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Swarm Intelligence on Graphs. Advanced Computer Networks: Part 2. Agenda. Graph Theory (Brief) Swarm Intelligence Multi-agent Systems Consensus Protocol Example of Work. Graph Theory. Graph Theory. Graph connection: nodes and links (undirected graph: balanced digraph) Identity matrix

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swarm intelligence on graphs

Swarm Intelligence on Graphs

Advanced Computer Networks: Part 2

agenda
Agenda
  • Graph Theory (Brief)
  • Swarm Intelligence
  • Multi-agent Systems
  • Consensus Protocol
  • Example of Work
graph theory1
Graph Theory
  • Graph connection: nodes and links (undirected graph: balanced digraph)
  • Identity matrix
    • or unit matrix of size n is the n×nsquare matrix with ones on the main diagonal and zeros elsewhere
        • AIn= A

Identity Matrix

graph theory2
Graph Theory
  • Adjacency matrix
    • a means of representing which or nodes of a graph are adjacent to which other nodes

n1

n2

n3

n4

n5

n6

n1

n2

n3

Node 1-6

n4

n5

n6

Graph

Adjacency Matrix

graph theory3
Graph Theory
  • Degree matrix

n1

n2

n3

n4

n5

n6

n1

n2

n3

Node 1-6

n4

n5

n6

Graph

Degree Matrix

graph theory4
Graph Theory
  • Laplacian matrix

L =

Graph

swarm behavior in nature
Swarm Behavior in Nature

Collective Behavior

Self-organized System

swarm intelligence
Swarm Intelligence
  • Ant Colony OptimizationAlgorithms

http://www.funpecrp.com.br/gmr/year2005/vol3-4/wob09_full_text.htm

swarm intelligence1
Swarm Intelligence
  • Ant Colony OptimizationAlgorithms
    • The Traveling Salesman Problem
  • A set of cities is given and the distance between each of them is known.
  • The goal is to find the shortest tour that allows each city to be visited once and only once.
swarm intelligence2
Swarm Intelligence
  • Ant Colony OptimizationAlgorithms
    • the Traveling Salesman Problem: An iterative algorithm
      • At each iteration, a number of artificial ants are considered.
      • Each of them builds a solution by walking from node to node on the graph with the constraint of not visiting any vertex that she has already visited in her walk.
      • An ant selects the following node to be visited according to a stochastic mechanism that is biased by the pheromone: when in node i, the following node is selected stochastically among the previously unvisited ones
      • if j has not been previously visited, it can be selected with a probability that is proportional to the pheromone associated with edge (i, j).
      • the pheromone values are modified in order to bias ants in future iterations to construct solutions similar to the best ones previously constructed.
swarm intelligence3
Swarm Intelligence
  • Ant Colony OptimizationAlgorithms
swarm intelligence4
Swarm Intelligence
  • Ant Colony OptimizationAlgorithms
    • ConstructAntSolutions:
      • A set of m artificial ants constructs solutions from elements of a finite set of available solution components.
    • ApplyLocalSearch:
      • Once solutions have been constructed, and before updating the pheromone, it is common to improve the solutions obtained by the ants through a local search.
    • UpdatePheromones:
      • The aim of the pheromone update is to increase the pheromone values associated with good or promising solutions, and to decrease those that are associated with bad ones.
      • Usually, this is achieved
        • by decreasing all the pheromone values through pheromone evaporation
        • by increasing the pheromone levels associated with a chosen set of good solutions.
swarm intelligence5
Swarm Intelligence
  • Particle Swarm OptimizationAlgorithms (PSO)
    • PSO emulates the swarm behavior of insects, animals herding, birds flocking, and fish schooling where these swarms search for food in a collaborative manner.
    • Each member in the swarm adapts its search patterns by learning from its own experience and other members’ experiences.
    • A member in the swarm, called a particle, represents a potential solution which is a point in the search space.
    • The global optimum is regarded as the location of food.
    • Each particle has a fitness value and a velocity to adjust its flying direction according to the bestexperiences of the swarm to search for the global optimum in the solution space.

http://science.howstuffworks.com/environmental/life/zoology/insects-arachnids/termite3.htm

swarm intelligence6
Swarm Intelligence
  • Particle Swarm OptimizationAlgorithms (PSO)

http://www.sciencedirect.com/science/article/pii/S0960148109001232

swarm intelligence7
Swarm Intelligence
  • Application of Swarm Principles: Swarm of Robotics
  • http://www.youtube.com/watch?feature=player_embedded&v=rYIkgG1nX4E#!

http://www.domesro.com/2008/08/swarm-robotics-for-domestic-use.html

multi agent systems
Multi-Agent Systems
  • Multi-agent system
    • Many agents:
      • homogeneous
      • heterogeneous
    • Interaction topology
      • complex network
  • How to control the global behavior of the multi-agent system?
  • How to apply the proposed model to solve the realistic problem?

17

consensus protocols
Consensus Protocols
  • Consensus problem
    • A group of agents
      • To make a decision
      • To reach an agreement
      • Depend on their shared state information
      • Information exchange among the agents
  • To design a suitable protocol for the group to reach a consensus
  • Shared information among agents is converged to the group decision value
    • but do not allow to reach a particular value

18

leader following discrete time consensus protocol
Leader-Following Discrete-time Consensus Protocol
  • Effective leadership and decision making in animal groups on the move

22

leader following discrete time consensus protocol1
Leader-Following Discrete-time Consensus Protocol
  • Leader-following consensus models
    • agreement of a group based on specific quantities of interest
  • Leader
    • an external input to control the global behavior of the system
    • determine the final state of the system
    • unaffected by the followers
    • send the information to the followers only
  • Followers
    • reach consensus following the leader\'s state
    • influenced by the leader directly
    • no feedback information from the followers to the leader

23

w ren 2007
W. Ren, 2007
  • Multi-vehicle consensus with a time-varying reference state

1

24

y cao 2009
Y. Cao, 2009
  • Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication

4

26

y cao 20091
Y. Cao, 2009

5

ζ1(0)=3, ζ2(0)=1, ζ3(0)=-1, ζ4(0)=-2

ζ1(-1)=0, ζ2(-1)=0, ζ3(-1)=0, ζ4(-1)=0

27

further work
Further Work
  • Large scale multi-agent networks with dynamical topologies
  • Partial information exchange between followers and leader
    • How to identify the leader?
    • How the leader control the group behavior?
  • Consensus on large scale multi-agent networks

34

references
References
  • www.wikipedia.com
  • Marco Dorigo, Mauro Birattari, and Thomas St¨utzle, “Ant Colony Optimization”, IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE, NOVEMBER, 2006.
  • J. J. Liang, A. K. Qin, “Comprehensive Learning Particle Swarm Optimizer for Global Optimization of Multimodal Functions”, IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 10, NO. 3, JUNE 2006.
  • J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations," IEEE Trans. Autom. Control, vol. 49, pp.1465-1476, 2004.
  • D. B. Kingston, R. W. Beard, "Discrete-time average-consensus under switching network topologies," in Proc. American Control Conf.,14-16 June 2006.
  • W. Ren, "Multi-vehicle consensus with a time -varying reference state, “Systems & Control Letters, vol. 56, pp. 474-483, 2007.
  • Y. Cao, W. Ren, Y. Li, "Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication," Automatica, vol. 45, pp. 1299-1305, 2009.
  • J. Hu, Y. Hong, "Leader-follower coordination of multi-agent systems with coupling time delays," Physica A: Statistical Mechanics and its Applications., vol. 374, iss. 2, pp.853-863, 2007.
  • D. Bauso, L. Giarr\'e, R. Pesenti, "Distributed consensus protocols for coordinating buyers," Proc. IEEE Decision and Control Conf., December, 2003.
  • R. E. Kranton, D. F. Minehart, "A theory of buyer-seller networks," The American Economic Review, vol. 91, no. 3, pp. 485-508, 2001.
  • I.D. Couzin, J. Krause, N.R. Franks, S. A. Levin, “Effective leadership and decision making in animal groups on the move,” Nature, iss. 433, pp. 513-516, 2005.
  • R.O. Saber, R.M. Murray, “Flocking with obstacle avoidance: cooperation with limited communication in mobile networks,” in Proc. IEEE Decision and Control Conf., vol.2, pp. 2022-2028, 2003.
  • E. Semsar-Kazerooni, K. Khorasani, “Optimal consensus algorithms for cooperative team of agents subject to partial information,” Automatica, 2008.
  • J. Zhou, W. Yu, X. Wu, M. Small, J. Lu, “Flocking of multi-agent dynamical systems based on pseudo-leader mechanism,” Chaotic Dynamics, 2009.

35

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