1. Particle Swarm Optimization Speaker: Lin, Wei-Kai 2008.10.28

2. 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

3. 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

4. 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)

5. 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

6. 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 particle’s best solution and the population’s best solution

7. The Particle Swarm in Real-Number Space A population of particles (individuals) With position x i and velocity v i Updates the velocity according to the individual’s previous best p i and the neighborhood’s best p g The weights φ 1 and φ 2 are random numbers bounded by a constant To prevent “explosion,” each component of the velocity vector is bounded by a constant ± V max

8. Schwefel's function

9. Initial State

10. After 5 Generations

11. After 10 Generations

12. After 15 Generations

13. After 20 Generations

14. After 25 Generations

15. After 100 Generations

16. After 500 Generations

17. A Model of Binary Search Space Similar concept, but x i is a binary string The velocity vector v i, or predisposition, corresponds to the probability of changing the string Where ρ id is a uniform random number in [0,1], and s(x) is the sigmoid function

18. Conclusions & Discussions Observations in social science applied to optimization problems The global communication and velocity properties plays an important role