Single Objective Particle Swarm

35.4 Single Objective Particle Swarm

Yes

Gen < MaxGen

Optimization Search Algorithm

No

(SOPSO)

End

PSO is an evolutionary computational technique (a search FIGURE 35.1 Flow chart for the GA minimizing search algorithm.

method based on a natural system), which was introduced

996 A. M. Sharaf and A. A. A. El-Gammal by Kennedy and Eberhart in 1995 [3]. This optimization and

related socially; that is, each particle is a member of one search technique models the natural swarm behavior seen in

or more neighborhoods. Each individual tries to emulate many species of birds returning to roost, group of fish, and

the behavior of the best of its neighbors. Each individual swarm of bees. . . etc. The PSO may be used to find optimal

can be thought of as moving through the feature space (or near optimal) solutions to numerical and qualitative prob-

with a velocity vector that is influenced by its neighbors. lems [4–8]. PSOs methods are inspired by particles moving around in the defined search-space. The individuals in a PSO have a position and a velocity. The PSO method remembers the

35.4.2 Basic Search Method

best position found by any particle. Additionally, each particle The position of each particle is represented by XY axis posi- remembers its own previously best-found position. A particle tion; and also the velocity is expressed by V x (the velocity of moves through the specified solution space along a trajectory

X axis) and V y (the velocity of Y axis). Modification of the defined by its velocity, the draw to return to a previous promis- particle position is realized by the position and velocity infor-

ing search area, and an attraction toward the best location mation. Each particle knows its best value so far (P best ) and its discovered by its close neighbors. PSO has been used for a wide XY position. This information represents the personal experi- range of search applications, as well as for specific optimization ences of each particle. Moreover, each particle knows the best tasks. PSO can be easily implemented in most programming value so far in the group (g

best ) among P bests . This infor- languages and has proven to be both effective and fast when mation represents the knowledge of how the other particles

applied to a diverse set of nonlinear optimization problems. around have performed. Namely, each particle tries to modify PSO has been successfully applied in many areas:

its position using the following information: • Function optimization;

• The current positions (x, y);

• Artificial neural network training;

• The current velocities (V x ,V y );

• Proportional and integral fuzzy system control; and • The distance between the current position and P best ; • Other near optimal search and optimization areas where

• The distance between the current position and g best . GA can be applied.

This modification can be represented by the concept of velocity. Velocity of each particle can be modified by the

35.4.1 Structure of the PSO Particle

following equation:

The basic structure of any particle in a selected population consists of five components:

V id =W×V id +C 1 × rand 1 × (P id −X id )

+C 2 × rand 2 × gd −X id (35.1) tion space. The size of

variables used by the problem that is being solved.

where:

• Fitness is the quality of the solution represented by the vector

• V id is the value of dimension d in the velocity vector function.

particle i;

V is a vector containing the velocity for each dimension • C 1 is the cognitive learning selected rate; of

• C 2 is the social learning selected rate; corresponding

• rand 1 and rand 2 are random values on the range [0.1];

• X id is the current position of particle i along dimension d; particle will move through in the search space, causing

V values changes the direction the

• W is the selected weighting factor; the particle to make a turn. The velocity vector is used to

• P id is the location along dimension d at which the particle control the range and resolution of the search.

previously had the best fitness measure; and • P best is the fitness value of the best solution yet found by

• P gd is the current location along dimension d of the

a particular particle. neighborhood particle with the best fitness.

The basic concept of the PSO technique lies in accelerating particle’s P best . Jointly, P best and

memory, which is used to control the particle to go back best locations, with a ran-

each particle toward its P best and g

dom weighted acceleration at each step and this is illustrated in toward a definite search region.

Fig. 35.2,

• Each particle is also aware of the current best fitness in

where

the neighborhood for any given iteration. A neighbor- hood may consist of some small group of particles, in

P k is the current position of a particle, which case the neighborhoods overlap and every parti-

P k +1 is its modified position,

cle is in multiple neighborhoods. Particles in a swarm are

V K is its initial velocity,

35 Novel AI-Based Soft Computing Applications in Motor Drives 997

has velocity). These particles are then “flown” through V K

P K +1

the search space of potential solutions.

2. Evaluate the fitness of each particle in the swarm. V K +1

3. For every iteration, compare each particle’s fitness with

its previous best fitness (P best ) obtained. If the current V pbest

P best

value is better than P best , then set P best equal to the cur- rent value and the P best location equal to the current

location in the d-dimensional space. P K

4. Compare P best of particles with each other and update FIGURE 35.2 Concept of modification of a searching point by PSO.

V gbest

g best

the swarm global best location with the greatest fitness (g best ).

5. The velocity of each particle is changed (accelerated) toward its P best and g best . This acceleration is weighted

Start

by a random term. A new position in the solution space is calculated for each particle by adding the new veloc-

Generation of initial condition of ity value to each component of the particle’s position

each agent

vector.

6. Repeat steps (2)–(5) until convergence is reached based on some desired single or multiple objective criteria.

Evaluation of searching point of

each agent