6852 Distributed AlgorithmsSpring, 2008
分布式系统 入门书
分布式系统入门书
- 《分布式系统原理与范型》(Distributed Systems: Principles and Paradigms):这本书涵盖了分布式系统的基本原理、设计和实现,是一本很好的入门书籍。
- 《大规模分布式系统设计》(Designing Data-Intensive Applications):这本书由Martin Kleppmann编写,介绍了构建可靠、高效和可扩展的分布式系统所需的各种技术。
- 《分布式系统概念与设计》(Distributed Systems: Concepts and Design):这是一本比较全面的分布式系统书籍,介绍了分布式系统的各个方面,包括通信、安全、一致性、故障处理等。
- 《分布式算法》(Distributed Algorithms):这是一本比较深入的分布式系统书籍,介绍了分布式算法的各种问题和解决方法。
这些书籍可以帮助你了解分布式系统的基础知识,并逐步深入到更复杂的主题。
如果你对某个特定的主题感兴趣,也可以根据相关的书籍进行更深入的学习。
Analyzing the Scalability of Algorithms
Analyzing the Scalability ofAlgorithmsAlgorithms are essential tools used in various fields such as computer science, data analysis, and machine learning. The scalability of algorithms refers to their ability to handle increasing amounts of data or growing computational demands efficiently without compromising performance. In this article, we will delve into the concept of scalability of algorithms and discuss various factors that influence it.One of the key factors that affect the scalability of algorithms is the input size. As the amount of data increases, the algorithm should be able to process it within a reasonable time frame. The efficiency of an algorithm can be measured in terms of its time complexity, which describes how the running time of the algorithm grows with the size of the input. Algorithms with a lower time complexity are more scalable as they can handle larger inputs without a significant increase in processing time.Another important factor to consider is the space complexity of an algorithm. Space complexity refers to the amount of memory or storage space required by the algorithm to solve a problem. As the input size grows, the algorithm should not consume an excessive amount of memory, as this can lead to performance degradation or even failure to complete the computation. Algorithms with lower space complexity are more scalable as they can operate efficiently even with limited memory resources.Moreover, the structure and design of an algorithm can greatly impact its scalability. Algorithms that are well-structured and modularized are easier to scale as they can be optimized or parallelized to improve performance. Additionally, the choice of data structures and algorithms used within the main algorithm can influence its scalability. For example, utilizing efficient data structures such as arrays or hash tables can improve the scalability of the algorithm by reducing the time and space required for processing.Furthermore, the scalability of algorithms can also be affected by external factors such as hardware limitations or network constraints. Algorithms that are designed towork in a distributed system or parallel computing environment are more scalable as they can distribute the workload across multiple processing units. However, algorithms that rely on a single processor or have high communication overhead may not scale well when faced with increasing computational demands.In conclusion, analyzing the scalability of algorithms is crucial for ensuring optimal performance in handling large datasets or complex computational tasks. Understanding the factors that influence scalability, such as time complexity, space complexity, algorithm structure, and external constraints, can help developers and researchers design and implement scalable algorithms. By considering these factors and optimizing the algorithm accordingly, we can improve efficiency, reduce resource consumption, and achieve better performance in various applications.。
多变量遗传算法python
多变量遗传算法python
多变量遗传算法(MGA)是一种优化算法,它结合了遗传算法和多变量优化的特点,用于解决多变量的优化问题。
在Python中,可以使用各种库和工具来实现多变量遗传算法的模型和求解过程。
首先,我们可以使用Python中的遗传算法库,如DEAP (Distributed Evolutionary Algorithms in Python)或Pyevolve来实现多变量遗传算法。
这些库提供了丰富的遗传算法工具和函数,可以帮助我们快速构建和求解多变量遗传算法模型。
其次,针对多变量优化问题,我们需要定义适当的变量编码方式,交叉和变异操作,以及适应度函数的计算方法。
在MGA中,通常会采用二进制、实数或其他编码方式来表示多个变量,并根据实际问题选择合适的交叉和变异操作。
另外,对于多变量遗传算法的求解过程,我们需要考虑种群大小、迭代次数、选择策略等参数的设置,以及如何有效地评估和改进种群的适应度。
在Python中,我们可以利用numpy、scipy等数值计算库来进行种群操作和适应度函数的计算。
除此之外,还可以使用Python中的可视化工具,如matplotlib、seaborn等库来对多变量遗传算法的求解过程和结果进行可视化分析,以便更直观地理解算法的性能和收敛情况。
总之,通过Python中丰富的库和工具,我们可以相对容易地实现和求解多变量遗传算法,从而解决复杂的多变量优化问题。
希望以上信息能够帮助你全面了解多变量遗传算法在Python中的应用。
运筹算法 分布式 加速方法
运筹算法分布式加速方法英文回答:Distributed Optimization Algorithms: Acceleration Methods.Distributed optimization algorithms are used to solve large-scale optimization problems that are distributed across multiple computing nodes. These algorithms can be used to solve a wide variety of problems, includingtraining machine learning models, optimizing supply chains, and scheduling tasks in a distributed system.One of the main challenges in distributed optimization is the communication overhead. Each time the nodes in the system need to share information, they must send messages over the network. This can be a significant bottleneck, especially for large-scale problems.Acceleration methods are a class of algorithms that canbe used to reduce the communication overhead in distributed optimization. These methods work by approximating the optimal solution to the optimization problem using a series of local updates. Each node in the system only needs to share information with its neighbors, and the updates can be computed in parallel.There are a number of different acceleration methods that can be used for distributed optimization. Some of the most popular methods include:Gossip averaging: This method is based on the idea of spreading information through a network by randomly exchanging messages between nodes.Conjugate gradient: This method is a classical optimization algorithm that can be used to solve a variety of problems, including distributed optimization.Nesterov's accelerated gradient: This method is a variant of the conjugate gradient method that can be used to accelerate convergence.The choice of which acceleration method to use will depend on the specific problem being solved and theavailable resources.中文回答:分布式优化算法,加速方法。
多智能体系统的分布式算法
多智能体系统的分布式算法(Distributed Algorithms for Multi-Agent Systems)多智能体系统是指由多个智能体组成的系统,智能体之间具有一定的互动和协作能力。
多智能体系统的设计和实现涉及到许多领域,其中一个重要的方向是分布式算法。
本文将介绍,包括基本概念、算法分类和应用案例。
1. 基本概念是一种通过智能体之间的协作,实现系统全局目标的一类算法。
在分布式算法中,每个智能体只能访问部分信息,没有全局信息的全局视图。
因此,分布式算法需要设计协议和机制,使得智能体之间能够协调和合作,达到系统的全局目标。
常见的分布式算法包括同步算法和异步算法。
同步算法是指智能体之间按照固定的时间步进行通信和计算;异步算法是指不同智能体之间的通信和计算时间不一定相同。
此外,常见的分布式算法还包括基于消息传递和共享内存的算法。
基于消息传递的算法是指智能体之间通过消息交换实现通信和合作;基于共享内存的算法是指智能体之间通过共享内存实现通信和合作。
2. 算法分类常见的分布式算法包括分布式图算法、分布式优化算法和分布式控制算法。
分布式图算法是指通过图模型来表示分布式系统,智能体之间的交互和协作通过图算法来实现。
其中,常见的图算法包括最短路径算法、连通性算法和拓扑排序算法等。
分布式优化算法是指通过优化问题来设计分布式算法。
其中,常见的优化问题包括最小生成树、最大流和最优策略等。
分布式控制算法是指通过控制理论和算法,设计和实现多智能体系统的控制和协作。
其中,常见的控制算法包括状态反馈控制、事件触发控制和模型预测控制等。
3. 应用案例在许多应用领域具有广泛的应用价值。
其中,一些典型的应用案例包括:(1)无人机编队控制。
无人机编队控制是指通过多个无人机之间的协作和控制,实现无人机编队的稳定运动和协同决策。
其中,分布式控制算法和机器学习算法是实现无人机编队控制的关键算法。
(2)智能交通系统。
智能交通系统是指通过智能交通管理、智能车辆控制和智能路网管理等手段,提高交通系统的效率和安全性。
FLP不可能原理
FLP不可能原理1. FLP impossibility背景FLP Impossibility(FLP不可能性)是分布式领域中⼀个⾮常著名的结果,该结果在专业领域被称为“定理”,其地位之⾼可见⼀斑。
该定理的论⽂是由Fischer, Lynch and Patterson三位作者于1985年发表,之后该论⽂毫⽆疑问得获得了Dijkstra奖。
顺便要提⼀句的是,Lynch是⼀位⾮常著名的分布式领域的⼥性科学家,研究遍布分布式的⽅⽅⾯⾯,对分布式领域有着极其卓越的贡献,其著有<<Distributed Algorithms>>⼀书,书中有⾮常严谨⽽简洁的逻辑讨论了许许多多的分布式算法。
FLP给出了⼀个令⼈吃惊的结论:在异步通信场景,即使只有⼀个进程失败,也没有任何算法能保证⾮失败进程达到⼀致性!因为同步通信中的⼀致性被证明是可以达到的,因此在之前⼀直有⼈尝试各种算法解决以异步环境的⼀致性问题,有个FLP的结果,这样的尝试终于有了答案。
FLP证明最难理解的是没有⼀个直观的sample,所有提到FLP的资料中也基本都回避了sample的要求。
究其原因,sample难以设计,除⾮你先设计⼏种⼀致性算法,并⽤FLP说明这些算法都是错误的。
2. 系统模型任何分布式算法或定理,都尤其对系统场景的假设,这称为系统模型。
FLP基于下⾯⼏点假设:异步通信与同步通信的最⼤区别是没有时钟、不能时间同步、不能使⽤超时、不能探测失败、消息可任意延迟、消息可乱序通信健壮只要进程⾮失败,消息虽会被⽆限延迟,但最终会被送达;并且消息仅会被送达⼀次(⽆重复)fail-stop模型进程失败如同宕机,不再处理任何消息。
相对Byzantine模型,不会产⽣错误消息失败进程数量最多⼀个进程失败在现实中,我们都使⽤TCP协议(保证了消息健壮、不重复、不乱序),每个节点都有NTP时钟同步(可以使⽤超时),纯的异步场景相对⽐较少。
计算机应用技术专业本科直博研究生培养方案(081203)
计算机应用技术专业本科直博研究生培养方案(081203)(信息科学技术学院)一、培养目标(一)较好地掌握马克思主义、毛泽东思想和中国特色社会主义理论体系,深入贯彻科学发展观,热爱祖国,遵纪守法,品德良好,学风严谨,身心健康,具有较强的事业心和献身精神,积极为社会主义现代化建设事业服务。
(二)在本门学科上掌握坚实宽广的基础理论和系统深入的专门知识,同时要掌握一定的相关学科知识,具有独立从事科学研究工作的能力,在科学或专门技术上做出创造性的成果。
(三)熟练掌握一门外语,能阅读本专业外文文献,具有运用外文写作和进行国际学术交流的能力。
二、培养方式与学习年限(一)培养方式本科直博研究生进入博士阶段的学习后,一方面进行必要的课程学习,夯实专业基础,拓展学术视野;另一方面开始着手科学研究。
对本科直博研究生的课程要重新设置,充分体现学科特色和培养需求;课程时间一般为一至二年。
以资格考核的结果作为能否进入下一阶段的依据。
通过资格考试的本科直博研究生进入科学研究和撰写博士学位论文阶段,学习年限一般为三到四年;未通过资格考试的可按照同专业硕士研究生的培养要求进行培养,时间一般为二到三年。
本科直博研究生,在科研能力、学位论文等方面的要求,均应高于同专业四年制博士研究生要求。
(二)学习年限本科直博研究生学习年限一般为五年至六年。
若在五年内不能完成预定的学业,可适当延长学习年限,但一般不超过六年。
三、主要研究方向1.计算机网络与通信2.网络与嵌入式系统3.普适计算与情景感知计算4.大数据分析与知识处理5.分布计算与云计算技术6.模式识别与机器学习7.模式识别与机器智能四、学分要求和课程设置(一)学分要求本科直博研究生课程包括学位公共课、学位基础课、学位专业课。
学位公共课包括政治理论、外国语等公共必修课程和公共选修课程,至少修读8学分(注:公共选修课指研究方法类课程。
如不选修则应以学位专业课相应学分抵充);学位基础课为学位必修课程,至少选修3门,不少于8学分;学位专业课包括以学科群为单位开设的专业必修课程和指向研究方向的专业选修课程,至少选修8门,不少于17学分。
遗传算法和粒子群算法结合代码python
遗传算法和粒子群算法结合代码python遗传算法和粒子群算法是两种非常实用的优化算法,在实际应用中具有广泛的适用性。
在本篇文章中,我们将介绍如何将遗传算法和粒子群算法结合起来,以实现更加高效和准确的优化过程。
具体来说,我们将以python语言为基础,编写代码来实现这种结合。
1. 遗传算法遗传算法是一种类似于进化过程的优化算法,它通过模拟生物进化过程来实现优化。
基本思路是将问题的可行解按照一定的方式编码成染色体序列,然后通过交叉、变异等操作产生新的染色体,按照适应度进行筛选,最终得出最优解。
在python中,我们可以使用遗传算法库DEAP(Distributed Evolutionary Algorithms in Python)快速地实现遗传算法。
以下是一段使用DEAP库实现遗传算法的代码:```import randomfrom deap import base, creator, tools# 定义一个求最小值的适应度函数def eval_func(individual):return sum(individual),# 创建遗传算法工具箱creator.create("FitnessMin", base.Fitness, weights=(-1.0,))creator.create("Individual", list, fitness=creator.FitnessMin)toolbox = base.Toolbox()# 注册染色体初始化函数(0或1)toolbox.register("attr_bool", random.randint, 0, 1)# 定义遗传算法实现函数def ga_algorithm():pop = toolbox.population(n=50)CXPB, MUTPB, NGEN = 0.5, 0.2, 50# 迭代遗传算法for gen in range(NGEN):# 交叉offspring = tools.cxBlend(pop, alpha=0.1)# 变异for mutant in offspring:if random.random() < MUTPB:toolbox.mutate(mutant)del mutant.fitness.values# 评估适应度fits = toolbox.map(toolbox.evaluate, offspring)for fit, ind in zip(fits, offspring):ind.fitness.values = fit# 选择pop = toolbox.select(offspring + pop, k=len(pop))gen_count += 1# 输出每代最小适应度和均值fits = [ind.fitness.values[0] for ind in pop]print("第 %d 代:最小适应度 %f, 平均适应度 %f" % (gen_count, min(fits), sum(fits) / len(pop)))# 返回最优解best_ind = tools.selBest(pop, 1)[0]print("最优解:", best_ind)```上述代码中,我们首先定义了一个求最小值的适应度函数,然后使用DEAP库创建了遗传算法工具箱。
DistributedSystemsPrinciplesandParadigms中文版书名分布
Marcus,Sten : Blueprints for High Availablity
Birman, Reliable Distributed Systems
Byzantine Failure问题:
Pease,M., “Reaching Agreement in the Presence of Faults” J.ACM,1980
Lamport,L.: “Byzantine Generals Problem. ” ACM T ng.syst. 1982
Shooman,M.L: Reliability of Computer Systems and Networks :Fault Tolerance, Analysis, and Design. 2002
Tanisch,P., “Atomic Commit in Concurrent Computing. ” IEEE Concurrency,2000
集中式体系结构:C/S
分布式体系结构:
点对点系统(peer-peer system):DHT(distributed hash table),例如Chord
随机图(random map)
混合体系结构:
协作分布式系统BitTorrent、Globule
自适应软件技术:
①要点分离
②计算映像
③基于组件的设计
Henning,M., “A New Approach to Object-Oriented Middleware”
第11章分布式文件系统
NFS (Network File System):远程访问模型
分布式算法详解
分布式算法详解Distributed algorithms are a crucial component of modern computing systems, allowing for complex tasks to be broken down and executed across multiple nodes in a network. These algorithms are designed to ensure efficiency, fault tolerance, and scalability in distributed systems. They play a foundational role in enabling the seamless functioning of applications that span across multiple servers and devices.分布式算法是现代计算系统的关键组成部分,允许将复杂任务分解并在网络中的多个节点上执行。
这些算法旨在确保分布系统的效率、容错性和可伸缩性。
它们在使跨多个服务器和设备的应用程序无缝运行方面发挥着基础性作用。
One of the key challenges faced by distributed algorithms is achieving consensus among the different nodes in the network. Consensus algorithms aim to ensure that all nodes agree on a certain value or decision, even in the presence of faults or failures. This is critical for maintaining the integrity and reliability of the system, especially in scenarios where nodes may fail or behave maliciously.分布式算法面临的关键挑战之一是在网络中的不同节点之间达成共识。
Consensus and Cooperation in Networked Multi-Agent Systems
Consensus and Cooperation in Networked Multi-Agent SystemsAlgorithms that provide rapid agreement and teamwork between all participants allow effective task performance by self-organizing networked systems.By Reza Olfati-Saber,Member IEEE,J.Alex Fax,and Richard M.Murray,Fellow IEEEABSTRACT|This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow,robustness to changes in network topology due to link/node failures,time-delays,and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided.Our analysis frame-work is based on tools from matrix theory,algebraic graph theory,and control theory.We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators,flocking,formation control,fast consensus in small-world networks,Markov processes and gossip-based algo-rithms,load balancing in networks,rendezvous in space, distributed sensor fusion in sensor networks,and belief propagation.We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms.A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions.Simu-lation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations.KEYWORDS|Consensus algorithms;cooperative control; flocking;graph Laplacians;information fusion;multi-agent systems;networked control systems;synchronization of cou-pled oscillators I.INTRODUCTIONConsensus problems have a long history in computer science and form the foundation of the field of distributed computing[1].Formal study of consensus problems in groups of experts originated in management science and statistics in1960s(see DeGroot[2]and references therein). The ideas of statistical consensus theory by DeGroot re-appeared two decades later in aggregation of information with uncertainty obtained from multiple sensors1[3]and medical experts[4].Distributed computation over networks has a tradition in systems and control theory starting with the pioneering work of Borkar and Varaiya[5]and Tsitsiklis[6]and Tsitsiklis,Bertsekas,and Athans[7]on asynchronous asymptotic agreement problem for distributed decision-making systems and parallel computing[8].In networks of agents(or dynamic systems),B con-sensus[means to reach an agreement regarding a certain quantity of interest that depends on the state of all agents.A B consensus algorithm[(or protocol)is an interaction rule that specifies the information exchange between an agent and all of its neighbors on the network.2 The theoretical framework for posing and solving consensus problems for networked dynamic systems was introduced by Olfati-Saber and Murray in[9]and[10] building on the earlier work of Fax and Murray[11],[12]. The study of the alignment problem involving reaching an agreement V without computing any objective functions V appeared in the work of Jadbabaie et al.[13].Further theoretical extensions of this work were presented in[14] and[15]with a look toward treatment of directed infor-mation flow in networks as shown in Fig.1(a).Manuscript received August8,2005;revised September7,2006.This work was supported in part by the Army Research Office(ARO)under Grant W911NF-04-1-0316. R.Olfati-Saber is with Dartmouth College,Thayer School of Engineering,Hanover,NH03755USA(e-mail:olfati@).J.A.Fax is with Northrop Grumman Corp.,Woodland Hills,CA91367USA(e-mail:alex.fax@).R.M.Murray is with the California Institute of Technology,Control and Dynamical Systems,Pasadena,CA91125USA(e-mail:murray@).Digital Object Identifier:10.1109/JPROC.2006.8872931This is known as sensor fusion and is an important application of modern consensus algorithms that will be discussed later.2The term B nearest neighbors[is more commonly used in physics than B neighbors[when applied to particle/spin interactions over a lattice (e.g.,Ising model).Vol.95,No.1,January2007|Proceedings of the IEEE2150018-9219/$25.00Ó2007IEEEThe common motivation behind the work in [5],[6],and [10]is the rich history of consensus protocols in com-puter science [1],whereas Jadbabaie et al.[13]attempted to provide a formal analysis of emergence of alignment in the simplified model of flocking by Vicsek et al.[16].The setup in [10]was originally created with the vision of de-signing agent-based amorphous computers [17],[18]for collaborative information processing in ter,[10]was used in development of flocking algorithms with guaranteed convergence and the capability to deal with obstacles and adversarial agents [19].Graph Laplacians and their spectral properties [20]–[23]are important graph-related matrices that play a crucial role in convergence analysis of consensus and alignment algo-rithms.Graph Laplacians are an important point of focus of this paper.It is worth mentioning that the second smallest eigenvalue of graph Laplacians called algebraic connectivity quantifies the speed of convergence of consensus algo-rithms.The notion of algebraic connectivity of graphs has appeared in a variety of other areas including low-density parity-check codes (LDPC)in information theory and com-munications [24],Ramanujan graphs [25]in number theory and quantum chaos,and combinatorial optimization prob-lems such as the max-cut problem [21].More recently,there has been a tremendous surge of interest V among researchers from various disciplines of engineering and science V in problems related to multia-gent networked systems with close ties to consensus prob-lems.This includes subjects such as consensus [26]–[32],collective behavior of flocks and swarms [19],[33]–[37],sensor fusion [38]–[40],random networks [41],[42],syn-chronization of coupled oscillators [42]–[46],algebraic connectivity 3of complex networks [47]–[49],asynchro-nous distributed algorithms [30],[50],formation control for multirobot systems [51]–[59],optimization-based co-operative control [60]–[63],dynamic graphs [64]–[67],complexity of coordinated tasks [68]–[71],and consensus-based belief propagation in Bayesian networks [72],[73].A detailed discussion of selected applications will be pre-sented shortly.In this paper,we focus on the work described in five key papers V namely,Jadbabaie,Lin,and Morse [13],Olfati-Saber and Murray [10],Fax and Murray [12],Moreau [14],and Ren and Beard [15]V that have been instrumental in paving the way for more recent advances in study of self-organizing networked systems ,or swarms .These networked systems are comprised of locally interacting mobile/static agents equipped with dedicated sensing,computing,and communication devices.As a result,we now have a better understanding of complex phenomena such as flocking [19],or design of novel information fusion algorithms for sensor networks that are robust to node and link failures [38],[72]–[76].Gossip-based algorithms such as the push-sum protocol [77]are important alternatives in computer science to Laplacian-based consensus algorithms in this paper.Markov processes establish an interesting connection between the information propagation speed in these two categories of algorithms proposed by computer scientists and control theorists [78].The contribution of this paper is to present a cohesive overview of the key results on theory and applications of consensus problems in networked systems in a unified framework.This includes basic notions in information consensus and control theoretic methods for convergence and performance analysis of consensus protocols that heavily rely on matrix theory and spectral graph theory.A byproduct of this framework is to demonstrate that seem-ingly different consensus algorithms in the literature [10],[12]–[15]are closely related.Applications of consensus problems in areas of interest to researchers in computer science,physics,biology,mathematics,robotics,and con-trol theory are discussed in this introduction.A.Consensus in NetworksThe interaction topology of a network of agents is rep-resented using a directed graph G ¼ðV ;E Þwith the set of nodes V ¼f 1;2;...;n g and edges E V ÂV .TheFig.1.Two equivalent forms of consensus algorithms:(a)a networkof integrator agents in which agent i receives the state x j of its neighbor,agent j ,if there is a link ði ;j Þconnecting the two nodes;and (b)the block diagram for a network of interconnecteddynamic systems all with identical transfer functions P ðs Þ¼1=s .The collective networked system has a diagonal transfer function and is a multiple-input multiple-output (MIMO)linear system.3To be defined in Section II-A.Olfati-Saber et al.:Consensus and Cooperation in Networked Multi-Agent Systems216Proceedings of the IEEE |Vol.95,No.1,January 2007neighbors of agent i are denoted by N i ¼f j 2V :ði ;j Þ2E g .According to [10],a simple consensus algorithm to reach an agreement regarding the state of n integrator agents with dynamics _x i ¼u i can be expressed as an n th-order linear system on a graph_x i ðt Þ¼X j 2N ix j ðt ÞÀx i ðt ÞÀÁþb i ðt Þ;x i ð0Þ¼z i2R ;b i ðt Þ¼0:(1)The collective dynamics of the group of agents following protocol (1)can be written as_x ¼ÀLx(2)where L ¼½l ij is the graph Laplacian of the network and itselements are defined as follows:l ij ¼À1;j 2N i j N i j ;j ¼i :&(3)Here,j N i j denotes the number of neighbors of node i (or out-degree of node i ).Fig.1shows two equivalent forms of the consensus algorithm in (1)and (2)for agents with a scalar state.The role of the input bias b in Fig.1(b)is defined later.According to the definition of graph Laplacian in (3),all row-sums of L are zero because of P j l ij ¼0.Therefore,L always has a zero eigenvalue 1¼0.This zero eigenvalues corresponds to the eigenvector 1¼ð1;...;1ÞT because 1belongs to the null-space of L ðL 1¼0Þ.In other words,an equilibrium of system (2)is a state in the form x üð ;...; ÞT ¼ 1where all nodes agree.Based on ana-lytical tools from algebraic graph theory [23],we later show that x Ãis a unique equilibrium of (2)(up to a constant multiplicative factor)for connected graphs.One can show that for a connected network,the equilibrium x üð ;...; ÞT is globally exponentially stable.Moreover,the consensus value is ¼1=n P i z i that is equal to the average of the initial values.This im-plies that irrespective of the initial value of the state of each agent,all agents reach an asymptotic consensus regarding the value of the function f ðz Þ¼1=n P i z i .While the calculation of f ðz Þis simple for small net-works,its implications for very large networks is more interesting.For example,if a network has n ¼106nodes and each node can only talk to log 10ðn Þ¼6neighbors,finding the average value of the initial conditions of the nodes is more complicated.The role of protocol (1)is to provide a systematic consensus mechanism in such a largenetwork to compute the average.There are a variety of functions that can be computed in a similar fashion using synchronous or asynchronous distributed algorithms (see [10],[28],[30],[73],and [76]).B.The f -Consensus Problem and Meaning of CooperationTo understand the role of cooperation in performing coordinated tasks,we need to distinguish between un-constrained and constrained consensus problems.An unconstrained consensus problem is simply the alignment problem in which it suffices that the state of all agents asymptotically be the same.In contrast,in distributed computation of a function f ðz Þ,the state of all agents has to asymptotically become equal to f ðz Þ,meaning that the consensus problem is constrained.We refer to this con-strained consensus problem as the f -consensus problem .Solving the f -consensus problem is a cooperative task and requires willing participation of all the agents.To demonstrate this fact,suppose a single agent decides not to cooperate with the rest of the agents and keep its state unchanged.Then,the overall task cannot be performed despite the fact that the rest of the agents reach an agree-ment.Furthermore,there could be scenarios in which multiple agents that form a coalition do not cooperate with the rest and removal of this coalition of agents and their links might render the network disconnected.In a dis-connected network,it is impossible for all nodes to reach an agreement (unless all nodes initially agree which is a trivial case).From the above discussion,cooperation can be infor-mally interpreted as B giving consent to providing one’s state and following a common protocol that serves the group objective.[One might think that solving the alignment problem is not a cooperative task.The justification is that if a single agent (called a leader)leaves its value unchanged,all others will asymptotically agree with the leader according to the consensus protocol and an alignment is reached.However,if there are multiple leaders where two of whom are in disagreement,then no consensus can be asymptot-ically reached.Therefore,alignment is in general a coop-erative task as well.Formal analysis of the behavior of systems that involve more than one type of agent is more complicated,partic-ularly,in presence of adversarial agents in noncooperative games [79],[80].The focus of this paper is on cooperative multi-agent systems.C.Iterative Consensus and Markov ChainsIn Section II,we show how an iterative consensus algorithm that corresponds to the discrete-time version of system (1)is a Markov chainðk þ1Þ¼ ðk ÞP(4)Olfati-Saber et al.:Consensus and Cooperation in Networked Multi-Agent SystemsVol.95,No.1,January 2007|Proceedings of the IEEE217with P ¼I À L and a small 90.Here,the i th element of the row vector ðk Þdenotes the probability of being in state i at iteration k .It turns out that for any arbitrary graph G with Laplacian L and a sufficiently small ,the matrix P satisfies the property Pj p ij ¼1with p ij !0;8i ;j .Hence,P is a valid transition probability matrix for the Markov chain in (4).The reason matrix theory [81]is so widely used in analysis of consensus algorithms [10],[12]–[15],[64]is primarily due to the structure of P in (4)and its connection to graphs.4There are interesting connections between this Markov chain and the speed of information diffusion in gossip-based averaging algorithms [77],[78].One of the early applications of consensus problems was dynamic load balancing [82]for parallel processors with the same structure as system (4).To this date,load balancing in networks proves to be an active area of research in computer science.D.ApplicationsMany seemingly different problems that involve inter-connection of dynamic systems in various areas of science and engineering happen to be closely related to consensus problems for multi-agent systems.In this section,we pro-vide an account of the existing connections.1)Synchronization of Coupled Oscillators:The problem of synchronization of coupled oscillators has attracted numer-ous scientists from diverse fields including physics,biology,neuroscience,and mathematics [83]–[86].This is partly due to the emergence of synchronous oscillations in coupled neural oscillators.Let us consider the generalized Kuramoto model of coupled oscillators on a graph with dynamics_i ¼ Xj 2N isin ð j À i Þþ!i (5)where i and !i are the phase and frequency of the i thoscillator.This model is the natural nonlinear extension of the consensus algorithm in (1)and its linearization around the aligned state 1¼...¼ n is identical to system (2)plus a nonzero input bias b i ¼ð!i À"!Þ= with "!¼1=n P i !i after a change of variables x i ¼ð i À"!t Þ= .In [43],Sepulchre et al.show that if is sufficiently large,then for a network with all-to-all links,synchroni-zation to the aligned state is globally achieved for all ini-tial states.Recently,synchronization of networked oscillators under variable time-delays was studied in [45].We believe that the use of convergence analysis methods that utilize the spectral properties of graph Laplacians willshed light on performance and convergence analysis of self-synchrony in oscillator networks [42].2)Flocking Theory:Flocks of mobile agents equipped with sensing and communication devices can serve as mobile sensor networks for massive distributed sensing in an environment [87].A theoretical framework for design and analysis of flocking algorithms for mobile agents with obstacle-avoidance capabilities is developed by Olfati-Saber [19].The role of consensus algorithms in particle-based flocking is for an agent to achieve velocity matching with respect to its neighbors.In [19],it is demonstrated that flocks are networks of dynamic systems with a dynamic topology.This topology is a proximity graph that depends on the state of all agents and is determined locally for each agent,i.e.,the topology of flocks is a state-dependent graph.The notion of state-dependent graphs was introduced by Mesbahi [64]in a context that is independent of flocking.3)Fast Consensus in Small-Worlds:In recent years,network design problems for achieving faster consensus algorithms has attracted considerable attention from a number of researchers.In Xiao and Boyd [88],design of the weights of a network is considered and solved using semi-definite convex programming.This leads to a slight increase in algebraic connectivity of a network that is a measure of speed of convergence of consensus algorithms.An alternative approach is to keep the weights fixed and design the topology of the network to achieve a relatively high algebraic connectivity.A randomized algorithm for network design is proposed by Olfati-Saber [47]based on random rewiring idea of Watts and Strogatz [89]that led to creation of their celebrated small-world model .The random rewiring of existing links of a network gives rise to considerably faster consensus algorithms.This is due to multiple orders of magnitude increase in algebraic connectivity of the network in comparison to a lattice-type nearest-neighbort graph.4)Rendezvous in Space:Another common form of consensus problems is rendezvous in space [90],[91].This is equivalent to reaching a consensus in position by a num-ber of agents with an interaction topology that is position induced (i.e.,a proximity graph).We refer the reader to [92]and references therein for a detailed discussion.This type of rendezvous is an unconstrained consensus problem that becomes challenging under variations in the network topology.Flocking is somewhat more challenging than rendezvous in space because it requires both interagent and agent-to-obstacle collision avoidance.5)Distributed Sensor Fusion in Sensor Networks:The most recent application of consensus problems is distrib-uted sensor fusion in sensor networks.This is done by posing various distributed averaging problems require to4In honor of the pioneering contributions of Oscar Perron (1907)to the theory of nonnegative matrices,were refer to P as the Perron Matrix of graph G (See Section II-C for details).Olfati-Saber et al.:Consensus and Cooperation in Networked Multi-Agent Systems218Proceedings of the IEEE |Vol.95,No.1,January 2007implement a Kalman filter [38],[39],approximate Kalman filter [74],or linear least-squares estimator [75]as average-consensus problems .Novel low-pass and high-pass consensus filters are also developed that dynamically calculate the average of their inputs in sensor networks [39],[93].6)Distributed Formation Control:Multivehicle systems are an important category of networked systems due to their commercial and military applications.There are two broad approaches to distributed formation control:i)rep-resentation of formations as rigid structures [53],[94]and the use of gradient-based controls obtained from their structural potentials [52]and ii)representation of form-ations using the vectors of relative positions of neighboring vehicles and the use of consensus-based controllers with input bias.We discuss the later approach here.A theoretical framework for design and analysis of distributed controllers for multivehicle formations of type ii)was developed by Fax and Murray [12].Moving in formation is a cooperative task and requires consent and collaboration of every agent in the formation.In [12],graph Laplacians and matrix theory were extensively used which makes one wonder whether relative-position-based formation control is a consensus problem.The answer is yes.To see this,consider a network of self-interested agents whose individual desire is to minimize their local cost U i ðx Þ¼Pj 2N i k x j Àx i Àr ij k 2via a distributed algorithm (x i is the position of vehicle i with dynamics _x i ¼u i and r ij is a desired intervehicle relative-position vector).Instead,if the agents use gradient-descent algorithm on the collective cost P n i ¼1U i ðx Þusing the following protocol:_x i ¼Xj 2N iðx j Àx i Àr ij Þ¼Xj 2N iðx j Àx i Þþb i (6)with input bias b i ¼Pj 2N i r ji [see Fig.1(b)],the objective of every agent will be achieved.This is the same as the consensus algorithm in (1)up to the nonzero bias terms b i .This nonzero bias plays no role in stability analysis of sys-tem (6).Thus,distributed formation control for integrator agents is a consensus problem.The main contribution of the work by Fax and Murray is to extend this scenario to the case where all agents are multiinput multioutput linear systems _x i ¼Ax i þBu i .Stability analysis of relative-position-based formation control for multivehicle systems is extensively covered in Section IV.E.OutlineThe outline of the paper is as follows.Basic concepts and theoretical results in information consensus are presented in Section II.Convergence and performance analysis of consensus on networks with switching topology are given in Section III.A theoretical framework for cooperative control of formations of networked multi-vehicle systems is provided in Section IV.Some simulationresults related to consensus in complex networks including small-worlds are presented in Section V.Finally,some concluding remarks are stated in Section VI.RMATION CONSENSUSConsider a network of decision-making agents with dynamics _x i ¼u i interested in reaching a consensus via local communication with their neighbors on a graph G ¼ðV ;E Þ.By reaching a consensus,we mean asymptot-ically converging to a one-dimensional agreement space characterized by the following equation:x 1¼x 2¼...¼x n :This agreement space can be expressed as x ¼ 1where 1¼ð1;...;1ÞT and 2R is the collective decision of the group of agents.Let A ¼½a ij be the adjacency matrix of graph G .The set of neighbors of a agent i is N i and defined byN i ¼f j 2V :a ij ¼0g ;V ¼f 1;...;n g :Agent i communicates with agent j if j is a neighbor of i (or a ij ¼0).The set of all nodes and their neighbors defines the edge set of the graph as E ¼fði ;j Þ2V ÂV :a ij ¼0g .A dynamic graph G ðt Þ¼ðV ;E ðt ÞÞis a graph in which the set of edges E ðt Þand the adjacency matrix A ðt Þare time-varying.Clearly,the set of neighbors N i ðt Þof every agent in a dynamic graph is a time-varying set as well.Dynamic graphs are useful for describing the network topology of mobile sensor networks and flocks [19].It is shown in [10]that the linear system_x i ðt Þ¼Xj 2N ia ij x j ðt ÞÀx i ðt ÞÀÁ(7)is a distributed consensus algorithm ,i.e.,guarantees con-vergence to a collective decision via local interagent interactions.Assuming that the graph is undirected (a ij ¼a ji for all i ;j ),it follows that the sum of the state of all nodes is an invariant quantity,or P i _xi ¼0.In particular,applying this condition twice at times t ¼0and t ¼1gives the following result¼1n Xix i ð0Þ:In other words,if a consensus is asymptotically reached,then necessarily the collective decision is equal to theOlfati-Saber et al.:Consensus and Cooperation in Networked Multi-Agent SystemsVol.95,No.1,January 2007|Proceedings of the IEEE219average of the initial state of all nodes.A consensus algo-rithm with this specific invariance property is called an average-consensus algorithm [9]and has broad applications in distributed computing on networks (e.g.,sensor fusion in sensor networks).The dynamics of system (7)can be expressed in a compact form as_x ¼ÀLx(8)where L is known as the graph Laplacian of G .The graph Laplacian is defined asL ¼D ÀA(9)where D ¼diag ðd 1;...;d n Þis the degree matrix of G with elements d i ¼Pj ¼i a ij and zero off-diagonal elements.By definition,L has a right eigenvector of 1associated with the zero eigenvalue 5because of the identity L 1¼0.For the case of undirected graphs,graph Laplacian satisfies the following sum-of-squares (SOS)property:x T Lx ¼12Xði ;j Þ2Ea ij ðx j Àx i Þ2:(10)By defining a quadratic disagreement function as’ðx Þ¼12x T Lx(11)it becomes apparent that algorithm (7)is the same as_x ¼Àr ’ðx Þor the gradient-descent algorithm.This algorithm globallyasymptotically converges to the agreement space provided that two conditions hold:1)L is a positive semidefinite matrix;2)the only equilibrium of (7)is 1for some .Both of these conditions hold for a connected graph and follow from the SOS property of graph Laplacian in (10).Therefore,an average-consensus is asymptotically reached for all initial states.This fact is summarized in the following lemma.Lemma 1:Let G be a connected undirected graph.Then,the algorithm in (7)asymptotically solves an average-consensus problem for all initial states.A.Algebraic Connectivity and Spectral Propertiesof GraphsSpectral properties of Laplacian matrix are instrumen-tal in analysis of convergence of the class of linear consensus algorithms in (7).According to Gershgorin theorem [81],all eigenvalues of L in the complex plane are located in a closed disk centered at Áþ0j with a radius of Á¼max i d i ,i.e.,the maximum degree of a graph.For undirected graphs,L is a symmetric matrix with real eigenvalues and,therefore,the set of eigenvalues of L can be ordered sequentially in an ascending order as0¼ 1 2 ÁÁÁ n 2Á:(12)The zero eigenvalue is known as the trivial eigenvalue of L .For a connected graph G , 290(i.e.,the zero eigenvalue is isolated).The second smallest eigenvalue of Laplacian 2is called algebraic connectivity of a graph [20].Algebraic connectivity of the network topology is a measure of performance/speed of consensus algorithms [10].Example 1:Fig.2shows two examples of networks of integrator agents with different topologies.Both graphs are undirected and have 0–1weights.Every node of the graph in Fig.2(a)is connected to its 4nearest neighbors on a ring.The other graph is a proximity graph of points that are distributed uniformly at random in a square.Every node is connected to all of its spatial neighbors within a closed ball of radius r 90.Here are the important degree information and Laplacian eigenvalues of these graphsa Þ 1¼0; 2¼0:48; n ¼6:24;Á¼4b Þ 1¼0; 2¼0:25; n ¼9:37;Á¼8:(13)In both cases, i G 2Áfor all i .B.Convergence Analysis for Directed Networks The convergence analysis of the consensus algorithm in (7)is equivalent to proving that the agreement space characterized by x ¼ 1; 2R is an asymptotically stable equilibrium of system (7).The stability properties of system (7)is completely determined by the location of the Laplacian eigenvalues of the network.The eigenvalues of the adjacency matrix are irrelevant to the stability analysis of system (7),unless the network is k -regular (all of its nodes have the same degree k ).The following lemma combines a well-known rank property of graph Laplacians with Gershgorin theorem to provide spectral characterization of Laplacian of a fixed directed network G .Before stating the lemma,we need to define the notion of strong connectivity of graphs.A graph5These properties were discussed earlier in the introduction for graphs with 0–1weights.Olfati-Saber et al.:Consensus and Cooperation in Networked Multi-Agent Systems220Proceedings of the IEEE |Vol.95,No.1,January 2007。
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provide the ability to sample the environment adaptively in space and time. By identifying evolving temperature and current gradients with higher accuracy and resolution than current static sensors, this technology could lead to the development and validation of improved oceanographic models. Optimal sensor allocation and coverage problems A fundamental prototype problem in this paper is that of characterizing and optimizing notions of quality-of-service provided by an adaptive sensor network in a dynamic environment. To this goal, we introduce a notion of sensor coverage that formalizes an optimal sensor placement problem. This spatial resource allocation problem is the subject of a discipline called locational optimization [5], [6], [7], [8], [9]. Locational optimization problems pervade a broad spectrum of scientific disciplines. Biologists rely on locational optimization tools to study how animals share territory and to characterize the behavior of animal groups obeying the following interaction rule: each animal establishes a region of dominance and moves toward its center. Locational optimization problems are spatial resource allocation problems (e.g., where to place mailboxes in a city or cache servers on the internet) and play a central role in quantization and information theory (e.g., how to design a minimumdistortion fixed-rate vector quantizer). Other technologies affected by locational optimization include mesh and grid optimization methods, clustering analysis, data compression, and statistical pattern recognition. Because locational optimization problems are so widely studied, it is not surprising that methods are indeed available to tackle coverage problems; see [5], [8], [10], [9]. However, most currently-available algorithms are not applicable to mobile sensing networks because they inherently assume a centralized computation for a limited size problem in a known static environment. This is not the case in multivehicle networks which, instead, rely on a distributed communication and computation architecture. Although an ad-hoc wireless network provides the ability to share some information, no global omniscient leader might be present to coordinate the group. The inherent spatially-distributed nature and limited communication capabilities of a mobile network invalidate classic approaches to algorithm design. Distributed asynchronous algorithms for coverage control In this paper we design coordination algorithms implementable by a multi-vehicle network with limited sensing and communication capabilities. Our approach is related to the classic Lloyd algorithm from quantization theory; see [11] for a reprint of the original report and [12] for a historical overview. We present Lloyd descent algorithms
多元算力 英语
多元算力英语Computational power, the cornerstone of modern digital infrastructure, has evolved significantly over the years. It is no longer confined to a single, monolithic entity but rather encompasses a diverse array of resources, techniques, and technologies that collectively form what we term as "multifaceted computational power." This concept represents a paradigm shift in how we harness, allocate, and utilize computing capabilities, enabling unprecedented advancements across various domains. This essay delves into the essence of multifaceted computational power, examining its key components, implications, and the transformative role it plays in today's data-driven world.Firstly, at the core of multifaceted computational power lies the notion of heterogeneity. It transcends the traditional boundaries of centralized, uniform hardware architectures and embraces a diverse ecosystem of devices, from high-performance supercomputers and cloud servers to edge devices like smartphones and Internet of Things (IoT) sensors. This diversity extends not only to the types ofdevices but also to their computational capabilities, energy efficiency, and specialized functions. For instance, Graphics Processing Units (GPUs) excel at parallel processing tasks such as deep learning, while Field-Programmable Gate Arrays (FPGAs) offer reconfigurability for customized, low-latency applications. The heterogeneous nature of multifaceted computational power allows for the most suitable resource to be allocated to each task, enhancing overall efficiency and performance.Secondly, this paradigm is inherently dynamic and distributed. Cloud computing, with its on-demand access to virtually unlimited computational resources, enables scalability and flexibility unattainable in conventional setups. Resources can be provisioned or decommissioned rapidly in response to fluctuating workloads, ensuring optimal utilization and cost-effectiveness. Moreover, distributed computing frameworks like Apache Hadoop and Spark facilitate the parallel processing of massive datasets across a network of interconnected devices, breaking down complex problems into smaller, more manageable chunks. This distributed nature not onlyaccelerates computation but also enhances fault tolerance and resilience, as the failure of a single node does not compromise the entire system.The advent of multifaceted computational power has profound implications for numerous sectors. In scientific research, it accelerates discoveries by expediting simulations, data analysis, and model training. For instance, Folding@Home utilizes idle computational power from millions of devices worldwide to simulate protein folding, advancing our understanding of diseases like Alzheimer's and cancer. In finance, high-frequency trading relies on ultra-low latency computing to execute trades within microseconds, exploiting fleeting market opportunities. In healthcare, wearable devices and IoT sensors generate vast amounts of patient data, which, when processed using distributed algorithms, can facilitate real-time monitoring, early diagnosis, and personalized treatment plans.Furthermore, multifaceted computational power fuels innovation in emerging technologies such as artificial intelligence, blockchain, and quantum computing. AI models, particularly deep neural networks, demand immensecomputational resources for training and inference. The ability to harness diverse, scalable resources accelerates AI development and deployment, driving advancements in fields like autonomous vehicles, natural language processing, and image recognition. Similarly, blockchain networks rely on distributed computing to maintain consensus and ensure transactional integrity, while quantum computing, still in its nascent stage, promises exponential speedups for specific computational problems through the exploitation of quantum entanglement and superposition.In conclusion, multifaceted computational power represents a fundamental shift in how we approach problem-solving in the digital realm. By embracing heterogeneity, dynamism, and distribution, it unlocks unprecedented efficiency, scalability, and innovation across a multitude of sectors. As technology continues to evolve, it is crucial that we harness the full potential of this multifaceted landscape, fostering a future where computational power is seamlessly integrated, accessible, and tailored to meet the ever-growing demands of our data-driven society.。
deap gp参数
DEAP GP参数介绍DEAP(Distributed Evolutionary Algorithms in Python)是一个用于快速原型设计和测试进化算法的Python框架。
它提供了一系列用于解决优化问题的进化算法的实现,其中之一就是遗传编程(Genetic Programming,GP)。
GP是一种通过模拟自然进化过程来生成计算机程序的方法。
DEAP GP参数是指在使用DEAP框架进行GP算法实现时,所需要设置的相关参数。
本文将详细介绍DEAP GP算法中的常用参数,包括遗传编程的基本概念、参数的作用、参数的取值范围以及参数的调优方法。
遗传编程基本概念遗传编程是一种通过模拟自然进化过程来生成计算机程序的方法。
它将计算机程序表示为一组符号,通过遗传算子(交叉和变异)对这些符号进行操作,以产生更好的程序。
遗传编程的基本概念包括:•个体(Individual):个体是遗传编程中的一个计算机程序,它由一组符号组成。
每个符号都代表了程序中的一个操作或变量。
•种群(Population):种群是由多个个体组成的集合。
初始种群中的个体是随机生成的,后续通过进化算子进行交叉和变异操作来生成新的个体。
•适应度函数(Fitness Function):适应度函数用于评估个体的适应度,即个体在解决问题上的表现好坏。
适应度函数的取值范围通常是一个实数,表示个体的适应程度。
•选择(Selection):选择操作用于从种群中选择适应度高的个体,作为下一代种群的父代。
•交叉(Crossover):交叉操作用于将两个父代个体的符号进行组合,生成新的子代个体。
交叉操作可以通过不同的方式进行,例如单点交叉、多点交叉等。
•变异(Mutation):变异操作用于对个体的符号进行随机变换,引入新的基因信息。
变异操作可以增加种群的多样性,避免陷入局部最优解。
DEAP GP参数DEAP GP算法中的参数可以分为两类:算法参数和问题参数。
DEAP分析过程及结果解释
DEAP分析过程及结果解释DEAP(Distributed Evolutionary Algorithms in Python)是一种基于Python语言开发的进化算法库,用于解决优化问题。
DEAP库使用了分布式计算模型,能够在多个计算节点上实现并行计算,提高算法的效率和性能。
DEAP提供了大量的进化算法模板和工具函数,方便用户快速构建自己的优化问题,并进行求解。
DEAP的分析过程主要包括以下几个步骤:1.定义问题:在使用DEAP进行优化之前,首先需要明确优化问题的目标和约束条件。
这包括定义问题的适应度函数以及变量的范围和类型。
DEAP提供了多种类型和范围的变量定义,如实数、整数、布尔型等,用户可以根据具体问题选择合适的变量类型。
2.编码个体:使用DEAP的编码工具,将问题的变量编码成个体。
个体是优化问题求解的基本单位,包含了问题的所有变量信息。
3.生成初始种群:通过DEAP的种群生成工具,生成初始的种群。
种群是由多个个体组成的集合,初始种群的个体数量可以用户自定义。
种群的生成可以使用随机生成器,也可以根据先验知识进行初始化。
4.指定进化算法参数和配置:在DEAP中,用户可以根据具体问题选择合适的进化算法模板,并指定相应的参数和配置。
DEAP提供了多种经典的进化算法模板,如遗传算法(GA)、差分进化算法(DE)、粒子群优化(PSO)等。
用户可以根据问题的特点选择最适合的算法模板,并对其进行参数优化。
5.进化迭代:在指定了进化算法的参数和配置之后,DEAP会自动迭代执行进化过程。
在每一代的迭代过程中,DEAP会根据选择、交叉、变异等算子对种群中的个体进行操作,从而产生下一代个体。
此过程重复进行,直到满足终止条件为止。
6.结果分析和后处理:进化算法迭代结束后,DEAP会返回优化的最优个体或种群信息。
在得到优化结果之后,用户可以进行结果分析和后处理。
DEAP提供了多种工具函数和方法,用于统计和可视化优化结果,如绘制适应度曲线、计算种群多样性等。
基于节点度优化的无线mesh网络拓扑控制算法
基于节点度优化的无线mesh网络拓扑控制算法谢琦;黄廷磊【摘要】由于网络节点之间资源竞争以及无线信号干扰增大,无线mesh网络的吞吐性能亟待得到进一步的优化.针对此问题,给出了一种基于节点度优化的拓扑控制算法.算法采用中继区方式构建网络逻辑邻域拓扑,利用RNG方法对网络拓扑进行局部节点度优化.仿真结果表明,该算法保证了网络的连通性,有效地提升网络的吞吐量.%Because of the increasing resources competition of network nodes and wireless signal interference, wireless mesh network throughput must be further optimized. To solve this problem > a topological control algorithm of wireless mesh networks based on proximity graph is presented. The algorithm introduces the relay region to construct network logical neighborhood topology and use s the RNG method to optimize local node degree of network topology. Simulation results show that the method not only ensures the network connectivity but also enhances the network throughput effectively.【期刊名称】《桂林电子科技大学学报》【年(卷),期】2012(032)003【总页数】4页(P233-236)【关键词】无线mesh网络;拓扑控制;节点度优化;吞吐量【作者】谢琦;黄廷磊【作者单位】桂林电子科技大学计算机科学与工程学院,广西桂林541004;桂林电子科技大学计算机科学与工程学院,广西桂林541004【正文语种】中文【中图分类】TP393.02无线mesh网络(wireless mesh networks,简称WMN)是一种新兴无线技术,它具有网络结构灵活、易于部署和配置以及网状连接多点到多点通信等特点。
神经网络同步与多智能体一致性问题研究的开题报告
神经网络同步与多智能体一致性问题研究的开题报告一、研究背景及意义随着科技的发展,神经网络和多智能体技术在各种领域中应用越来越广泛。
神经网络主要用于数据挖掘、图像处理、模式识别等方面,而多智能体则可以应用于交通调度、无人机控制、机器人协同等方面。
但是,在实际应用过程中,神经网络同步和多智能体一致性问题经常会出现,例如神经网络同步不完全会导致不能准确地预测结果,而多智能体没有达到一致性则会降低整个系统的效率。
因此,研究神经网络同步和多智能体一致性问题对于提高系统的性能具有重要意义。
二、研究内容和方法本文拟重点研究神经网络同步和多智能体一致性问题。
具体研究内容包括:(1)探究神经网络同步不完全的原因和机理,分析同步不完全对系统影响,并提出改进方法;(2)深入研究多智能体一致性的实现原理和机制,针对多智能体系统的特点,设计实用的一致性算法。
本文将采用数学建模和仿真实验相结合的方法进行研究。
首先,通过建立神经网络同步和多智能体一致性的数学模型,分析同步/一致性问题的本质,找出问题所在。
其次,利用MATLAB等仿真工具,对不同算法进行仿真模拟,验证算法的有效性和性能。
最后,通过实验对算法的性能进行测试验证以及评估,得出综合结论。
三、研究预期成果通过本研究,预期得到以下成果:(1)发现神经网络同步不完全的原因和机理,提出相应的改进方法,进一步提高神经网络的性能。
(2)研究多智能体一致性的实现原理和机制,提出实用的一致性算法,进一步提高多智能体系统的效率。
(3)实验验证算法的有效性和性能,得出综合结论,对实际应用具有指导意义。
四、研究进度安排第一年:1、文献综述阶段:查阅关于神经网络同步和多智能体一致性的文献,建立研究框架。
2、数学模型建立阶段:根据文献综述,建立神经网络同步和多智能体一致性的数学模型。
3、算法研究阶段: 在数学模型的基础上,设计、实现和优化神经网络同步和多智能体一致性算法。
第二年:4、仿真和实验阶段:利用MATLAB等工具进行仿真模拟,验证算法的有效性和性能,并对算法进行测试和改进。
国际学术会议影响因子
Estimated impact of publication venues in Computer Science (higher is better) - May 2003 (CiteSeer)Generated from documents in the CiteSeer database. This analysis does not include citations where one or more authors of the citing and cited articles match. This list is automatically generated and may contain errors. Only venues with at least 25 articles are shown.Impact is estimated using the average citation rate, where citations are normalized using the average citation rate for all articles in a given year, and transformed using ln (n+1) where n is the number of citations.Publication details obtained from DBLP by Michael Ley. Only venues contained in DBLP are included.1. OSDI: 3.31 (top 0.08%)2. USENIX Symposium on Internet Technologies and Systems:3.23 (top 0.16%)3. PLDI: 2.89 (top 0.24%)4. SIGCOMM: 2.79 (top 0.32%)5. MOBICOM: 2.76 (top 0.40%)6. ASPLOS: 2.70 (top 0.49%)7. USENIX Annual Technical Conference: 2.64 (top 0.57%)8. TOCS: 2.56 (top 0.65%)9. SIGGRAPH: 2.53 (top 0.73%)10. JAIR: 2.45 (top 0.81%)11. SOSP: 2.41 (top 0.90%)12. MICRO: 2.31 (top 0.98%)13. POPL: 2.26 (top 1.06%)14. PPOPP: 2.22 (top 1.14%)15. Machine Learning: 2.20 (top 1.22%)16. 25 Years ISCA: Retrospectives and Reprints: 2.19 (top 1.31%)17. WWW8 / Computer Networks: 2.17 (top 1.39%)18. Computational Linguistics: 2.16 (top 1.47%)19. JSSPP: 2.15 (top 1.55%)20. VVS: 2.14 (top 1.63%)21. FPCA: 2.12 (top 1.71%)22. LISP and Functional Programming: 2.12 (top 1.80%)23. ICML: 2.12 (top 1.88%)24. Data Mining and Knowledge Discovery: 2.08 (top 1.96%)25. SI3D: 2.06 (top 2.04%)26. ICSE - Future of SE Track: 2.05 (top 2.12%)27. IEEE/ACM Transactions on Networking: 2.05 (top 2.21%)28. OOPSLA/ECOOP: 2.05 (top 2.29%)29. WWW9 / Computer Networks: 2.02 (top 2.37%)30. Workshop on Workstation Operating Systems: 2.01 (top 2.45%)31. Journal of Computer Security: 2.00 (top 2.53%)32. TOSEM: 1.99 (top 2.62%)33. Workshop on Parallel and Distributed Debugging: 1.99 (top 2.70%)34. Workshop on Hot Topics in Operating Systems: 1.99 (top 2.78%)35. WebDB (Informal Proceedings): 1.99 (top 2.86%)36. WWW5 / Computer Networks: 1.97 (top 2.94%)37. Journal of Cryptology: 1.97 (top 3.03%)38. CSFW: 1.96 (top 3.11%)39. ECOOP: 1.95 (top 3.19%)40. Evolutionary Computation: 1.94 (top 3.27%)41. TOPLAS: 1.92 (top 3.35%)42. SIGSOFT FSE: 1.88 (top 3.43%)43. CA V: 1.88 (top 3.52%)44. AAAI/IAAI, Vol. 1: 1.87 (top 3.60%)45. PODS: 1.86 (top 3.68%)46. Artificial Intelligence: 1.85 (top 3.76%)47. NOSSDA V: 1.85 (top 3.84%)48. OOPSLA: 1.84 (top 3.93%)49. ACM Conference on Computer and Communications Security: 1.82 (top 4.01%)50. IJCAI (1): 1.82 (top 4.09%)51. VLDB Journal: 1.81 (top 4.17%)52. TODS: 1.81 (top 4.25%)53. USENIX Winter: 1.80 (top 4.34%)54. HPCA: 1.79 (top 4.42%)55. LICS: 1.79 (top 4.50%)56. JLP: 1.78 (top 4.58%)57. WWW6 / Computer Networks: 1.78 (top 4.66%)58. ICCV: 1.78 (top 4.75%)59. IEEE Real-Time Systems Symposium: 1.78 (top 4.83%)60. AES Candidate Conference: 1.77 (top 4.91%)61. KR: 1.76 (top 4.99%)62. TISSEC: 1.76 (top 5.07%)63. ACM Conference on Electronic Commerce: 1.75 (top 5.15%)64. TOIS: 1.75 (top 5.24%)65. PEPM: 1.74 (top 5.32%)66. SIGMOD Conference: 1.74 (top 5.40%)67. Formal Methods in System Design: 1.74 (top 5.48%)68. Mobile Agents: 1.73 (top 5.56%)69. REX Workshop: 1.73 (top 5.65%)70. NMR: 1.73 (top 5.73%)71. Computing Systems: 1.72 (top 5.81%)72. LOPLAS: 1.72 (top 5.89%)73. STOC: 1.69 (top 5.97%)74. Distributed Computing: 1.69 (top 6.06%)75. KDD: 1.68 (top 6.14%)76. Symposium on Testing, Analysis, and Verification: 1.65 (top 6.22%)77. Software Development Environments (SDE): 1.64 (top 6.30%)78. SIAM J. Comput.: 1.64 (top 6.38%)79. CRYPTO: 1.63 (top 6.47%)80. Multimedia Systems: 1.62 (top 6.55%)81. ICFP: 1.62 (top 6.63%)82. Lisp and Symbolic Computation: 1.61 (top 6.71%)83. ECP: 1.61 (top 6.79%)84. CHI: 1.61 (top 6.87%)85. ISLP: 1.60 (top 6.96%)86. ACM Symposium on User Interface Software and Technology: 1.59 (top 7.04%)87. ESOP: 1.58 (top 7.12%)88. ECCV: 1.58 (top 7.20%)89. ACM Transactions on Graphics: 1.57 (top 7.28%)90. CSCW: 1.57 (top 7.37%)91. AOSE: 1.57 (top 7.45%)92. ICCL: 1.57 (top 7.53%)93. Journal of Functional Programming: 1.57 (top 7.61%)94. RTSS: 1.57 (top 7.69%)95. ECSCW: 1.56 (top 7.78%)96. TOCHI: 1.56 (top 7.86%)97. ISCA: 1.56 (top 7.94%)98. SIGMETRICS/Performance: 1.56 (top 8.02%)99. IWMM: 1.55 (top 8.10%)100. JICSLP: 1.54 (top 8.19%)101. Automatic Verification Methods for Finite State Systems: 1.54 (top 8.27%) 102. WWW: 1.54 (top 8.35%)103. IEEE Transactions on Pattern Analysis and Machine Intelligence: 1.54 (top 8.43%) 104. AIPS: 1.53 (top 8.51%)105. IEEE Transactions on Visualization and Computer Graphics: 1.53 (top 8.59%) 106. VLDB: 1.52 (top 8.68%)107. Symposium on Computational Geometry: 1.51 (top 8.76%)108. FOCS: 1.51 (top 8.84%)109. A TAL: 1.51 (top 8.92%)110. SODA: 1.51 (top 9.00%)111. PPCP: 1.50 (top 9.09%)112. AAAI: 1.49 (top 9.17%)113. COLT: 1.49 (top 9.25%)114. USENIX Summer: 1.49 (top 9.33%)115. Information and Computation: 1.48 (top 9.41%)116. Java Grande: 1.47 (top 9.50%)117. ISMM: 1.47 (top 9.58%)118. ICLP/SLP: 1.47 (top 9.66%)119. SLP: 1.45 (top 9.74%)120. Structure in Complexity Theory Conference: 1.45 (top 9.82%)121. IEEE Transactions on Multimedia: 1.45 (top 9.90%)122. Rules in Database Systems: 1.44 (top 9.99%)123. ACL: 1.44 (top 10.07%)124. CONCUR: 1.44 (top 10.15%)125. SPAA: 1.44 (top 10.23%)126. J. Algorithms: 1.42 (top 10.31%)127. DOOD: 1.42 (top 10.40%)128. ESEC / SIGSOFT FSE: 1.41 (top 10.48%)129. ICDT: 1.41 (top 10.56%)130. Advances in Petri Nets: 1.41 (top 10.64%)131. ICNP: 1.40 (top 10.72%)132. SSD: 1.39 (top 10.81%)133. INFOCOM: 1.39 (top 10.89%)134. IEEE Symposium on Security and Privacy: 1.39 (top 10.97%)135. Cognitive Science: 1.38 (top 11.05%)136. TSE: 1.38 (top 11.13%)137. Storage and Retrieval for Image and Video Databases (SPIE): 1.38 (top 11.22%) 138. NACLP: 1.38 (top 11.30%)139. SIGMETRICS: 1.38 (top 11.38%)140. JACM: 1.37 (top 11.46%)141. PODC: 1.37 (top 11.54%)142. International Conference on Supercomputing: 1.36 (top 11.62%)143. Fast Software Encryption: 1.35 (top 11.71%)144. IEEE Visualization: 1.35 (top 11.79%)145. SAS: 1.35 (top 11.87%)146. TACS: 1.35 (top 11.95%)147. International Journal of Computer Vision: 1.33 (top 12.03%)148. JCSS: 1.32 (top 12.12%)149. Algorithmica: 1.31 (top 12.20%)150. TOCL: 1.30 (top 12.28%)151. Information Hiding: 1.30 (top 12.36%)152. Journal of Automated Reasoning: 1.30 (top 12.44%)153. ECCV (1): 1.29 (top 12.53%)154. PCRCW: 1.29 (top 12.61%)155. Journal of Logic and Computation: 1.29 (top 12.69%)156. KDD Workshop: 1.28 (top 12.77%)157. ML: 1.28 (top 12.85%)158. ISSTA: 1.28 (top 12.94%)159. EUROCRYPT: 1.27 (top 13.02%)160. PDIS: 1.27 (top 13.10%)161. Hypertext: 1.27 (top 13.18%)162. IWDOM: 1.27 (top 13.26%)163. PARLE (2): 1.26 (top 13.34%)164. Hybrid Systems: 1.26 (top 13.43%)165. American Journal of Computational Linguistics: 1.26 (top 13.51%)166. SPIN: 1.25 (top 13.59%)167. ICDE: 1.25 (top 13.67%)168. FMCAD: 1.25 (top 13.75%)169. SC: 1.25 (top 13.84%)170. EDBT: 1.25 (top 13.92%)171. Computational Complexity: 1.25 (top 14.00%)172. International Journal of Computatinal Geometry and Applications: 1.25 (top 14.08%) 173. ESORICS: 1.25 (top 14.16%)174. IJCAI (2): 1.24 (top 14.25%)175. TACAS: 1.24 (top 14.33%)176. Ubicomp: 1.24 (top 14.41%)177. MPC: 1.24 (top 14.49%)178. AWOC: 1.24 (top 14.57%)179. TLCA: 1.23 (top 14.66%)180. Emergent Neural Computational Architectures Based on Neuroscience: 1.23 (top 14.74%) 181. CADE: 1.22 (top 14.82%)182. PROCOMET: 1.22 (top 14.90%)183. ACM Multimedia: 1.22 (top 14.98%)184. IEEE Journal on Selected Areas in Communications: 1.22 (top 15.06%)185. Science of Computer Programming: 1.22 (top 15.15%)186. LCPC: 1.22 (top 15.23%)187. CT-RSA: 1.22 (top 15.31%)188. ICLP: 1.21 (top 15.39%)189. Financial Cryptography: 1.21 (top 15.47%)190. DBPL: 1.21 (top 15.56%)191. AAAI/IAAI: 1.20 (top 15.64%)192. Artificial Life: 1.20 (top 15.72%)193. Higher-Order and Symbolic Computation: 1.19 (top 15.80%)194. TKDE: 1.19 (top 15.88%)195. ACM Computing Surveys: 1.19 (top 15.97%)196. Computational Geometry: 1.18 (top 16.05%)197. Autonomous Agents and Multi-Agent Systems: 1.18 (top 16.13%)198. EWSL: 1.18 (top 16.21%)199. Learning for Natural Language Processing: 1.18 (top 16.29%)200. TAPOS: 1.17 (top 16.38%)201. : 1.17 (top 16.46%)202. International Journal of Computational Geometry and Applications: 1.17 (top 16.54%)203. TAPSOFT: 1.17 (top 16.62%)204. IEEE Transactions on Parallel and Distributed Systems: 1.17 (top 16.70%) 205. Heterogeneous Computing Workshop: 1.16 (top 16.78%)206. Distributed and Parallel Databases: 1.16 (top 16.87%)207. DAC: 1.16 (top 16.95%)208. ICTL: 1.16 (top 17.03%)209. Performance/SIGMETRICS Tutorials: 1.16 (top 17.11%)210. IEEE Computer: 1.15 (top 17.19%)211. IEEE Real Time Technology and Applications Symposium: 1.15 (top 17.28%) 212. : 1.15 (top 17.36%)213. ACM Workshop on Role-Based Access Control: 1.15 (top 17.44%)214. WCRE: 1.14 (top 17.52%)215. Applications and Theory of Petri Nets: 1.14 (top 17.60%)216. ACM SIGOPS European Workshop: 1.14 (top 17.69%)217. ICDCS: 1.14 (top 17.77%)218. Mathematical Structures in Computer Science: 1.14 (top 17.85%)219. Workshop on the Management of Replicated Data: 1.13 (top 17.93%)220. ECCV (2): 1.13 (top 18.01%)221. PPSN: 1.13 (top 18.09%)222. Middleware: 1.13 (top 18.18%)223. OODBS: 1.12 (top 18.26%)224. Electronic Colloquium on Computational Complexity (ECCC): 1.12 (top 18.34%) 225. UML: 1.12 (top 18.42%)226. Real-Time Systems: 1.12 (top 18.50%)227. FME: 1.12 (top 18.59%)228. Evolutionary Computing, AISB Workshop: 1.11 (top 18.67%)229. IEEE Conference on Computational Complexity: 1.11 (top 18.75%)230. IOPADS: 1.11 (top 18.83%)231. IJCAI: 1.10 (top 18.91%)232. ISWC: 1.10 (top 19.00%)233. SIGIR: 1.10 (top 19.08%)234. Symposium on LISP and Functional Programming: 1.10 (top 19.16%)235. PASTE: 1.10 (top 19.24%)236. HPDC: 1.10 (top 19.32%)237. Application and Theory of Petri Nets: 1.09 (top 19.41%)238. ICCAD: 1.09 (top 19.49%)239. Category Theory and Computer Science: 1.08 (top 19.57%)240. Recent Advances in Intrusion Detection: 1.08 (top 19.65%)241. JIIS: 1.08 (top 19.73%)242. TODAES: 1.08 (top 19.81%)243. Neural Computation: 1.08 (top 19.90%)244. CCL: 1.08 (top 19.98%)245. SIGPLAN Workshop: 1.08 (top 20.06%)246. DPDS: 1.07 (top 20.14%)247. ACM Multimedia (1): 1.07 (top 20.22%)248. MAAMAW: 1.07 (top 20.31%)249. Computer Graphics Forum: 1.07 (top 20.39%)250. HUG: 1.06 (top 20.47%)251. Hybrid Neural Systems: 1.06 (top 20.55%)252. SRDS: 1.06 (top 20.63%)253. TPCD: 1.06 (top 20.72%)254. ILP: 1.06 (top 20.80%)255. ARTDB: 1.06 (top 20.88%)256. NIPS: 1.06 (top 20.96%)257. Formal Aspects of Computing: 1.06 (top 21.04%)258. ECHT: 1.06 (top 21.13%)259. ICMCS: 1.06 (top 21.21%)260. Wireless Networks: 1.05 (top 21.29%)261. Advances in Data Base Theory: 1.05 (top 21.37%)262. WDAG: 1.05 (top 21.45%)263. ALP: 1.05 (top 21.53%)264. TARK: 1.05 (top 21.62%)265. PATAT: 1.05 (top 21.70%)266. ISTCS: 1.04 (top 21.78%)267. Concurrency - Practice and Experience: 1.04 (top 21.86%)268. CP: 1.04 (top 21.94%)269. Computer Vision, Graphics, and Image Processing: 1.04 (top 22.03%) 270. FTCS: 1.04 (top 22.11%)271. RTA: 1.04 (top 22.19%)272. COORDINATION: 1.03 (top 22.27%)273. CHDL: 1.03 (top 22.35%)274. Theory of Computing Systems: 1.02 (top 22.44%)275. CTRS: 1.02 (top 22.52%)276. COMPASS/ADT: 1.02 (top 22.60%)277. TOMACS: 1.02 (top 22.68%)278. IEEE Micro: 1.02 (top 22.76%)279. IEEE PACT: 1.02 (top 22.85%)280. ASIACRYPT: 1.01 (top 22.93%)281. MONET: 1.01 (top 23.01%)282. WWW7 / Computer Networks: 1.01 (top 23.09%)283. HUC: 1.01 (top 23.17%)284. Expert Database Conf.: 1.00 (top 23.25%)285. Agents: 1.00 (top 23.34%)286. CPM: 1.00 (top 23.42%)287. SIGPLAN Symposium on Compiler Construction: 1.00 (top 23.50%) 288. International Conference on Evolutionary Computation: 1.00 (top 23.58%) 289. TAGT: 1.00 (top 23.66%)290. Workshop on Parallel and Distributed Simulation: 1.00 (top 23.75%)292. TPHOLs: 1.00 (top 23.91%)293. Intelligent User Interfaces: 0.99 (top 23.99%)294. Journal of Functional and Logic Programming: 0.99 (top 24.07%)295. Cluster Computing: 0.99 (top 24.16%)296. ESA: 0.99 (top 24.24%)297. PLILP: 0.99 (top 24.32%)298. COLING-ACL: 0.98 (top 24.40%)299. META: 0.97 (top 24.48%)300. IEEE MultiMedia: 0.97 (top 24.57%)301. ICALP: 0.97 (top 24.65%)302. IATA: 0.97 (top 24.73%)303. FPGA: 0.97 (top 24.81%)304. EuroCOLT: 0.97 (top 24.89%)305. New Generation Computing: 0.97 (top 24.97%)306. Automated Software Engineering: 0.97 (top 25.06%)307. GRID: 0.97 (top 25.14%)308. ISOTAS: 0.96 (top 25.22%)309. LPNMR: 0.96 (top 25.30%)310. PLILP/ALP: 0.96 (top 25.38%)311. UIST: 0.96 (top 25.47%)312. IPCO: 0.95 (top 25.55%)313. ICPP, Vol. 1: 0.95 (top 25.63%)314. PNPM: 0.95 (top 25.71%)315. HSCC: 0.95 (top 25.79%)316. ILPS: 0.95 (top 25.88%)317. RIDE-IMS: 0.95 (top 25.96%)318. Int. J. on Digital Libraries: 0.95 (top 26.04%)319. STTT: 0.94 (top 26.12%)320. MFPS: 0.94 (top 26.20%)321. Graph-Grammars and Their Application to Computer Science: 0.93 (top 26.28%) 322. Graph Drawing: 0.93 (top 26.37%)323. VRML: 0.93 (top 26.45%)324. VDM Europe: 0.93 (top 26.53%)325. AAAI/IAAI, Vol. 2: 0.93 (top 26.61%)326. Z User Workshop: 0.93 (top 26.69%)327. Constraints: 0.93 (top 26.78%)328. SCM: 0.93 (top 26.86%)329. IEEE Software: 0.92 (top 26.94%)330. World Wide Web: 0.92 (top 27.02%)331. HOA: 0.92 (top 27.10%)332. Symposium on Reliable Distributed Systems: 0.92 (top 27.19%)333. SIAM Journal on Discrete Mathematics: 0.92 (top 27.27%)334. SMILE: 0.91 (top 27.35%)336. ICPP, Vol. 3: 0.91 (top 27.51%)337. FASE: 0.91 (top 27.60%)338. TCS: 0.91 (top 27.68%)339. IEEE Transactions on Information Theory: 0.91 (top 27.76%) 340. C++ Conference: 0.91 (top 27.84%)341. ICSE: 0.90 (top 27.92%)342. ARTS: 0.90 (top 28.00%)343. Journal of Computational Biology: 0.90 (top 28.09%)344. SIGART Bulletin: 0.90 (top 28.17%)345. TREC: 0.89 (top 28.25%)346. Implementation of Functional Languages: 0.89 (top 28.33%) 347. Acta Informatica: 0.88 (top 28.41%)348. SAIG: 0.88 (top 28.50%)349. CANPC: 0.88 (top 28.58%)350. CACM: 0.87 (top 28.66%)351. PADL: 0.87 (top 28.74%)352. Networked Group Communication: 0.87 (top 28.82%)353. RECOMB: 0.87 (top 28.91%)354. ACM DL: 0.87 (top 28.99%)355. Computer Performance Evaluation: 0.87 (top 29.07%)356. Journal of Parallel and Distributed Computing: 0.86 (top 29.15%) 357. PARLE (1): 0.86 (top 29.23%)358. DISC: 0.85 (top 29.32%)359. FGCS: 0.85 (top 29.40%)360. ELP: 0.85 (top 29.48%)361. IEEE Transactions on Computers: 0.85 (top 29.56%)362. JSC: 0.85 (top 29.64%)363. LOPSTR: 0.85 (top 29.72%)364. FoSSaCS: 0.85 (top 29.81%)365. World Congress on Formal Methods: 0.85 (top 29.89%)366. CHARME: 0.84 (top 29.97%)367. RIDE: 0.84 (top 30.05%)368. APPROX: 0.84 (top 30.13%)369. EWCBR: 0.84 (top 30.22%)370. CC: 0.83 (top 30.30%)371. Public Key Cryptography: 0.83 (top 30.38%)372. CA: 0.83 (top 30.46%)373. CHES: 0.83 (top 30.54%)374. ECML: 0.83 (top 30.63%)375. LCTES/OM: 0.83 (top 30.71%)376. Information Systems: 0.83 (top 30.79%)377. IJCIS: 0.83 (top 30.87%)378. Journal of Visual Languages and Computing: 0.82 (top 30.95%)380. Random Structures and Algorithms: 0.81 (top 31.12%)381. ICS: 0.81 (top 31.20%)382. Data Engineering Bulletin: 0.81 (top 31.28%)383. VDM Europe (1): 0.81 (top 31.36%)384. SW AT: 0.80 (top 31.44%)385. Nordic Journal of Computing: 0.80 (top 31.53%)386. Mathematical Foundations of Programming Semantics: 0.80 (top 31.61%)387. Architectures and Compilation Techniques for Fine and Medium Grain Parallelism: 0.80 (top 31.69%)388. KBSE: 0.80 (top 31.77%)389. STACS: 0.80 (top 31.85%)390. EMSOFT: 0.80 (top 31.94%)391. IEEE Data Engineering Bulletin: 0.80 (top 32.02%)392. Annals of Mathematics and Artificial Intelligence: 0.79 (top 32.10%)393. WOSP: 0.79 (top 32.18%)394. VBC: 0.79 (top 32.26%)395. RTDB: 0.79 (top 32.35%)396. CoopIS: 0.79 (top 32.43%)397. Combinatorica: 0.79 (top 32.51%)398. International Journal of Geographical Information Systems: 0.78 (top 32.59%)399. Autonomous Robots: 0.78 (top 32.67%)400. IW-MMDBMS: 0.78 (top 32.76%)401. ESEC: 0.78 (top 32.84%)402. W ADT: 0.78 (top 32.92%)403. CAAP: 0.78 (top 33.00%)404. LCTES: 0.78 (top 33.08%)405. ZUM: 0.77 (top 33.16%)406. TYPES: 0.77 (top 33.25%)407. Symposium on Reliability in Distributed Software and Database Systems: 0.77 (top 33.33%) 408. TABLEAUX: 0.77 (top 33.41%)409. International Journal of Parallel Programming: 0.77 (top 33.49%)410. COST 237 Workshop: 0.77 (top 33.57%)411. Data Types and Persistence (Appin), Informal Proceedings: 0.77 (top 33.66%)412. Evolutionary Programming: 0.77 (top 33.74%)413. Reflection: 0.76 (top 33.82%)414. SIGMOD Record: 0.76 (top 33.90%)415. Security Protocols Workshop: 0.76 (top 33.98%)416. XP1 Workshop on Database Theory: 0.76 (top 34.07%)417. EDMCC: 0.76 (top 34.15%)418. DL: 0.76 (top 34.23%)419. EDAC-ETC-EUROASIC: 0.76 (top 34.31%)420. Protocols for High-Speed Networks: 0.76 (top 34.39%)421. PPDP: 0.75 (top 34.47%)422. IFIP PACT: 0.75 (top 34.56%)423. LNCS: 0.75 (top 34.64%)424. IWQoS: 0.75 (top 34.72%)425. UK Hypertext: 0.75 (top 34.80%)426. Selected Areas in Cryptography: 0.75 (top 34.88%)427. ICA TPN: 0.74 (top 34.97%)428. Workshop on Computational Geometry: 0.74 (top 35.05%)429. Integrated Network Management: 0.74 (top 35.13%)430. ICGI: 0.74 (top 35.21%)431. ICPP (2): 0.74 (top 35.29%)432. SSR: 0.74 (top 35.38%)433. ADB: 0.74 (top 35.46%)434. Object Representation in Computer Vision: 0.74 (top 35.54%)435. PSTV: 0.74 (top 35.62%)436. CAiSE: 0.74 (top 35.70%)437. On Knowledge Base Management Systems (Islamorada): 0.74 (top 35.79%) 438. CIKM: 0.73 (top 35.87%)439. WSA: 0.73 (top 35.95%)440. RANDOM: 0.73 (top 36.03%)441. KRDB: 0.73 (top 36.11%)442. ISSS: 0.73 (top 36.19%)443. SIGAL International Symposium on Algorithms: 0.73 (top 36.28%)444. INFORMS Journal on Computing: 0.73 (top 36.36%)445. Computer Supported Cooperative Work: 0.73 (top 36.44%)446. CSL: 0.72 (top 36.52%)447. Computational Intelligence: 0.72 (top 36.60%)448. ICCBR: 0.72 (top 36.69%)449. ICES: 0.72 (top 36.77%)450. AI Magazine: 0.72 (top 36.85%)451. JELIA: 0.72 (top 36.93%)452. VR: 0.71 (top 37.01%)453. ICPP (1): 0.71 (top 37.10%)454. RIDE-TQP: 0.71 (top 37.18%)455. ISA: 0.71 (top 37.26%)456. Data Compression Conference: 0.71 (top 37.34%)457. CIA: 0.71 (top 37.42%)458. COSIT: 0.71 (top 37.51%)459. IJCSLP: 0.71 (top 37.59%)460. DISCO: 0.71 (top 37.67%)461. DKE: 0.71 (top 37.75%)462. IWAN: 0.71 (top 37.83%)463. Operating Systems Review: 0.70 (top 37.91%)464. IEEE Internet Computing: 0.70 (top 38.00%)465. LISP Conference: 0.70 (top 38.08%)466. C++ Workshop: 0.70 (top 38.16%)467. SPDP: 0.70 (top 38.24%)468. Fuji International Symposium on Functional and Logic Programming: 0.69 (top 38.32%) 469. LPAR: 0.69 (top 38.41%)470. ECAI: 0.69 (top 38.49%)471. Hypermedia: 0.69 (top 38.57%)472. Artificial Intelligence in Medicine: 0.69 (top 38.65%)473. AADEBUG: 0.69 (top 38.73%)474. VL: 0.69 (top 38.82%)475. FSTTCS: 0.69 (top 38.90%)476. AMAST: 0.68 (top 38.98%)477. Artificial Intelligence Review: 0.68 (top 39.06%)478. HPN: 0.68 (top 39.14%)479. POS: 0.68 (top 39.23%)480. Research Directions in High-Level Parallel Programming Languages: 0.68 (top 39.31%) 481. Performance Evaluation: 0.68 (top 39.39%)482. ASE: 0.68 (top 39.47%)483. LFCS: 0.67 (top 39.55%)484. ISCOPE: 0.67 (top 39.63%)485. Workshop on Software and Performance: 0.67 (top 39.72%)486. European Workshop on Applications and Theory in Petri Nets: 0.67 (top 39.80%) 487. ICPP: 0.67 (top 39.88%)488. INFOVIS: 0.67 (top 39.96%)489. Description Logics: 0.67 (top 40.04%)490. JCDKB: 0.67 (top 40.13%)491. Euro-Par, Vol. I: 0.67 (top 40.21%)492. RoboCup: 0.67 (top 40.29%)493. Symposium on Solid Modeling and Applications: 0.66 (top 40.37%)494. TPLP: 0.66 (top 40.45%)495. CVRMed: 0.66 (top 40.54%)496. POS/PJW: 0.66 (top 40.62%)497. FORTE: 0.66 (top 40.70%)498. IPMI: 0.66 (top 40.78%)499. ADL: 0.66 (top 40.86%)500. ICCS: 0.66 (top 40.95%)501. ISSAC: 0.66 (top 41.03%)502. Advanced Programming Environments: 0.66 (top 41.11%)503. COMPCON: 0.66 (top 41.19%)504. LCR: 0.65 (top 41.27%)505. Digital Libraries: 0.65 (top 41.35%)506. ALENEX: 0.65 (top 41.44%)507. AH: 0.65 (top 41.52%)508. CoBuild: 0.65 (top 41.60%)509. DS-6: 0.65 (top 41.68%)511. Computer Networks and ISDN Systems: 0.64 (top 41.85%)512. IWACA: 0.64 (top 41.93%)513. MobiDE: 0.64 (top 42.01%)514. WOWMOM: 0.64 (top 42.09%)515. IEEE Expert: 0.64 (top 42.17%)516. IRREGULAR: 0.64 (top 42.26%)517. TOMS: 0.63 (top 42.34%)518. Multiple Classifier Systems: 0.63 (top 42.42%)519. Parallel Computing: 0.63 (top 42.50%)520. ANTS: 0.63 (top 42.58%)521. ACSAC: 0.63 (top 42.66%)522. RCLP: 0.63 (top 42.75%)523. Multimedia Tools and Applications: 0.63 (top 42.83%)524. ALT: 0.63 (top 42.91%)525. ICCD: 0.63 (top 42.99%)526. ICVS: 0.62 (top 43.07%)527. Workshop on Web Information and Data Management: 0.62 (top 43.16%)528. Software - Concepts and Tools: 0.62 (top 43.24%)529. ICSM: 0.62 (top 43.32%)530. The Visual Computer: 0.62 (top 43.40%)531. SARA: 0.62 (top 43.48%)532. IS: 0.61 (top 43.57%)533. Information Retrieval: 0.61 (top 43.65%)534. CARDIS: 0.61 (top 43.73%)535. DOA: 0.61 (top 43.81%)536. Cryptography: Policy and Algorithms: 0.60 (top 43.89%)537. Electronic Publishing: 0.60 (top 43.98%)538. SSTD: 0.60 (top 44.06%)539. Algebraic Methods: 0.60 (top 44.14%)540. AGTIVE: 0.59 (top 44.22%)541. Computational Logic: 0.59 (top 44.30%)542. Computer Communications: 0.59 (top 44.38%)543. QofIS: 0.59 (top 44.47%)544. Journal of Logic, Language and Information: 0.59 (top 44.55%)545. Expert Database Workshop: 0.59 (top 44.63%)546. IFL: 0.58 (top 44.71%)547. Nonmonotonic and Inductive Logic: 0.58 (top 44.79%)548. Algorithmic Number Theory: 0.58 (top 44.88%)549. Graph-Grammars and Their Application to Computer Science and Biology: 0.58 (top 44.96%) 550. Structured Programming: 0.58 (top 45.04%)551. Information Processing Letters: 0.58 (top 45.12%)552. SIGKDD Explorations: 0.58 (top 45.20%)553. Parallel Symbolic Computing: 0.58 (top 45.29%)555. MIT-JSME Workshop: 0.57 (top 45.45%)556. Knowledge and Information Systems: 0.57 (top 45.53%)557. International Journal of Man-Machine Studies: 0.57 (top 45.61%)558. Software - Practice and Experience: 0.57 (top 45.70%)559. Scale-Space: 0.57 (top 45.78%)560. AI Communications: 0.57 (top 45.86%)561. Kurt Gödel Colloquium: 0.56 (top 45.94%)562. DBSec: 0.56 (top 46.02%)563. ER: 0.56 (top 46.10%)564. IBM Journal of Research and Development: 0.56 (top 46.19%)565. QCQC: 0.56 (top 46.27%)566. Gesture Workshop: 0.56 (top 46.35%)567. CIAC: 0.56 (top 46.43%)568. Artificial Evolution: 0.55 (top 46.51%)569. RANDOM-APPROX: 0.55 (top 46.60%)570. Information Processing and Management: 0.55 (top 46.68%)571. EKAW: 0.55 (top 46.76%)572. Operating Systems of the 90s and Beyond: 0.55 (top 46.84%)573. International Zurich Seminar on Digital Communications: 0.55 (top 46.92%) 574. Annals of Software Engineering: 0.55 (top 47.01%)575. AII: 0.55 (top 47.09%)576. DOLAP: 0.55 (top 47.17%)577. Fundamenta Informaticae: 0.55 (top 47.25%)578. PARLE: 0.55 (top 47.33%)579. Advanced Course: Distributed Systems: 0.54 (top 47.42%)580. BCEC: 0.54 (top 47.50%)581. Digital Technical Journal: 0.54 (top 47.58%)582. IJCAR: 0.54 (top 47.66%)583. Formal Methods in Programming and Their Applications: 0.54 (top 47.74%) 584. IPPS: 0.54 (top 47.82%)585. Knowledge Based Systems: 0.53 (top 47.91%)586. PDK: 0.53 (top 47.99%)587. East/West Database Workshop: 0.53 (top 48.07%)588. International ACM Conference on Assistive Technologies: 0.53 (top 48.15%) 589. Mathematical Systems Theory: 0.53 (top 48.23%)590. ICFEM: 0.53 (top 48.32%)591. DMDW: 0.53 (top 48.40%)592. International Journal of Foundations of Computer Science: 0.52 (top 48.48%) 593. LACL: 0.52 (top 48.56%)594. Advances in Computers: 0.52 (top 48.64%)595. Workshop on Conceptual Graphs: 0.52 (top 48.73%)596. FM-Trends: 0.52 (top 48.81%)597. GREC: 0.52 (top 48.89%)598. Advanced Visual Interfaces: 0.52 (top 48.97%)599. Agents Workshop on Infrastructure for Multi-Agent Systems: 0.52 (top 49.05%) 600. Euro-Par, Vol. II: 0.52 (top 49.14%)601. ICPP (3): 0.52 (top 49.22%)602. Telecommunication Systems: 0.52 (top 49.30%)603. AISMC: 0.52 (top 49.38%)604. ISAAC: 0.51 (top 49.46%)605. ICIP (2): 0.51 (top 49.54%)606. IEEE Symposium on Mass Storage Systems: 0.51 (top 49.63%)607. FAPR: 0.51 (top 49.71%)608. EHCI: 0.51 (top 49.79%)609. CHI Conference Companion: 0.51 (top 49.87%)610. Open Distributed Processing: 0.51 (top 49.95%)611. AUSCRYPT: 0.51 (top 50.04%)612. WWCA: 0.50 (top 50.12%)613. ICIP: 0.50 (top 50.20%)614. ICIP (1): 0.50 (top 50.28%)615. Annals of Pure and Applied Logic: 0.50 (top 50.36%)616. CISMOD: 0.50 (top 50.45%)617. Algorithm Engineering: 0.50 (top 50.53%)618. CASES: 0.50 (top 50.61%)619. EWSPT: 0.50 (top 50.69%)620. ICMCS, Vol. 1: 0.50 (top 50.77%)621. BIT: 0.50 (top 50.85%)622. Computer Performance Evaluation (Tools): 0.50 (top 50.94%)623. Information and Control: 0.50 (top 51.02%)624. Machine Vision and Applications: 0.50 (top 51.10%)625. Discrete Applied Mathematics: 0.50 (top 51.18%)626. PKDD: 0.50 (top 51.26%)627. ESCQARU: 0.49 (top 51.35%)628. IDS: 0.49 (top 51.43%)629. ACISP: 0.49 (top 51.51%)630. Computer Languages: 0.49 (top 51.59%)631. MFDBS: 0.49 (top 51.67%)632. QL: 0.49 (top 51.76%)633. Requirements Engineering: 0.49 (top 51.84%)634. International Journal of Human Computer Studies: 0.48 (top 51.92%)635. IBM Systems Journal: 0.48 (top 52.00%)636. Aegean Workshop on Computing: 0.48 (top 52.08%)637. Spatial Cognition: 0.48 (top 52.17%)638. MFCS: 0.48 (top 52.25%)639. Discrete & Computational Geometry: 0.48 (top 52.33%)640. ITC: 0.47 (top 52.41%)641. A TL: 0.47 (top 52.49%)。
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• (Mutual exclusion)
– No two processes are in the critical region, in any state in .
• (Progress)
– If in some state of , someone is in T and no one is in C, then sometime thereafter, someone C. – If in some state of , someone is in E, then sometime thereafter, someone R.
• To simplify, avoids internal process actions---combines these with sends, receives, or register access steps. • Sometimes considers message losses (“loss” steps). • Many models, must specify which in each case. • Defines executions:
• [ Dolev book, 00 ] summarizes main ideas of the field.
Today…
• Basic ideas, from [ Dolev, Chapter 2 ] • Rest of the book describes:
– – – – – – – Many more self-stabilizing algorithms. General techniques for designing them. Converting non-SS algorithms to SS algorithms. Transformations between models, preserving SS. SS in presence of ongoing failures. Efficient SS. Etc.
6.852: Distributed Algorithms Spring, 2008
Class 24
Today’s plan
• Self-stabilization • Self-stabilizing algorithms:
– Breadth-first spanning tree – Mutual exclusion
• Composing self-stabilizing algorithms • Making non-self-stabilizing algorithms selfstabilizing • Reading:
– [ Dolev, Chapter 2 ]
Self-stabilization
• A useful fault-tolerance property for distributed algorithms. • Algorithm can start in any state---arbitrarily corrupted. • From there, if it runs normally (usually, without any further failures), it eventually gravitates back to correct behavior. • [ Dijkstra 73: Self-stabilizing systems in spite of distributed control ]
• Q: Require that L be “suffix-closed”?
Self-stabilization: Definition
• A global state of algorithm A is safe with respect to legal set L, provided that every fair execution fragment of A that starts with s is in L. • Algorithm A is self-stabilizing with respect to legal set L if every fair execution fragment of A contains a state s that is safe with respect to L.
• Example: Self-stabilizing mutual exclusion algorithm A
Weaker definition of SS?
• Sometimes, [Dolev] appears to be using a slightly weaker definition of self-stabilization. • Instead of:
– Algorithm A is self-stabilizing for legal set L if every fair execution fragment of A contains a state s that is safe with respect to L.
• Uses:
– Algorithm A is self-stabilizing for legal set L if every fair execution fragment has a suffix in L.
– Dijkstra’s most important contribution to distributed computing theory. – [ Lamport talk, PODC 83 ] Reintroduced the paper, explained its importance, popularized it. – Became (still is) a major research direction. – Won PODC Influential Paper award, in 2002, died 2 weeks later; award renamed the Dijkstra Prize.
• Same argument for shared-memory algorithms.
SS Algorithm 1: Breadth-first spanning tree
• Shared-memory model • Connected, undirected graph G = (V,E), where V = { 1,2,…,n }. • Processes P1,…,Pn, where P1 is a designated root process. • Some knowledge is permanent:
– Like ours, but needn’t start in initial state. – Same as our “execution fragments”.
• Fair executions: Described informally, but our task-based definition is fine.
– rij written by Pi, read by Pj.
– rij.parent = 1 if j is i’s parent, 0 otherwise. – rij.dist = distance from root to i in the BFS tree = smallest number of hops on any path from 1 to i in G. – Moreover, the values in the registers should remain constant from some point onward.
• Bypassing the safe state requirement. • Q: Equivalent definition? Seems not, in general. • We’ll generally assume the stronger, “safe state” definition.
Legal execution fragments
• Given a distributed algorithm A, define a set L of “legal” execution fragments of A. • L can include both safety and liveness conditions. • Example: Mutual exclusion
Self-stabilization
• Considers:
– Message-passing models, FIFO reliable channels – Shared-memory models, read/write registers – Asynchronous, synchronous models
– Implies that the suffix of starting with s is in L. – Also implies that any other fair execution fragment starting with s is in L. – If L is suffix-closed, implies that every suffix of starting from s or a later state is in L. – Start A in any state, possibly with > 1 process in the critical region. – Eventually A reaches a state after which any fair execution fragment is legal: satisfies mutual exclusion + progress.