Swarm Intelligence on Graphs
description
Transcript of Swarm Intelligence on Graphs
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Swarm Intelligence on Graphs
Advanced Computer Networks: Part 2
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Agenda
Graph Theory (Brief)
Swarm Intelligence
Multi-agent Systems
Consensus Protocol
Example of Work
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Graph Theory
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Graph Theory
Graph connection: nodes and links (undirected graph: balanced digraph)
Identity matrix or unit matrix of size n is the n×n square matrix w
ith ones on the main diagonal and zeros elsewhere
AIn = A
Identity Matrix
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Graph Theory
Adjacency matrix a means of representing which or nodes of a
graph are adjacent to which other nodes
Graph Adjacency Matrix
Node 1-6
n1 n2 n3 n4 n5 n6n1n2n3n4n5n6
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Graph Theory
Degree matrix
Graph
n1 n2 n3 n4 n5 n6
Node 1-6
n1n2n3n4n5n6
Degree Matrix
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Graph Theory
Laplacian matrix
Graph
L =
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Swarm Behavior in Nature
Collective Behavior
Self-organized System
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Swarm Intelligence
Ant Colony Optimization Algorithms
http://www.funpecrp.com.br/gmr/year2005/vol3-4/wob09_full_text.htm
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Swarm Intelligence
Ant Colony Optimization Algorithms 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.
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Swarm Intelligence Ant Colony Optimization Algorithms
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.
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Swarm Intelligence
Ant Colony Optimization Algorithms
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Swarm Intelligence Ant Colony Optimization Algorithms
ConstructAntSolutions: A set of m artificial ants constructs solutions from elements of a finite set of availab
le solution components.
ApplyLocalSearch: Once solutions have been constructed, and before updating the pheromone, it is c
ommon 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.
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Swarm Intelligence Particle Swarm Optimization Algorithms (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
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Swarm Intelligence
Particle Swarm Optimization Algorithms (PSO)
http://www.sciencedirect.com/science/article/pii/S0960148109001232
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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
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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?
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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
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Consensus Protocols
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Consensus Protocols
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Calculation Examination
100100021100013110111410001131000011
L
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Leader-Following Discrete-time Consensus Protocol Effective leadership
and decision making in animal groups on the move
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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
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W. Ren, 2007
Multi-vehicle consensus with a time-varying reference state
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W. Ren, 2007
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Y. Cao, 2009
Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication
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Y. Cao, 2009
5ζ1(0)=3, ζ2(0)=1, ζ3(0)=-1, ζ4(0)=-2
ζ1(-1)=0, ζ2(-1)=0, ζ3(-1)=0, ζ4(-1)=0
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Example of Work: Leader-Following
Behavior
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Proposed work: Leader-Following Behavior
0 5 10 15 20 25 30 35 40 45 50-0.5
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node 1node 2node 3node 4LEADER
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Leader-Following Behavior
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Leader-Following Behavior leader connects to node 1, 2, 3, 4 respectively
1Compared with
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Leader-Following Behavior 5
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Leader-Following Behavior
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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
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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.