1. Swarm Intelligence

2. Content Overview Swarm Particle Optimization (PSO) – Example Ant Colony Optimization (ACO)

3. Swarm Intelligence Overview

4. 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

5. Swarm Intelligence http://www.scs.carleton.ca/~arpwhite/courses/95590Y/notes/SI%20Lecture%203.pdf

6. Swarm Intelligence

10. Swarm Intelligence Particle Swarm Optimization (PSO) Basic Concept

11. The Inventors Russell EberhartJames Kennedy social-psychologistelectrical engineer

12. Particle Swarm Optimization (PSO) 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. Developed in 1995 by James Kennedy and Russell Eberhart.

13. 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.

14. 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.

15. Particle Flying Model

16. 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.

17. 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 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 * **

18. Swarm Intelligence Particle Swarm Optimization (PSO) Examples

19. Simulation  Initialization

20. Simulation  After 5 Generations

21. Simulation  After 10 Generations

22. Simulation  After 15 Generations

23. Simulation  After 20 Generations

24. Simulation  After 25 Generations

25. Simulation  After 100 Generations

26. Simulation  After 500 Generations

27. Summary IterationsgBest 0416.245599 5515.748796 10759.404006 15793.732019 20834.813763 100837.911535 500837.965771 Optimun837.9658