1 / 69

Intelligent Computing — Chapter 4 — Swarm Intelligence

Intelligent Computing — Chapter 4 — Swarm Intelligence. What is swarm intelligence?. Collective system capable of accomplishing difficult tasks in dynamic and varied environments without any external guidance or control and with no central coordination (Prof. White Carleton)

rhea-howe
Télécharger la présentation

Intelligent Computing — Chapter 4 — Swarm Intelligence

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Intelligent Computing— Chapter 4 —Swarm Intelligence

  2. Shandong UNIVERSITY

  3. Shandong UNIVERSITY

  4. Shandong UNIVERSITY What is swarm intelligence? • Collective system capable of accomplishing difficult tasks in dynamic and varied environments without any external guidance or control and with no central coordination (Prof. White Carleton) • Achieving a collective performance which could not normally be achieved by an individual acting alone (Prof. White) • Ants, bees and even bacteria are amongst the many organisms that display sophisticated kinds of cooperative behavior as a survival strategy. • Constituting a natural model particularly suited to distributed problem solving

  5. Shandong UNIVERSITY Characteristics • 分布式：能够适应当前网络环境下的工作状态; • 鲁棒性：没有中心的控制与数据，个体的故障不影响整个问题的求解; • 扩充性：个体的增加，系统的通信开销增加小; • 简单性：个体简单，实现也比较简单。

  6. Shandong UNIVERSITY Characteristics • 群体智能的研究不仅在多主体仿真、系统复杂性以及NP问题等方面为人工智能、认识科学、计算经济学等领域的基础理论问题的研究开辟了新的研究途径，同时也为诸如组合优化、机器人协作、电信路由控制等实际工程问题提供了新的解决方法。因此，群体智能的研究具有重要意义和广阔的应用前景。

  7. Shandong UNIVERSITY Researches • 美国的SDG在系统复杂性方面开展了研究。他们主要通过多主体的仿真来研究系统复杂性。他们开发的SWARM软件包为多学科进行基于多主体的建模提供了一个基础平台； • 加州工学院专门开设了群体智能的课程； • 欧洲联盟资助的SWARM-BOTS项目的主要目标是研究设计和实现自组织和自装配的装置的新途径。它的理论基础是群体智能和蚁群算法的近期研究成果，即对群居性昆虫和其它动物群体的自组织和自装配能力的研究。

  8. Shandong UNIVERSITY Researches • 国家自然科学基金“十五”期间学科交叉类优先资助领域第一类属于把握科学前沿，推动源头创新的项目。 其中第7项认知科学及其信息处理的研究内容就明确列出了群体智能的进化、自适应与现场认知。相关项目还有第9项复杂系统与复杂性。

  9. Shandong UNIVERSITY Swarm Intelligent Algorithms Inspiration from swarm intelligence has led to some highly successful optimisation algorithms. For example: • Particle Swarm Optimization — a different way to solve optimization problems, based on the swarming behaviour of several kinds of organisms. • Ant Colony Optimization – a way to solve optimization problems

  10. Shandong UNIVERSITY Ant Colony Optimization (ACO) • The ACO is first introduced by Marco Dorigo • M.Dorigo, 'Optimization learning and natural algorithms,' Ph.D.Thesis, Dip.Elettronica e Informazione, Politecnico di Milano, Italy, 1992 • Marco Dorigo, Vittorio Maniezzo, and Alberto Colorni. The Ant System: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, 26(1):29--41, 1996. • Nature

  11. Shandong UNIVERSITY Ant Colony Optimization • Inspiration from ant colonies’ foraging behavior (actions of the colony finding food)

  12. Shandong UNIVERSITY foraging behavior

  13. Shandong UNIVERSITY foraging behavior

  14. Shandong UNIVERSITY Ants mean intelligent • Almost blind. • Incapable of achieving complex tasks alone. • Rely on the phenomena of swarm intelligence for survival. • Capable of establishing shortest-route paths from their colony to feeding sources and back. • Use stigmergic communication via pheromone trails.

  15. Shandong UNIVERSITY Pheromone trail • Shortest path is discovered via pheromone trails • each ant moves at random • pheromone is deposited on path • ants detect lead ant’s path, inclined to follow • more pheromone on path increases probability of path being followed • After some time, the shortest path has the highest probability • So it is a positive feedback mechanism

  16. Shandong UNIVERSITY Natural ants: How do they do it? • The pheromone concentration on trailB will increase at a higher rate than on A, and soon the ants on route A will choose to follow route B • Since most ants will no longer travel on route A, and since the pheromone is volatile, trail A will start evaporating • Only the shortest route will remain! • Since the route B is shorter, the ants on this path will complete the travel more times and thereby lay more pheromone over it.

  17. Shandong UNIVERSITY ACO for TSP • TSP-Traveling Salesman Problem

  18. Shandong UNIVERSITY Ant SystemStep Start Initialization To represent problem with route initialize pheromone State Transition Rule It satisfies the condition? Yes Pheromone Updating Rule No Every ant finds a route End Update the pheromone

  19. Shandong UNIVERSITY Ant System • While ( termination not satisfied ) • create ants • Find solutions • Transition probability: • Pheromone update • Daemon activities {optional} Quantity of pheromone Heuristic distance α,β constants

  20. Shandong UNIVERSITY Ant System • While ( termination not satisfied ) • create ants • Find solutions • Pheromone update • Daemon activities {optional} Pheromone laid by each ant that uses edge (i,j) Evaporation rate

  21. Shandong UNIVERSITY Ant System • Pheromone update : • T is the tour done at time t by ant k, L is the length, Q is a heuristic parameter. • Pheromone decay:

  22. Shandong UNIVERSITY Global updating rule: Once all ants have built their complete tours, pheromone is updated on all edges as follows: where m = the number of ants.

  23. Shandong UNIVERSITY A simple TSP example [] [] [] [] [] 5 2 4 1 3 A B C D E dAB =100;dBC = 60…;dDE =150

  24. Shandong UNIVERSITY Iteration 1 [B] [C] [E] [A] [D] 2 3 4 1 5 A B C D E

  25. Shandong UNIVERSITY How to build next sub-solution? [A] [A] [A] [A] [A,D] 1 1 1 1 1 A B C D E

  26. Shandong UNIVERSITY Iteration 2 [B,C] [A,D] [E,A] [C,B] [D,E] 2 1 4 3 5 A B C D E

  27. Shandong UNIVERSITY Iteration 3 [B,C,D] [C,B,E] [E,A,B] [D,E,A] [A,D,C] 2 3 1 4 5 A B C D E

  28. Shandong UNIVERSITY Iteration 4 [A,DCE] [E,A,B,C] [B,C,D,A] [D,E,A,B] [C,B,E,D] 1 5 3 4 2 A B C D E

  29. Shandong UNIVERSITY Iteration 5 [B,C,D,A,E] [D,E,A,B,C] [C,B,E,D,A] [A,D,C,E,B] [E,A,B,C,D] 2 4 5 1 3 A B C D E

  30. Shandong UNIVERSITY Path and Pheromone Evaluation [C,B,E,D,A] [B,C,D,A,E] [E,A,B,C,D] [D,E,A,B,C] [A,D,C,E,B] 5 1 2 4 3 L1 =300 L2 =450 L3 =260 L4 =280 L5 =420

  31. Shandong UNIVERSITY Problems • Ant System tends to converge quickly • This means that its exploitation of the best solution found is too high, it should be exploring solution space more • Pheromone evaporation/update rule (better rule may exist) • what is the evaporation rate? • Led to extensions of the ant system • MAX-MIN Ant system • Ant colony system • Foot-Stepping • Others (will not be discussed)

  32. Shandong UNIVERSITY MAX-MIN Ant System • Developed by Stutzle and Hoos 2000 • An improvement over the original Ant System to allow for more exploration • Introduced use of tending to global best from iteration best solution over time • i.e., only the best ant updates the pheromone trails, and that, • the value of the pheromone is bound, upper and lower bound imposed • bounds on pheromone that are dependant on solution quality • Bounds set empirically • Max-min has obtained good results for many types of problems

  33. Shandong UNIVERSITY MAX-MIN Ant System • MMAS • High exploration at the beginning • Only best ant can add pheromone • Sometimes uses local search to improve its performance

  34. Shandong UNIVERSITY Ant Colony System (ACS) • Most popular/interesting contribution of ACS is • introduction of a local pheromone update in addition to the pheromone update performed at the end of the construction process (known as offline pheromone update) • Local pheromone update is performed by all ants after each construction step • Each ant applies it only to the last edge traversed: where is the pheromone decay coefficient

  35. Shandong UNIVERSITY Ant Colony System (ACS) • The offline pheromone update, similary to MAX-MIN is applied to the end of each iteration, by only one ant, which can either be the iteration-best, or best-so-far. • The update rule is slightly different from MAX-MIN though (see paper) • Another important difference between ACS and Ant System is in the decision rule used by the ants during the construction process by using the so called pseudo random proportional rule.

  36. Shandong UNIVERSITY Other applications • Scheduling problem • Vehicle routing problem(VRP) • Graph coloring problem(GCP) • Data mining • Imagine processing • Protein folding problem • Network routing problem • Clustering

  37. Shandong UNIVERSITY Application to clustering

  38. Shandong UNIVERSITY Procedure • 主要步骤： • 随机分布待聚类模式； • 每只蚂蚁计算当前对象在局部环境的群体相似度，并通过概率转换函数得到拾起或放下对象的概率，以这个概率行动； • 经过群体大量的相互作用，最终得到若干聚类中心； • 最后收集聚类结果。

  39. Shandong UNIVERSITY What can we do on it? • Theory • Parameter problem • Combine it with other algorithms • Applications to new research fields

  40. Shandong UNIVERSITY PSO • 粒子群算法(particle swarm optimization，PSO)由Kennedy和Eberhart在1995年提出，该算法模拟鸟集群飞行觅食的行为，鸟之间通过集体的协作使群体达到最优目的，是一种基于Swarm Intelligence的优化方法。 • 同遗传算法类似，也是一种基于群体叠代的，但并没有遗传算法用的交叉以及变异，而是粒子在解空间追随最优的粒子进行搜索。 • PSO的优势在于简单容易实现同时又有深刻的智能背景，既适合科学研究，又特别适合工程应用，并且没有许多参数需要调整。

  41. Shandong UNIVERSITY PSO • James Kennedy received the Ph.D. degree from theUniversity of North Carolina, Chapel Hill, in 1992.He is with the U.S. Department of Labor, Washington,DC. He is a Social Psychologist who has been working with the particle swarm algorithm since 1994. He has published dozens of articles and chapters on particle swarms and related topics, in computer science and social science journals and proceedings. He is a coauthor of Swarm Intelligence (San Mateo, CA: Morgan Kaufmann, 2001), with R.C. Eberhart and Y. Shi, now in its third printing.

  42. Shandong UNIVERSITY PSO • Russell C. Eberhart (M’88–SM’89–F’01) received the Ph.D. degree in electrical engineering from Kansas State University, Manhattan.He is the Chair and Professor of Electrical and Computer Engineering, Purdue School of Engineering and Technology, Indiana University–Purdue University Indianapolis (IUPUI),Indianapolis, IN. He is coeditor of Neural Network PC Tools(1990),coauthor of Computational Intelligence PC Tools (1996), coauthor of Swarm Intelligence(2001), Computational Intelligence: Concepts to Implementations(2004). He has published over 120 technical papers.Dr. Eberhart was awarded the IEEE Third Millenium Medal. In 2002, he became a Fellow of the American Institute for Medical and Biological Engineering.

  43. Shandong UNIVERSITY PSO • 粒子群优化算法源于1987年Reynolds对鸟群社会系统boids的仿真研究，boids是一个CAS。在boids中，一群鸟在空中飞行，每个鸟遵守以下三条规则： • 避免与相邻的鸟发生碰撞冲突； • 尽量与自己周围的鸟在速度上保持协调和一致； • 尽量试图向自己所认为的群体中靠近。 • 仅通过使用这三条规则，boids系统就出现非常逼真的群体聚集行为，鸟成群地在空中飞行，当遇到障碍时它们会分开绕行而过，随后又会重新形成群体。

  44. Shandong UNIVERSITY PSO • Reynolds仅仅将其作为CAS的一个实例作仿真研究，而并未将它用于优化计算中 。 • Kennedy和Eberhart在中加入了一个特定点，定义为食物，鸟根据周围鸟的觅食行为来寻找食物。 • 他们的初衷是希望通过这种模型来模拟鸟群寻找食源的现象，然而实验结果却揭示这个仿真模型中蕴涵着很强的优化能力，尤其是在多维空间寻优中。

  45. Shandong UNIVERSITY PSO • PSO中，每个优化问题的解都是搜索空间中的一只鸟。称之为“粒子(Particle)”。所有的粒子都有一个由被优化的函数决定的适应值，每个粒子还有一个速度决定他们飞翔的方向和距离。然后粒子们就追随当前的最优粒子在解空间中搜索。 • PSO初始化为一群随机粒子。然后通过叠代找到最优解。在每一次叠代中，粒子通过跟踪两个"极值"来更新自己。第一个就是粒子本身所找到的最优解。这个解叫做个体极值pBest. 另一个极值是整个种群目前找到的最优解。这个极值是全局极值gBest。另外,也可以不用整个种群而只是用其中一部分的邻居。

  46. Shandong UNIVERSITY PSO • PSO算法数学表示如下： • 设搜索空间为D维，总粒子数为n。第i个粒子位置表示为向量Xi=( xi1, xi2,…, xiD)；第i个粒子 “飞行”历史中的过去最优位置（即该位置对应解最优）为Pi=( pi1,pi2,…,piD )，其中第g个粒子的过去最优位置Pg为所有Pi ( i=1, …,n)中的最优；第i个粒子的位置变化率（速度）为向量Vi=(vi1, vi2,…, viD)。每个粒子的位置按如下公式进行变化（“飞行”）： 其中，C1,C2为正常数，称为加速因子；rand( )为[0，1]之间的随机数；w称惯性因子，w较大适于对解空间进行大范围探查(exploration)，w较小适于进行小范围开挖(exploitation)。第d（1≤d≤D）维的位置变化范围为[-XMAXd , XMAXd]，速度变化范围为[-VMAXd , VMAXd]，迭代中若位置和速度超过边界范围则取边界值。

  47. Shandong UNIVERSITY PSO • 粒子群初始位置和速度随机产生，然后按公式(1)(2)进行迭代，直至找到满意的解。目前，常用的粒子群算法将全体粒子群(Global)分成若干个有部分粒子重叠的相邻子群，每个粒子根据子群(Local)内历史最优Pl调整位置，即公式(2)中Pgd换为Pld。

  48. Shandong UNIVERSITY Basic Particle Swarm Optimization • A PSO algorithm maintains a swarm of particles, where each particle represents a potential solution. In analogy with evolutionary computation paradigms, a swarm is similar to a population, while a particle is similar to an individual. In simple terms, the particles are “flown” through a multidimensional search space, where the position of each particle is adjusted according to its own experience and that of its neighbors. • Let xi(t) denote the position of particle i in the search space at time step t; unless otherwise stated, t denotes discrete time steps. The position of the particle is changed by adding a velocity, vi(t), to the current position

More Related