PSO Introduction Proposed by James Kennedy Russell Eberhart
PSO -Introduction Ø Proposed by James Kennedy & Russell Eberhart in 1995 Ø Inspired by social behavior of birds and fishes Ø Combines self-experience with social experience Ø Population-based optimization
PSO -Introduction Ø Finds global optimum with a probability of almost one Ø Suitable for optimizing non-linear nondifferentiable and discontinuous functions – Irrespective of shapes of the objective function. Ø A robust search technique. Ø Suitable for solving large-sized problems. Ø Steps extremely simple -Velocity calculation - Position updation
PSO Concept • Uses a number of particles that constitute a swarm moving around in the search space looking for the best solution. • Each particle in search space adjusts its “flying” according to its own flying experience as well as the flying experience of other particles
PSO –how its works Emulates the behavior of creatures such as a flock of birds or a school of fish. Basic principle: Ø Let particle swarm move towards the best position in search space. Ø Remembering each particle’s best known position (Pbest) and global (swarm’s) best known position (gbest)
PSO –how its works • Swarm: a set of particles (S) • Particle: a potential solution – Position: – Velocity: • Each particle maintains – Individual best position (PBest) • Swarm maintains its global best (GBest) S Fitness function Fitness value
Basic algorithm of PSO 1. Initialize the swarm form the solution space 2. Evaluate the fitness of each particle 3. Update individual and global bests 4. Update velocity and position of each particle 5. Go to step 2, and repeat until termination condition
PSO Flow Chart
PSO-Steps
Velocity and Position Updating • Original velocity update equation w, c 1, c 2: Constant – random 1(), random 2(): random variable • Position update
Velocity and Position Updating
Particle’s velocity x(k+1) PBest social v(k+1 ) cognitive v(k) x(k) Inertia
Updating the Velocity of a Particle
PSO Algorithm
Tuning of Parameters for PSO
PSO solution update in 2 D GBest PBest x(k) - Current solution (4, 2) PBest - Particle’s best solution (9, 1) GBest-Global best solution (5, 10)
PSO solution update in 2 D Inertia: v(k)=(-2, 2) GBest x(k) - Current solution (4, 2) PBest - Particle’s best solution (9, 1) GBest-Global best solution (5, 10) PBest Current solution (4, 2) Particle’s best solution (9, 1) Global best solution (5, 10)
PSO solution update in 2 D Ø Inertia: v(k)=(-2, 2) Ø Cognitive: PBest-x(k)=(9, 1)-(4, 2)=(5, -1) Ø Social: GBest-x(k)=(5, 10)-(4, 2)=(1, 8) GBest x(k) - Current solution (4, 2) PBest - Particle’s best solution (9, 1) GBest-Global best solution (5, 10) PBest Current solution (4, 2) Particle’s best solution (9, 1) Global best solution (5, 10)
PSO solution update in 2 D Ø Inertia: v(k)=(-2, 2) Ø Cognitive: PBest-x(k)=(9, 1)-(4, 2)=(5, -1) Ø Social: GBest-x(k)=(5, 10)(4, 2)=(1, 8) GBest v(k+1)=(-2, 2)+0. 8*(5, -1) +0. 2*(1, 8) = (2. 2, 2. 8) v(k+1) PBest x(k) - Current solution (4, 2) PBest - Particle’s best solution (9, 1) GBest-Global best solution (5, 10)
PSO solution update in 2 D Ø Inertia: v(k)=(-2, 2) Ø Cognitive: PBest-x(k)=(9, 1)-(4, 2)=(5, -1) Ø Social: GBest-x(k)=(5, 10)(4, 2)=(1, 8) Ø v(k+1)=(2. 2, 2. 8) GBest x(k+1)=x(k)+v(k+1)= (4, 2)+(2. 2, 2. 8)=(6. 2, 4. 8) PBest x(k) - Current solution (4, 2) PBest - Particle’s best solution (9, 1) GBest-Global best solution (5, 10)
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