Particle Swarm Optimization

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Particle Swarm Optimization

• Speaker Lin, Wei-Kai
• 2008.10.28

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What is Swarm?

• A large number of small animals or insects A
  swarm of bees -- Webster
• Swarming is the natural means of reproduction of
  honey bee colonies -- Wikipedia

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Swarm Intelligence

• Based on the collective behavior of
  decentralized, self-organized systems
• Introduced by Gerardo Beni and Jing Wang in 1989,
  in the context of cellular robotic systems
• Emphasis on the interactions between agents, that
  is, the social behavior
• Related to the game of life

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The Family of Swarm Intelligence

• Ant colony optimization
• Particle Swarm Optimization (PSO)
• Stochastic Diffusion Search (SDS)
• First described by Bishop in 1989
• Partial evaluation on the hypotheses
• One-to-one communication between agents
• Share information about hypotheses (diffusion)

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Particle Swarm Optimization

• Was first described in 1995 by James Kennedy and
  Russell C. Eberhart
• Two assertions
• Mind is social
• Particle swarms are a useful computational
  intelligence (soft computing) methodology
• Provides a useful paradigm
• It is an extension of cellular automata

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The Concepts of The Algorithm

• Each particle has a position, which is a
  candidate solution to the problem to solve,
• And a velocity, which is the rate of position
  changing
• The velocity is updated according to the
  particles best solution and the populations
  best solution

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The Particle Swarm inReal-Number Space

• A population of particles (individuals)
• With position xi and velocity vi
• Updates the velocity according to the
  individuals previous best pi and the
  neighborhoods best pg
• The weights f1 and f2 are random numbers bounded
  by a constant
• To prevent explosion, each component of the
  velocity vector is bounded by a constant Vmax

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Schwefel's function
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Initial State
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After 5 Generations
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After 10 Generations
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After 15 Generations
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After 20 Generations
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After 25 Generations
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After 100 Generations
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After 500 Generations
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A Model of Binary Search Space

• Similar concept, but xi is a binary string
• The velocity vector vi, or predisposition,
  corresponds to the probability of changing the
  string
• Where ?id is a uniform random number in 0,1,
  and s(x) is the sigmoid function

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Conclusions Discussions

• Observations in social science applied to
  optimization problems
• The global communication and velocity properties
  plays an important role