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Zhangang Han Beijing Normal University BNU Complex Systems Summer School July 20, 2008

Zhangang Han Beijing Normal University BNU Complex Systems Summer School July 20, 2008

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Zhangang Han Beijing Normal University BNU Complex Systems Summer School July 20, 2008

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  1. The Bottom Up Approach Zhangang Han Beijing Normal University BNU Complex Systems Summer School July 20, 2008

  2. Complexity Problems Representation/Model Results Simple Simple Simple Simple Complex Complex Complex Complex Complex Complex Simple Plenty and adjustable The Micro-level Mechanism of Macro-level phenomena

  3. Bottom Up • Theory Driven • Data Driven • Agent-Oriented

  4. Mathematical Models vs. Evolving Agents • Math formulas are used to model physics, biology, economics systems: Ordinary Differential Equations, Partial Diff. Equ. • Evolving agents: • Self-interested autonomous individuals • Environment • Rules • Actions • Mutual interactions • Adaptation

  5. Mathematical Models vs. Evolving Agents • MM: global, collective variables • EA: individual variables • MM: represent complex macro-phenomena • EA: how these phenomena emerges • MM: represent interactions with math formulas • EA: represent interactions with rules and actions • MM: interaction style are fixed with the formula • EA: the rules can evolve

  6. Mathematical Models vs. Evolving Agents • MM: behavior of the model is determined by the formula employed • EA: behavior of the system can adapt with environment and rules • MM: individuals are identical in statistical manner • EA: individuals are distinguishable, actions traced

  7. Mathematical Models vs. Evolving Agents • MM: Distinguish endogenous/exogenous variables • EA: Some times exogenous elements are hidden (e.g. agents “decide” what to do, rules can “adapt”) • MM: More computationally efficient in case of very large systems, eg., a typical chemical process (6.02pow(10, 23)) • EA: Computationally inefficient for very large number of agents

  8. 遗传算法

  9. What Are Genetic Algorithms • Charles Robert Darwin, 1809-1882 • The Origin of Species: Survival of the fittest • A Basic GA: • Survival of the fittest • Crossover • Mutation

  10. What Are Genetic Algorithms (2) • 60`s Adaptive Systems • GAs • John Holland, 1975, Adaptation in Natural and Artificial Systems • Kenneth De Jong, 1975, Function Optimization • Evolutionary Programming • Lawrence J. Forgel, 1966 • David B. Forgel, 1992

  11. What Are Genetic Algorithms (3) • Evolutionary Strategies • Ingo Rechenberg, 1973 • Hans Paul Schwefel, 1975 • 一种组合(搜索)算法,基于自然界的基因组合与性状反映和自然选择思想,由基因结构体的一个外界适应性函数指导搜索。

  12. GAs 特性 • Robust(鲁棒性) • Parallel • Adaptive • Domain Independent (领域无关) • 可解决multi-modal的问题 • 不一定每次运行都能找到最优解,但是可以很快找到一个近似解。

  13. GAs 基础 • 描述一个问题的一组变量 x1, x2, ..., xm,可以编码为一个长为 l 的字符串 : • S={a1,a2,..., am} • 字符串有适应性函数f(x1,x2,...xm),问题的解可表示为求f(x1,x2,...xm)的最大值 • 构成集 • 搜索空间

  14. 算法 • Initial Population • 010101110 f1=f(.) • 001110010 f2= • ... ..... fi= • 110110110 fn= • Reproduction • (Roulette Wheel) • Crossover • 000000/000 000000111 • 111111/111 111111000 • Mutation 0--1

  15. 结束条件: • 规定代数 • Fitness达到规定条件 • Max{fi} • Avg{fi} • 例:Fitness函数 • 变量区间: • 表示精度:0.1

  16. and sin log not or x1 x2 x3 x1 x2 x3 Genetic Programming 表示内容,构成集, 杂交,变异

  17. 实数遗传算法 • 个体: 实数 23.56, 36.78 • 优点: 速度快 • 1992, Nicol N Schraudolph (University of California, San Diego) • Dynamic Parameter Encoding • 复制,杂交,变异, • Alpha, beta杂交: • alpha1=(1-lamda)*alpha+lamda*beta • Beta1=lamda*alpha+(1-lamda)*beta

  18. 遗传算法的改进 • 1,按照Rank复制:Advantages, Disadvantages • 2,社会:杂交时选择性别,社会地位 • 3,Niche:定义,相似性,复制,杂交:新个体替换从原群体中选出的S个与新个体相似的个体中,最差的 • 4,寻优速度和成功度 • Re-scale: rescale the fitness function • Convergence speed, and diversity

  19. 履行推销员问题(TSP) • TSP:城市,距离,NP hard (Non-polynomial) • Crossover的不同寻常 • A=9 8 4 | 5 6 7 | 1 3 2 10 • B=8 7 1 | 2 3 10| 9 5 4 6 • C=9 8 4 2 3 10 1 6 5 7 • D=8 10 1 5 6 7 9 2 4 3 • 大于30个城市是效果明显

  20. 任务排队 • 已知n个任务,m个加工程序,每个任务在每道工序的加工时间 t11,……tnm, 任务如何排队,使得所有任务的等待时间和最小. • (NP) • 个体:每个任务在每一道工序的排列顺序 • Fitness: 所需总时间

  21. 人工神经网络 xi

  22. 参数学习:Hebb学习规则 • 两端神经元同步激活时,增强 • 用遗传算法来学习参数(权值与阈值) • 用于拓扑结构设计

  23. 从数据中发现规律 • Knowledge Discovery in Databases • Data Mining • Scientific Discovery

  24. Chromosome Scheme Source: John Holland

  25. 画影图形 • VLSI • 超市:哪4种商品一起卖得最多 • 不规则器件的剪裁 • 机器学习

  26. 股票价格预测 • 2000,M.A.,Kaboudan (Penn State) 结果与Naïve 模型(pt=pt-1)比较 GP可预测性

  27. 例: Find the best x,y locations for three radio towers to cover the most towns (and therefore reach the most listeners). Each of the radio towers has a different range.

  28. 例:Select the most effective advertising plan to reach the largest audience while meeting your budget of $50,000. TV and magazines allows discount rates if you advertise with them often.

  29. 例:risk of loss

  30. 收敛复杂性 • Valiant, 1984, Probably Approximately Correct, ACM Communication • 算法步骤随问题的复杂性、所要求的概率、误差精度的提高,多项式地增加。

  31. Valiant’s theory of the learnable considers learning of unknown Boolean concepts with two protocols, EXAMPLES and ORACLE(). Let D be a probability distribution on the set of vectors v such that

  32. A predicate is learnable if and only if there exists an algorithm such that: • • it runs in polynomial time in l and in a parameter h • • with probability1-1/h , the deduced predicate never outputs 1 when it should not, but outputs 1 almost always when it should.

  33. L(h,l) is defined as the smallest integer such that in L independent Bernoulli trials each with probability 1/h of success, the probability of having fewer than l successes is less than 1/h. • • For all integers l>=1 and all real h>1, .

  34. 收敛复杂性定义 • 假设一个问题类中的每一个问题都可以编码为一个字符串,串长l;问题的解决可以转化为找到串的适应度值的最优值。这类问题是利用遗传算法概率意义上近似收敛可解的,

  35. 如果对问题类中的任意一个问题,对任意小的ε≥0和任意小的0≤δ≤1,存在一个遗传算法Ag,存在一个l,δ,ε的多项式,如果对问题类中的任意一个问题,对任意小的ε≥0和任意小的0≤δ≤1,存在一个遗传算法Ag,存在一个l,δ,ε的多项式, • 使得遗传算法Ag在N= 步内可以以一个概率p≥1-δ找到一个最大值 与最优值的差为

  36. ICNC09 • Of the theory researches • K. De Jong “Evolutionary Computation: a unified approach”, the Genetic and Evolutionary Computation Conference (GECCO 07), 2007. • “AI in China: a survey”, IEEE Intelligent Systems, vol. 23, no. 6, 2008 • Of practice researches • pattern recognition, evolvable hardware, VLSI routing, computer vision, diesel engine preferences for pollution emission controlling, and network safety and optimization.

  37. Theoretical researches of EA • Convergence speed VS. diversity • The combination of EA with other methods • Computation complexity

  38. Theoretical researches of EA 1. Premature remains to be the hard issue 2.Incorporating new algorithms • EA incorporates with such methods as PSO, multi-agent, quantum theory, immunity etc. • Quantum Genetic Algorithm. • Orthogonal Genetic Algorithm (OGA) . • Multi-Agent Genetic Algorithm (MAGA)3 Incorporating new algorithms • GA based on Immunity (IGA)4 Organizational Co-evolutionary Algorithm for Classification (OCEC)5

  39. Application of EA • Burnable Poisons (BP) placement optimization problem for a core loading in pressurized water reactors (BP loading pattern)6 • To minimize the total Gd amount in the core together with the residual binding at End-of-Cycle (EOC) and to keep the maximum peak pin power and Soluble Boron Concentration (SOB) at the Beginning of Cycle (BOC) both less than their limit values during core depletion. • A practical, simple and efficient GA tool 6. S. Yilmaz and K. Ivanov, “Application of Genetic Algorithm tooptimize Burnable Poison Placement in Pressurized Water Reactors,”the Genetic and Evolutionary Computation Conference (GECCO 05),2005, pp. 1477-1483.

  40. Application of EA • To find UXO (buried unexploded ordnance)7 • A variety of evolutionary computing approaches includes GP, GA, and decision-tree methods. • Predictions were then compared with a ground-truth file and the number of false positives and negatives determined. A 5% of false negative (ordnance not found) is achieved. 7. E. R. Banks, E. Núñez, and C. Owens et al., “Genetic ProgrammingDiscrimination of Buried Unexploded Ordnance (UXO),” the Geneticand Evolutionary Computation Conference (GECCO 05), 2005.

  41. Application of EA • To optimize cancer chemotherapy, find effective chemotherapeutic treatments8 • A methodology for using heuristic search methods • Two evolutionary algorithms - Population Based Incremental Learning (PBIL) and GA • By comparing and analyzing the performance of both algorithms, a conclusion was made as to which approach to cancer chemotherapy optimization is more efficient and helpful in the decision-making activity led by the oncologists. 8. A. Petrovski, S. Shakya, and J.McCall, “Optimising CancerChemotherapy using an Estimation of Distribution Algorithm andGenetic Algorithms,” the Genetic and Evolutionary ComputationConference (GECCO 06), 2006, pp. 413-418.

  42. Application of EA • Fingerprint compression and reconstruction (develop the wavelet scale)9 • A revised GA • Found that the evolution of new wavelet and scaling numbers for optimized transformed that consistently outperform the 9/7 Discrete Wavelet Transform (DWT). 9. B. Babb, “Evolved transforms surpass the FBI Wavelet for ImprovedFingerprint Compression and Reconstruction,” the Genetic andEvolutionary Computation Conference (GECCO 07), 2007, pp. 2603-2606.

  43. Application of EA • Evolvable Hardware (EHW)10 • Combine EA with Programmable Logical Devices (PLD), re-configurable, binary bit • It is booming in circuit design, cybernetics and robotics, fault-tolerant system, pattern recognition and Very Large Scale Integrated circuits (VLSI) design The difficulties in implementing speed and evaluating speed for chromosome. 10. T. G. W. Gordon, P. J. Bentley, On evolvable hardware, in: S.Ovaska, L. Sztandera (Eds.), Soft Computing in IndustrialElectronics, Physica-Verlag, Heidelberg, Germany, 2002, pp. 279-323.

  44. Agents

  45. Bridge bt. Macro-Micro Levels Previous Phys. or Econ. did not cover the gap Irreversible non-equilibrium macro level phenomena Emergence: Evolving Agents Bottom-up Simulation Simple reversible micro level interactions

  46. Adaptation Self-Reinforcement Learning Previous Experiences (Memory ) Pos. & Neg. Feedback Balance

  47. 什么是? • 什么是一个Agent系统,现在并没有一个各个领域公认的,严格的定义。由于应用领域不同,研究人员们对于Agent系统的定义也都从不同的角度出发来建立。 • 有研究者认为,Agent的定义,更像一个研究建模思路,而不是一个具体的技术[Bonabeau, 2002]。另外的研究者认为,Agent的定义,更应该是对一个系统建立模型的工具或方法的描述,而不是用来严格界定现实中或模型中的组成单元,什么是Agent或什么不是Agent[Russell and Norvig, 2003]。

  48. Characteristics • 自主性(Autonomy) • 同质性/异质性(Homogeneity/ Heterogeneity) • 反应与感知(Reactive/Perceptive) • 有限理性(Bounded Rationality) • 相互作用与通讯(Interactive/ Communicative) • 自适应性与学习(Adaptation/ Learning)

  49. Global Pattern Formation and Ethnic/Cultural Violence May Lim, Richard Metzler, Yaneer Bar-Yam New England Complex Systems Institute Science 317, 1540 (Sep. 14, 2007)