Practical Swarm Optimization (PSO)

Department of Mechanical and Material Engineering

Practical Swarm Optimization (PSO)

Goal of Optimization

Find values of the variables that minimize or maximize the objective function while satisfying the constraints.

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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

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.


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.


• 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.

Particle Swarm OptimizationHow 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.

Particle Swarm OptimizationHow 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.


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.

21( ) * ( 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


AlgorithmFor each particle

Initialize particle with feasible random numberEndDo 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


Swarm Topology

• In PSO, there have been two basic topologies used in the literature

I4

I0

I1

I2 I3

I4

I0

I1

I2 I3

Star Topology (global neighborhood)

Ring Topology (neighborhood of 3)


Variant of PSO

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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)

Particle Swarm Optimizationin 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).

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Practical Swarm Optimization (PSO)