Particle Swarm optimisation e.com Particle Swarm optimisation: A mini tutorial

Particle Swarm optimisation e.com The “inventors” (1) Russell Eberhart

Particle Swarm optimisation e.com The “inventors” (2) James Kennedy

Particle Swarm optimisation e.com Part 1: United we stand

Particle Swarm optimisation e.com Cooperation example

Particle Swarm optimisation e.com Initialization. Positions and velocities

Particle Swarm optimisation e.com Neighbourhoods geograph ical social

Particle Swarm optimisation e.com The circular neighbourhood Virtual circle Particle 1’s 3- neighbourho od

Particle Swarm optimisation e.com Psychosocial compromise Here I am! The best perf. of my neighbours My best perf. x pgpg pipi v i-proximity g-proximity

Particle Swarm optimisation e.com The historical algorithm for each particle update the velocity then move for each component d At each time step t Randomn ess inside the loop

Particle Swarm optimisation e.com Random proximity x pgpg pipi v i-proximity g-proximity Hyperparallelepiped => Biased

Particle Swarm optimisation e.com Animated illustration Global optimu m

Particle Swarm optimisation e.com Part 2: How to choose parameters The right way This way Or this way

Particle Swarm optimisation e.com Type 1” form with Usual values:  =1  =4.1 =>  =0.73 swarm size=20 hood size=3 Non divergence criterion Global constriction coefficient

Particle Swarm optimisation e.com 5D complex space } } Convergence Non diverge nce A 3D section  Re(y) Re(v)

Particle Swarm optimisation e.com Move in a 2D section (attractor)

Particle Swarm optimisation e.com Some functions... Rosenbrock Griewank Rastrigin

Particle Swarm optimisation e.com... and some results Optimum=0, dimension=30 Best result after evaluations

Particle Swarm optimisation e.com Beat the swarm! Your current position Your best perf. Best perf. of the swarm

Particle Swarm optimisation e.com Part 3: Beyond real numbers Bingo!

Particle Swarm optimisation e.com Minimun requirements Comparing positions in the search space H Algebraic operators

Particle Swarm optimisation e.com velocity = pos_minus_pos(position 1, position 2 ) velocity = linear_combin( ,velocity 1, ,velocity 2 ) position = pos_plus_vel(position, velocity) (position,velocity) = confinement(position t+1,position t ) Pseudo code form } algebra ic operat ors =>

Particle Swarm optimisation e.com Fifty-fifty N=100, D=20. Search space: [1,N] D 105 evaluations: = (=450) granularity=1

Particle Swarm optimisation e.com Knapsack N=100, D=10, S=100, 870 evaluations: run 1 => (9, 14, 18, 1, 16, 5, 6, 2, 12, 17) run 2 => (29, 3, 16, 4, 1, 2, 6, 8, 26, 5) granularity=1

Particle Swarm optimisation e.com Graph Coloring Problem = pos - plus - vel

Particle Swarm optimisation e.com The Tireless Traveller Example of position: X=(5,3,4,1,2,6) Example of velocity: v=((5,3),(2,5),(3,1))

Particle Swarm optimisation e.com n1n1 n3n3 n2n2 Apple trees Swarm size=3 Best position

Particle Swarm optimisation e.com Part 4: Some variants

Particle Swarm optimisation e.com Unbiased random proximity x pgpg pipi v i-proximity g-proximity Hyperparallelepiped => Biased Dimension Volume Hypersphere vs hypercube

Particle Swarm optimisation e.com Clusters and queens Each particle is weighted by its perf. Dynamic clustering Centroids = queens = temporary new “particles”

Particle Swarm optimisation e.com Think locally, act locally (Adaptive versions)

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

Particle Swarm optimisation e.com Adaptive coefficients 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 vv rand(0… b )(p-x)

Particle Swarm optimisation e.com Energies: classical process Rosenbrock 2D. Swarm size=20, constant coefficients

Particle Swarm optimisation e.com Energies: adaptive process Rosenbrock 2D. Adaptive swarm size, adaptive coefficients

Particle Swarm optimisation e.com Part 5: Real applications (hybrid) Medical diagnosis Industrial mixer Electrical generatorElectrical vehicle

Particle Swarm optimisation e.com Real applications (stand alone) Cockshott A. R., Hartman B. E., "Improving the fermentation medium for Echinocandin B production. Part II: Particle swarm optimization", Process biochemistry, vol. 36, 2001, p He Z., Wei C., Yang L., Gao X., Yao S., Eberhart R. C., Shi Y., "Extracting Rules from Fuzzy Neural Network by Particle Swarm Optimization", IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, USA, Secrest B. R., Traveling Salesman Problem for Surveillance Mission using Particle Swarm Optimization, AFIT/GCE/ENG/01M-03, Air Force Institute of Technology, Yoshida H., Kawata K., Fukuyama Y., "A Particle Swarm Optimization for Reactive Power and Voltage Control considering Voltage Security Assessment", IEEE Trans. on Power Systems, vol. 15, 2001, p

Particle Swarm optimisation e.com To know more Clerc M., Kennedy J., "The Particle Swarm-Explosion, Stability, and Convergence in a Multidimensional Somplex space", IEEE Transaction on Evolutionary Computation, 2002,vol. 6, p Clerc M., "L'optimisation par essaim particulaire. Principes et pratique", Hermès, Techniques et Science de l'Informatique, Particle Swarm Central, THE site: Self advert

Particle Swarm optimisation e.com Appendix

Particle Swarm optimisation e.com Canonical form    M Eigen values e 1 and e 2

Particle Swarm optimisation e.com Constriction Constriction coefficients

Particle Swarm optimisation e.com Convergence criterion 

Particle Swarm optimisation e.com Magic Square (1)

Particle Swarm optimisation e.com Magic Square (2) D=3x3, N= runs evaluations 10 solutions

Particle Swarm optimisation e.com Non linear system Search space [0,1] 2 1 run 143 evaluations 1 solution 10 runs 1430 evaluations 3 solutions

Particle Swarm optimisation e.com