**5. Various types of research about PSO**


3.Different parameters influence on PSO.

4.Different topology influence on PSO.

5.Parallel study of PSO algorithm.

6.Discrete study of PSO algorithm.

7.Multi-objective optimization study of PSO algorithm.

8.Use PSO algorithm for various fields in Engineering.

### **5.1 PSO for multi objective optimization**

The single objective optimization is not correct practically Because the effective outcome is not accurate in single objective optimization. This problem has overcome by multi objective (MO) optimization. This MO has become the latest area in research. In this multi-objective optimization issues, all the target functions independently optimized and finally determine the best value for every target. But there is a conflict between objects. Because of conflicting between objects, unfortunately the finding of optimal solution is highly impossible for every objective hence only a pareto perfect solution has been determined.

Particles are independent agents in traditional PSO. Based on their own companion and its own experience problem space can be search by particles. As given earlier formula for particles update cognitive is the former and the social part is the latter. Here, selection of gbest and pbest (social and cognitive guide) is the important issue of Multi-Objective PSO (MOPSO). In both, i.e., in traditional PSO and MOPSO, choosing cognitive guide is same. But the guide must be found based on pareto dominance. There are two steps involved in choosing social guide.

Step-1: Candidate pool creation used for the guide selection.

In PSO traditional, this guide has been chosen from pbest (or) local (or) pbest of neighbors. While in case of MOPSO, to save more pareto optimal solutions, the normal technique is using an external pool.

Step 2: Guide Selection: Choosing of gbest must satisfy the below standards.

The chosen guide should be capable of provide particles guidance effectively. This is because of improve the speed of convergence.

The selected guide required to give balanced search with pareto frontier. This is because to maintain population diversity.

To select social guide here two methods are specified.


```
Pseudo code for PSO algorithm:
```

```
Initialize population
for t = 1: maximum generation
  for i = 1: population size
     if f (xi,d (t)) < f (pi (t)) then pi (t) = xi,d (t)
       f (pg (t)) = min (f (pi (t)))
     end
     for d = 1: dimension
     vi,d (t + 1) = wvi,d (t) + C1* r1(pi – xi,d (t)) + C2* r2 (pg – xi,d (t))
     xi,d (t + 1) = xi,d (t) + vi,d (t + 1)
     if vi,d (t + 1) > vmax then vi,d (t + 1) = vmax
     else if vi,d (t + 1) < vmin then vi,d (t + 1) = vmin
     end
     if xi,d (t + 1) > xmax then xi, d(t + 1) = xmax
     else if xi,d (t + 1) < xmin then xi,d (t + 1) = xmin
     end
  end
  end
end
For each particle
     Initialize particle
END
Do
  For each particle
       Calculate 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
Update particle position
End
```
*While maximum iterations or minimum error criteria is not attained* (**Table 1**).

*Particle Swarm Optimization DOI: http://dx.doi.org/10.5772/intechopen.107156*


**Table 1.**

*The basic variant of PSO [3].*

The PSO algorithm can be hybridized with several metaheuristic algorithm to balance the exploration and exploitation. Some algorithms have better efficiency in exploration, but they are poor in exploitation. Some algorithms will take high iteration to reach convergence and show poor performance. In this case the PSO is introduced to enhance the performance using,

$$\mathbf{V}\_{i}(\mathbf{K}+\mathbf{1}) = \alpha V\_{i}(\mathbf{K}) + \rho\_{i} \ast \mathbf{C}\_{1} \left(\mathbf{P}\_{i}^{\mathrm{bet}} - \mathbf{X}\_{i}(\mathbf{K})\right) + \rho\_{2} \ast \mathbf{C}\_{2}(\mathbf{G}\mathbf{X}\_{i}(\mathbf{K})) \tag{17}$$

$$X\_i(K+\mathbf{1}) = X\_i(K) + V\_i(K+\mathbf{1})\tag{18}$$

The proposed algorithm using PSO is written as,


6.end for

7. repeat


PSOA will be applied in various optimization areas, example, Energy-Storage Optimization, Image Processing, Economic operation of power system, Optimal location identification, analysis of slope stability, foundation and pile engineering, soil, and rock mechanics, underground and tunneling space design etc. PSOA will simulate the particle movement and will be applied in visual effects and special effects in some films.

#### **Figure 3.**

*The flowchart of the hybridization with PSOA [2].*

Along with the conventional applications optimization problems, Swarm Intelligence (SI) will be used in acquisition of material from library, communications, classification of medical dataset, dynamic control, planning of heating system, tracking of moving objects, and prediction.

PSO Algorithm Visual Explanation:

Let us suppose a group of birds are flying randomly in an area in search of their food (**Figure 4**).

No bird knows exactly where the food is, but they know how far they are in each iteration, (**Figure 5**).

Birds they do not know the best position. If any member can find the desirable path to go, the rest of the members will follow quickly (**Figure 6**).

Finally, following the bird which is nearest to the food is an aim.

**Figure 4.** *Random movement of birds [4].*

**Figure 5.** *Birds moving toward the food [4].*

**Figure 6.** *Finding best path [4].*
