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Particle Swarm optimizat ion

Particle Swarm optimizat ion. Cooperation example. Outline. Basic Idea of PSO Neighborhood topologies Velocity and position Update rules Choice of parameter value Applications. The basic idea. Each particle is searching for the optimum

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Particle Swarm optimizat ion

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  1. Particle Swarm optimization

  2. Cooperation example

  3. Outline • Basic Idea of PSO • Neighborhood topologies • Velocity and position Update rules • Choice of parameter value • Applications

  4. The basic idea • Each particle is searching for the optimum • Each particle is moving and hence has a velocity. • Each particle remembers the position it was in where it had its best result so far (its personal best) • But this would not be much good on its own; particles need help in figuring out where to search.

  5. The basic idea II • The particles in the swarm co-operate. They exchange information about what they’ve discovered in the places they have visited • The co-operation is very simple. In basic PSO it is like this: • A particle has a neighbourhood associated with it. • A particle knows the fitnesses of those in its neighbourhood, and uses the position of the one with best fitness. • This position is simply used to adjust the particle’s velocity

  6. Initialization. Positions and velocities

  7. What a particle does • In each timestep, a particle has to move to a new position. It does this by adjusting its velocity. • The adjustment is essentially this: • The current velocity PLUS • A weighted random portion in the direction of its personal best PLUS • A weighted random portion in the direction of the neighbourhood best. • Having worked out a new velocity, its position is simply its old position plus the new velocity.

  8. Neighbourhoods geographical social

  9. Neighbourhoods Global

  10. Particles Adjust their positions according to a ``Psychosocial compromise’’ between what an individual is comfortable with, and what society reckons My best perf. pi Here I am! The best perf. of my neighbours x pg v

  11. Pseudocodehttp://www.swarmintelligence.org/tutorials.php

  12. PSO with global best (gbest) model

  13. PSO with local best (lbest) model

  14. Velocity clamping

  15. Animated illustration Global optimum

  16. Parameters • Inertia weight W • Number of particles • C1 (importance of personal best) • C2 (importance of neighbourhood best) • Neighborhood size for lbest model

  17. The right way This way Or this way How to choose parameters

  18. Parameters • Number of particles (5—30) are reported as usually sufficient. • C1 (importance of personal best) • C2 (importance of neighbourhood best) • Usually C1+C2 = 4. • Vmax – too low, too slow; too high, too unstable. • Neighborbood: 2-3, or probability; p=1-pow(1-1/(size),3);

  19. Rastrigin Griewank Rosenbrock Some functions often used for testing real-valued optimisation algorithms

  20. ... and some typical results Optimum=0, dimension=30 Best result after 40 000 evaluations

  21. Adaptive swarm size I try to kill myself There has been enough improvement although I'm the worst I try to generate a new particle I'm the best but there has been not enough improvement

  22. Adaptive coefficients rand(0…b)(p-x) av The better I am, the more I follow my own way The better is my best neighbour, the more I tend to go towards him

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