Practical Swarm Optimization (PSO)
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The document discusses Particle Swarm Optimization (PSO), which is an optimization technique inspired by swarm intelligence and the social behavior of bird flocking. PSO initializes a population of random solutions and searches for optima by updating generations of candidate solutions. Each candidate, or particle, updates its position based on its own experience and the experience of neighboring highly-ranked particles. The algorithm is simple to implement and converges quickly to produce approximate solutions to difficult optimization problems.
![Particle Swarm Optimization
Each particle tries to modify its current position and velocity according to the distance between its
current position and pbest, and the distance between its current position and gbest.
2
1( ) * ( CurrentPosition ) 2( ) * ( CurrentPositionn n1 1 best,n best,n
)randv v c rand p c gnn
Current Position[n+1] = Current Position [n] + v[n+1]
current position[n+1]: position of particle at n+1th
iteration
current position[n]: position of particle at nth iteration
v[n+1]: particle velocity at n+1th iteration
vn+1: Velocity of particle at n+1 th iteration
Vn : Velocity of particle at nth iteration
c1 : acceleration factor related to gbest
c2 : acceleration factor related to lbest
rand1( ): random number between 0 and 1
rand2( ): random number between 0 and 1
gbest: gbest position of swarm
pbest: pbest position of particle](https://image.slidesharecdn.com/pso-130627232148-phpapp01/85/Practical-Swarm-Optimization-PSO-9-320.jpg)
![The Basic Variant of PSO
PSO Basic Variant Function Advantages Disadvantages
Velocity Clamping (VC)
Control the global exploration of
the particle.
Reduces the size of the step
velocity, so that the particles remain
in the search area, but it cannot
change the search direction of the
particle
VC reduces the size of the step
velocity so it will control the
movement of the particle
If all the velocity becomes equal to
the particle will continue to
conduct searches within a
hypercube and will probably remain
in the optima but will not converge
in the local area.
Inertia Weight
Controls the momentum of the
particle by weighing the
contribution of the previous
velocity,
A larger inertia weight in the end
of search will foster the
convergence ability.
Achieve optimality convergence
strongly influenced by the inertia
weight
Constriction Coefficient
To ensure the stable convergence
of the PSO algorithm [21]
Similar with inertia weight
when the algorithm converges,
the fixed values of the parameters
might cause the unnecessary
fluctuation of particles
Synchronous and
Asynchronous Updates
Optimization in parallel processing Improved convergence rate
Higher throughput:
More sophisticated finite element
formulations
Higher accuracy (mesh densities)](https://image.slidesharecdn.com/pso-130627232148-phpapp01/85/Practical-Swarm-Optimization-PSO-13-320.jpg)
Practical Swarm Optimization (PSO)
- 1. Department of Mechanical and Material Engineering Practical Swarm Optimization (PSO)
- 2. Goal of Optimization Find values of the variables that minimize or maximize the objective function while satisfying the constraints.
- 3. . Need for optimization Choose design variables Formulate constraints Formulate objective function Set up variable bounds Select an optimization algorithm Obtain solution(s) Flowchart of Optimal Design Procedure
- 4. Particle Swarm Optimization Swarm Intelligence (SI) • SI is artificial intelligence, based on the collective behavior of decentralized, self- organized systems. • The expression was introduced by Gerardo Beni and Jing Wang in 1989, in the context of cellular robotic systems. • SI systems are typically made up of a population of simple agents interacting locally with one another and with their environment. • Natural examples of SI include ant colonies, bird flocking, animal herding, bacterial growth, and fish schooling.
- 5. Particle Swarm Optimization Some SI Application • U.S. military is investigating swarm techniques for controlling unmanned vehicles. • NASA is investigating the use of swarm technology for planetary mapping.
- 6. Particle Swarm Optimization • The PSO algorithm was first described in 1995 by James Kennedy and Russell C. Eberhart inspired by social behavior of bird flocking or fish schooling. • PSO is an artificial intelligence (AI) technique that can be used to find approximate solutions to extremely difficult or impossible numeric maximization and minimization problems. • Hypotheses are plotted in this space and seeded with an initial velocity, as well as a communication channel between the particles. • Simple algorithm, easy to implement and few parameters to adjust mainly the velocity.
- 7. Particle Swarm Optimization How it works: • PSO is initialized with a group of random particles (solutions) and then searches for optimal by updating generations. • Particles move through the solution space, and are evaluated according to some fitness criterion after each time step. In every iteration, each particle is updated by following two "best" values. • The first one is the best solution (fitness) it has achieved so far (the fitness value is also stored). This value is called pbest.
- 8. Particle Swarm Optimization How it works: • Another "best" value that is tracked by the particle swarm optimizer is the best value obtained so far by any particle in the population. This second best value is a global best and called gbest. • When a particle takes part of the population as its topological neighbors, the second best value is a local best and is called lbest. Neighborhood bests allow parallel exploration of the search space and reduce the susceptibility of PSO to falling into local minima, but slow down convergence speed.
- 9. Particle Swarm Optimization Each particle tries to modify its current position and velocity according to the distance between its current position and pbest, and the distance between its current position and gbest. 2 1( ) * ( CurrentPosition ) 2( ) * ( CurrentPositionn n1 1 best,n best,n )randv v c rand p c gnn Current Position[n+1] = Current Position [n] + v[n+1] current position[n+1]: position of particle at n+1th iteration current position[n]: position of particle at nth iteration v[n+1]: particle velocity at n+1th iteration vn+1: Velocity of particle at n+1 th iteration Vn : Velocity of particle at nth iteration c1 : acceleration factor related to gbest c2 : acceleration factor related to lbest rand1( ): random number between 0 and 1 rand2( ): random number between 0 and 1 gbest: gbest position of swarm pbest: pbest position of particle
- 10. Particle Swarm Optimization Algorithm For each particle Initialize particle with feasible random number End Do For each particle Calculate the 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 to velocity update equation Update particle position according to position update equation End While maximum iterations or minimum error criteria is not attained
- 11. Particle Swarm Optimization Swarm Topology • In PSO, there have been two basic topologies used in the literature I4 I0 I1 I2I3 I4 I0 I1 I2I3 Star Topology (global neighborhood)Ring Topology (neighborhood of 3)
- 12. Particle Swarm Optimization Variant of PSO .
- 13. The Basic Variant of PSO PSO Basic Variant Function Advantages Disadvantages Velocity Clamping (VC) Control the global exploration of the particle. Reduces the size of the step velocity, so that the particles remain in the search area, but it cannot change the search direction of the particle VC reduces the size of the step velocity so it will control the movement of the particle If all the velocity becomes equal to the particle will continue to conduct searches within a hypercube and will probably remain in the optima but will not converge in the local area. Inertia Weight Controls the momentum of the particle by weighing the contribution of the previous velocity, A larger inertia weight in the end of search will foster the convergence ability. Achieve optimality convergence strongly influenced by the inertia weight Constriction Coefficient To ensure the stable convergence of the PSO algorithm [21] Similar with inertia weight when the algorithm converges, the fixed values of the parameters might cause the unnecessary fluctuation of particles Synchronous and Asynchronous Updates Optimization in parallel processing Improved convergence rate Higher throughput: More sophisticated finite element formulations Higher accuracy (mesh densities)
- 14. Particle Swarm Optimization in Summary The process of PSO algorithm in finding optimal values follows the work of an animal society which has no leader. Particle swarm optimization consists of a swarm of particles, where particle represent a potential solution (better condition). Particle will move through a multidimensional search space to find the best position in that space (the best position may possible to the maximum or minimum values).