new methods: shortest-workflow-first, priority-based backfilling, preemptive task execution and All-EFT task allocation, for scheduling online mixed-parallel workflows of rigid tasks in speed-heterogeneous multi-cluster environments. To evaluate the proposed scheduling methods, we conducted a series of simulation studies and made comparisons with previously proposed approaches in the literature. The experimental results indicate that each of the four proposed methods outperforms existing approaches significantly and all these approaches in MOWS together can achieve more than 20% performance improvement in terms of average turnaround time.     

基于PCA优化的PSO-FCM聚类算法

为解决PSO-FCM聚类算法针对多聚类问题,性能不足,容易陷入局部最优解,影响多聚类结果的准确度.提出一种基于PCA优化的PSO-FCM聚类算法,通过引入PCA分析方法,在粒子的各维度上设定不同的移动权重,降低粒子的敏感度,合理的控制粒子各维度上移动的速度,有效的降低粒子各维度上粒子无约束,位于多个聚类群交界处的粒子过分敏感,移动到错误的聚类的可能性增加.本文简要介绍了PSO-FCM算法的相关情况,详细介绍了本文的优化算法,最后通过实验证明,本文提出的优化算法在多个数据集上结果总体优于其他算法.     

A genetic algorithm application using fuzzy processing times in non-identical parallel machine scheduling problem

There are many scheduling problems which are NP-hard in the literature. Several heuristics and dispatching rules are proposed to solve such hard combinatorial optimization problems. Genetic algorithms (GA) have shown great advantages in solving the combinatorial optimization problems in view of its characteristic that has high efficiency and that is fit for practical application [1]. Two different scale numerical examples demonstrate the genetic algorithm proposed is efficient and fit for larger scale identical parallel machine scheduling problem for minimizing the makespan. But, even though it is a common problem in the industry, only a small number of studies deal with non-identical parallel machines. In this article, a kind of genetic algorithm based on machine code for minimizing the processing times in non-identical machine scheduling problem is presented. Also triangular fuzzy processing times are used in order to adapt the GA to non-identical parallel machine scheduling problem in the paper. Fuzzy systems are excellent tools for representing heuristic, commonsense rules. That is why we try to use fuzzy systems in this study.     

On construction of a well-balanced allocation strategy for heterogeneous multi-cluster computing environments

With the rapid increment of the heterogeneity of hardware devices, cluster computing has to encounter the problem of handling heterogeneous resources for exploiting the utilization of system resources. This paper introduces a new job allocation strategy based on multi-clusters in diskless environments. By adopting Ganglia as the resource monitor and Condor as the queue system, a heterogeneous multi-cluster system is also constructed with and without storage devices for evaluating the system performance. The proposed algorithm is called the Well-Balanced Allocation Strategy (WBAS) in which the scheduler dispatches MPI-based jobs to appropriate resources across multi-clusters. The strategy focuses on dispatching jobs to nodes with similar performance, thus equalizing execution times among all the required nodes. The WBAS is implemented on the constructed heterogeneous multi-cluster system to evaluate the performance of the scheduling strategy. The experimental results show that the proposed strategy performs well and could efficiently improve the system performance.     

Polynomial Approach to Optimal One-wafer Cyclic Scheduling of Treelike Hybrid Multi-Cluster Tools via Petri Nets

A treelike hybrid multi-cluster tool is composed of both single-arm and dual-arm cluster tools with a treelike topology. Scheduling such a tool is challenging. For a hybrid treelike multi-cluster tool whose bottleneck individual tool is process-bound, this work aims at finding its optimal one-wafer cyclic schedule. It is modeled with Petri nets such that a onewafer cyclic schedule is parameterized as its robots' waiting time. Based on the model, this work proves the existence of its onewafer cyclic schedule that features with the ease of industrial implementation. Then, computationally efficient algorithms are proposed to find the minimal cycle time and optimal onewafer cyclic schedule. Multi-cluster tool examples are given to illustrate the proposed approach. The use of the found schedules enables industrial multi-cluster tools to operate with their highest productivity.