Swarm Intelligence

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Swarm Intelligence

• ???

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Content

• Overview
• Swarm Particle Optimization (PSO)
• Example
• Ant Colony Optimization (ACO)

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Swarm Intelligence

• Overview

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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
• Achieving a collective performance which could
  not normally be achieved by an individual acting
  alone
• Constituting a natural model particularly suited
  to distributed problem solving

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Swarm Intelligence
http//www.scs.carleton.ca/arpwhite/courses/95590
Y/notes/SI20Lecture203.pdf
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Swarm Intelligence
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Swarm Intelligence
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Swarm Intelligence
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Swarm Intelligence
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Swarm Intelligence Particle Swarm Optimization
(PSO)

• Basic Concept

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The Inventors
Russell Eberhart
James Kennedy
social-psychologist
electrical engineer
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Particle Swarm Optimization (PSO)
Developed in 1995 by James Kennedy and Russell
Eberhart.

• PSO is a robust stochastic optimization technique
  based on the movement and intelligence of swarms.
• PSO applies the concept of social interaction to
  problem solving.

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PSO Search Scheme

• It uses a number of agents, i.e., particles, that
  constitute a swarm moving around in the search
  space looking for the best solution.
• Each particle is treated as a point in a
  N-dimensional space which adjusts its flying
  according to its own flying experience as well as
  the flying experience of other particles.

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Particle Flying Model

• pbest ? the best solution achieved so far by that
  particle.
• gbest ? the best value obtained so far by any
  particle in the neighborhood of that particle.

• The basic concept of PSO lies in accelerating
  each particle toward its pbest and the gbest
  locations, with a random weighted acceleration at
  each time.

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Particle Flying Model
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Particle Flying Model

• Each particle tries to modify its position using
  the following information
• the current positions,
• the current velocities,
• the distance between the current position and
  pbest,
• the distance between the current position and the
  gbest.

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Particle Flying Model
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PSO Algorithm


For each particle     Initialize
particle END Do    For each particle        
Calculate fitness value         If the fitness
value is better than the best fitness value
(pbest) in history            set current value
as the new pbest    End    Choose the particle
with the best fitness value of all the particles
as the gbest    For each particle        
Calculate particle velocity according equation
()         Update particle position according
equation ()    End While maximum iterations or
minimum error criteria is not attained
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Swarm Intelligence Particle Swarm Optimization
(PSO)

• Examples

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Schwefel's Function
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Simulation ? Initialization
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Simulation ? After 5 Generations
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Simulation ? After 10 Generations
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Simulation ? After 15 Generations
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Simulation ? After 20 Generations
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Simulation ? After 25 Generations
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Simulation ? After 100 Generations
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Simulation ? After 500 Generations
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Summary
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Exercises

• Compare PSO with GA
• Can we use PSO to train neural networks? How?

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Particle Swarm Optimization (PSO)

• Ant Colony Optimization (ACO)

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Facts

• Many discrete optimization problems are difficult
  to solve, e.g., NP-Hard
• Soft computing techniques to cope with these
  problems
• Simulated Annealing (SA)
• Based on physical systems
• Genetic algorithm (GA)
• based on natural selection and genetics
• Ant Colony Optimization (ACO)
• modeling ant colony behavior

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Ant Colony Optimization
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Background

• Introduced by Marco Dorigo (Milan, Italy), and
  others in early 1990s.
• A probabilistic technique for solving
  computational problems which can be reduced to
  finding good paths through graphs.
• They are inspired by the behaviour of ants in
  finding paths from the colony to food.

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Typical Applications

• TSP ? Traveling Salesman Problem
• Quadratic assignment problems
• Scheduling problems
• Dynamic routing problems in networks

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Natural Behavior of Ant
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ACO Concept

• Ants (blind) navigate from nest to food source
• Shortest path is discovered via pheromone trails
• each ant moves at random, probabilistically
• pheromone is deposited on path
• ants detect lead ants path, inclined to follow,
  i.e.,
• more pheromone on path increases probability of
  path being followed

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ACO System

• Virtual trail accumulated on path segments
• Starting node selected at random
• Path selection philosophy
• based on amount of trail present on possible
  paths from starting node
• higher probability for paths with more trail
• Ant reaches next node, selects next path
• Continues until goal, e.g., starting node for
  TSP, reached
• Finished tour is a solution

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ACO System
, cont.

• A completed tour is analyzed for optimality
• Trail amount adjusted to favor better solutions
• better solutions receive more trail
• worse solutions receive less trail
• ?higher probability of ant selecting path that is
  part of a better-performing tour
• New cycle is performed
• Repeated until most ants select the same tour on
  every cycle (convergence to solution)

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Ant Algorithm for TSP

• Randomly position m ants on n cities
• Loop
• for step 1 to n
• for k 1 to m
• Choose the next city to move by
  applying
• a probabilistic state transition rule
  (to be described)
• end for
• end for
• Update pheromone trails
• Until End_condition

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Pheromone Intensity
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Ant Transition Rule
Probability of ant k going from city i to j
the set of nodes applicable to ant k at city i
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Ant Transition Rule
Probability of ant k going from city i to j

• ? 0 a greedy approach
• ? 0 a rapid selection of tours that may not
  be optimal.
• Thus, a tradeoff is necessary.

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Pheromone Update
Q a constant Tk(t) the tour of ant k at time
t Lk(t) the tour length for ant k at time t
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Demonstration