WHAT IS OPTIMIZATION?

Optimization can be defined as the art of obtaining best policies to satisfy certain objectives, at the same time satisfying fixed requirements.

It is of two types:i. Unconstrained Optimizationii. Constrained Optimization

Particle Swarm Optimization (PSO)

Developed by Dr. Eberhart & Dr. Kennedy in 1995

How can birds or fish exhibitsuch a coordinatedcollective behavior?

About pso The particle swarm optimization concept

consists of, at each time step, changing the velocity of (accelerating) each particle toward its pbest as

well as gbest locations and acceleration is weighted by a random term, with separate random numbers being generated for acceleration towards pbest and gbest locations.

Terms used in PSO:pbest : The best solution that each particle has

achieved so far.

gbest : When a particle takes all the population as its topological neihbours,the best value is a global best.

• Each particle tries to modify its position using the following information:

the current positions, the current velocities, the distance between the current position and pbest, the distance between the current position and the gbest. • The modification of the particle’s position can be mathematically

modeled according the following equation : Vi

k+1 = wVik +c1 rand1(…) x (pbesti-si

k) + c2 rand2(…) x (gbest-sik) ….. (1)

where, vik : velocity of agent i at iteration k,

w: weighting function, cj : weighting factor, rand : uniformly distributed random number between 0 and 1, si

k : current position of agent i at iteration k, pbesti : pbest of agent i, gbest: gbest of the group.

The following weighting function is usually utilized in (1) w = wMax-[(wMax-wMin) x iter]/maxIter (2) where wMax= initial weight, wMin = final weight, maxIter = maximum iteration number, iter = current iteration number. si

k+1 = sik + Vi

k+1 (3)

sk : current searching point. sk+1: modified searching point. vk: current velocity. vk+1: modified velocity. vpbest : velocity based on pbest. vgbest : velocity based on gbest

PSO

sk

vk

vpbest

vgbest

sk+1

vk+1

sk

vk

vpbest

vgbest

sk+1

vk+1

Multi-agent (Informed/Non-Informed) Optimization

RandomlyInitialized Agents

Agents

Most Agents are nearGlobal Optima

Af ter Convergence

ALGORITHM FOR PSO

Step 1. Initialize randomly the particles of the population according to the limit of each unit including individual dimensions, searching points and velocities. These initial particles must be feasible candidate solutions that satisfy the practical operating constraints.

Step 2. Calculate the fitness of each individual in the population.

Step 3. Compare each particle’s fitness value with that of its pbest. The particle with the best cost value among the pbests is denoted as gbest.

Step 4. Modify the member velocity of each particle.CONTD…….

Step 5. Modify the member position of each particle .

Step 6. If the new fitness value for any kth particle is less than its previous value, the new coordinates for that particle will be stored as its pbestk. Also compare the fitness values of all the pbestk for each particle k and determine gbest.

Step 7. If the number of iterations reaches the maximum, then go to Step 8. Otherwise, go to Step 4.

Step 8. The individual that generates the latest gbest is the solution of the problem.

FLOWCHART

PSO ApplicationEconomic dispatch considering the generator

constraints A hybrid particle swarm optimization applied

to loss power minimization A novel approach for unit commitment

problem via an effective hybrid particle swarm optimization

Congestion Management Using Multiobjective Particle Swarm Optimization

Pitfalls of PSOParticles tend to cluster, i.e., converge too

fast and get stuck at local optimumMovement of particle carried it into

infeasible regionInappropriate mapping of particle space into

solution space

Similarity: 1. Both algorithms start with a group of a randomly generated population.

2. Both have fitness values to evaluate the population.

3. Both update the population and search for the optimium with random

techniques.

Comparisons betweenG.A. and P.S.O.

Difference: 1. Compared to GA, the advantages of PSO are that PSO is easy to implement and there are few parameters to adjust.

2. One of the advantages of PSO is that PSO takes real numbers as particles. It is not like GA, which needs to change to binary encoding, or special genetic operators have to be used.

Comparisons betweenG.A. and P.S.O.

Difference:

3. PSO does not have genetic operators like reproduction, crossover, and mutation. Particles update themselves with the internal velocity.

4. Particles also have memory, which is important to the algorithm.

Comparisons betweenG.A. and P.S.O.

Difference: 5. In GAs, chromosomes share information with each other. So the whole population moves like a one group towards an optimal area.

6. In PSO, only gBest (or lBest) gives out the information to others. It is a one-way information sharing mechanism. The

evolution only looks for the best solution.

Comparisons betweenG.A. and P.S.O.

REFERENCES Wang, C., Shahidehpour, S.M., “Power generation Scheduling for multi- area

hydrothermal power systems with tie-line constraints, cascaded reservoirs and uncertain data.”, IEEE Trans. PWRS, Vol. 8, No. 3, 1993, pp. 1333-1340

A.J.Wood, B.F.Wollenberg, “Power Generation Operation and Control”, John Wileyand Sons, New York, 1984 K. Y. Lee and M. A. El-Sharkawi (Editors), Modern Heuristic

Optimization Techniques with Applications to Power Systems, IEEE Power Engineering Society (02TP160), 2002.

R. Caponetto, L. Fortuna, S. Fazzino, and M. G. Xibilia, “Chaoticsequences to improve the performance of evolutionary algorithms,”IEEE Trans. on Evolutionary Computation, Vol. 7, No. 3, pp. 289-304,Jun. 2003.

[15] L. Shengsong, W. Min, and H. Zhijian, “Hybrid algorithm of chaosoptimization and SLP for optimal power flow problems with multimodalcharacteristic,” IEE Proc.-Gener. Transm. Distrib., Vol. 150, No. 5, pp.543-547,SEP 2003