PARTICLE SWARM OPTIMIZATION

(PSO)

PREPARED BY:-VRAJESH CHOKSHI

(08CE10)

ARTIFICIAL INTELLIGENCENow a days the concepts of artificial intelligence have came into existence, basically they are related to producing such artificial things which act totally as an human being or has the memory and functionality same as the human brain.

Artificial Intelligence includes many topics on the Swarm optimization, soft computing, memetic algorithm , genetic algorithm many more topics.

One of the main type of algorithm for artificial inteligence is the PARTICLE SWARM OPTIMIZATION. Which provides how the collective behavior of the realworld entities make it possible work effficiently .

SWARM INTELLIGENCESwarms consist of many simple entitiesthat have local interactions,including interacting with the environment.

The emergence of complex,or macroscopic, behaviors and theability to achieve significant results asa team result from combining simple,or microscopic, behaviors.

Swarm intelligence techniques (note the difference from intelligentswarms) are population-based stochastic methods used in combinatorialoptimization problems in which the collective behavior of relatively simpleindividuals arises from their local interactions with their environment toproduce functional global patterns.

PARTICLE SWARM OPTIMIZATION

Introduction Particle Swarm Optimization (PSO) is a relatively new, evolution-based

search and optimization technique. We explain the PSO algorithm in detail and demonstrate its performance on one- and two-dimensional continuous search problems.

PSO algorithms are especially useful for parameter optimization in continuous, multi-dimensional search spaces. PSO is mainly inspired by social behaviour patterns of organisms that live and interact within large groups. In particular, PSO incorporates swarming behaviours observed in flocks of birds, schools of fish, or swarms of bees.

The term PSO refers to a relatively new family of algorithms that may be used to find optimal or near to optimal solutions to numerical and qualitative problems. It is implemented easily in most of the programming languages since the core of the program can be written in a single line of code and has proven both very effective and quick when applied to a diverse set of optimization problems.

 PSO is an established method for parameter optimization . it represents a population based adative optimization technique that is influenced by several strategic parameters choosing reasonable parameters for its convergence behavior and depends on optimization task.

(Cont.)

What does it basically mean???? Particle swarm optimization (PSO) is one of the evolutionary

computation techniques . like the other evolutionary computation techniques ,PSO is a population based search alogorithm and is initialize evoluted with a population of random solution , called particles .unlike in the other evolutionary ideas and techniques,each particle in PSO is also associated with the velocity.

The idea of PSO is to have swarm of particles “flying” through a multidimensional search space , looking for the global optimum . by exchanging information the particles can influence each others movements . each particle retains an individual (or “cognitive”)memory of the best position it has visited , as well as a global (or “social”)memory of the best position visited by all the particles in the swarm. A particle calculates its next position based on a combination of its last movement vector , the individual and global memories , and a random component.

(Cont.) PSO is a global optimization algorithm for dealing with problems in which

a point or surface in an ndimensional space best represents a solution. Potential solutions are plotted in this space and seeded with an initial velocity. Particles move through the solution space, and certain fitness criteria evaluate them. Over time, particles accelerate toward those with better fitness values.

  Particle Swarm Optimization (PSO) applies to concept of social interaction

to problem solving.

It has been applied successfully to a wide variety of search and optimization problems.

In PSO, a swarm of n individuals communicate either directly or indirectly with one another search directions (gradients).

  PSO is a simple but powerful search technique. 

Who basically found it????

Mayor. James kennedy Mr.Russell Eberhart

It was developed in 1995 by James Kennedy and Russ Eberhart [Kennedy, J. and Eberhart, R. (1995). “Particle Swarm Optimization”, Proceedings of the 1995 IEEE International Conference on Neural Networks, pp. 1942-1948, IEEE Press.]

Advantages The main advantage of such an approach over other global

minimization strategies such as simulated annealing is that the large numbers of the members that make up the particle swarm make the technique impressively resilient to the problem of the local minima

An advantage of PSO is its ability to handle the particle swarm optimization problem with multiple local optima reasonably well and it s simplicity of implementation. Especially in the comparison to related strategies like genetic algorithm. In the field of chemiformatics, PSO has successfully been applied to the quantitative structure activity relationship(QSAR) modeling , including k-nearest neighbor and kernel regression , minimum spanning tree for piecewise modeling , partial least square modeling , and neutral network training.

How it works!!!

The basic algorithm funda:

The social metaphor that led to this algorithm can be summarized as follows:

  The individuals that are part of a society hold an opinion that is

part of a “belief space”(search space ) shared by every possible individual.

Individuals may modify this “opinion state” based on three factors: The knowledge of the environment(its fitness value) The individual’s previous history of states(its memory) The previous history of states of the individual’s neighbourhood.

Algorithm 1.Initialize the particles randomly in the search space2.Set the generation count3.While not teminate :  a.Evaluate the fitness of individual particles(pbest)

b.Find the best instance of particle against generation / keep track of the individual’s highest fitness(gbest)

c.Calculate particle velocities

d.Update particle position / location.

  e.Terminate if condition is best4.Terminate if generation count expires.

Working of algorithm  The PSO algorithm is simple in concept , easy to implement and

conceptual efficient . the original procedure for implementing PSO is as follows:

Initialize a population of particle with random positions and velocities on D dimensions in the problem space

For each particle , evaluate the desired optimization fitness function in D variable.

Compare particle’s fitness evaluation with its pbest . if current value is better than the pbest , then the set pbest equal to the current value ,and pi equals to the current location xi in D-dimensional space

 Identify the particle in the neighborhood with the best success so far and assign its index to be variable g.

(Cont.) Change the velocity and position of the particle according to the

following equation

Vid=vid+c1rand()(pid-xid)+c2rand()(pgd-xid)Xid=xid+vid

Loop to step b until a critetion is met, usually a sufficiently good fitness or maximum number of iterations.

Concepts to apply & how its works The connection to search and optimization is made by assigning direction

vectors and velocities to each point in a multidimensional search space.

Each point the ‘moves’ or ‘flies’ through the seach space following its velocity vector , which is influenced by the directions and velocities of other points in its neighborhood .

These localized interaction with neighboring points propogates through the entire ‘swarm’ of potential solution.

How much influence a particular point has on the other points is determined by the ‘fitness’ , that is assigned to a potential solution , which captures how good it is compared to all other solution

Each solution is represented as a series of co-ordinates in n dimensional space . a number of particles are initialized randomly within the search space.

(Cont.)

Each particle has a very simple memory of its personal best solution stored as pbest

The global best solution for each iterartion is given as the gbest

On each iteration , every article is moved a certain diatance from its current location , influenced a random amount by the pbest and gbest values.

Each particle keeps track of its coordinates in the problem space which are associated with the best solution it has achieved.the fitness value is also stored The value is pbest .When a particle takes all population as its topological neighbors, the best value is a global best given as gbest.

(Cont.)

After fining this best value, particle calculates its new velocity and position using forula a & b respectively

V[]=v[]+c1*rand()*(pbest[]-present[]) + c2*rand[](gbest[]-present[])

Present[]=present[]+v[]

APPLICATION Solving the constrained optimization problem 

Solving min-max problem  Solving multiobjective optimization problem

Also used for solvig the travelling salesman problem:

(Cont.)

Her e in travelling sales man problem the PSO is applied so as to get the minimum distance travelled by the sales man , coloured dot is a beginning point whle others are destination.

Dynamic tracking

Evolve weights and structure of the neutral network.

Analyse human tremor.

Register 3d-to-3d biomedical image

Conclusion Particle swarm optimization is an extremely simple algorithm that

seems to be effective for optimizing a wide range of functions.

We view it as a mid-level form of A-life or biologically derived algorithm, occupying the space in nature between evolutionary search, which requires eons, and neural processing, which occurs on the order of milliseconds. Social optimization occurs in the time frame of ordinary experience - in fact, it is ordinary experience.

In addition to its ties with A-life, particle swarm optimization has obvious ties with evolutionary computation.

Conceptually, it seems to lie somewhere between genetic algorithms and evolutionary programming. It is highly dependent on stochastic processes, like evolutionary programming

QUESTIONS?

Thank You!!!