**STEP – 3: CALCULATION OF POSITION AND VELOCITY FOR EVERY PARTICLE**


*Velocity Update for at iteration (t = 0) for First Particle:*

$$v\_1^{0+1} = \omega v\_1^0 + C\_1 r\_1 \left( \mathbf{x} \text{Best}\_1^0 - \mathbf{x}\_1^0 \right) + C\_2 r\_2 \left( \mathbf{g} \text{Best}\_1^0 - \mathbf{x}\_1^0 \right)$$

$$v\_1^1 = \mathbf{0}.9 \ast \mathbf{0}.8 + \mathbf{2} \ast \mathbf{rand}() \ast \left( \mathbf{8.8} - \mathbf{8.8} \right) + \mathbf{2} \ast \mathbf{rand}() \ast \left( \mathbf{9.9} - \mathbf{8.8} \right)$$

$$v\_1^1 = \mathbf{1.0667}$$

*Calculating all the values as:*

$$v\_1^1 = 1.0667 
for \, x\_1$$

$$v\_1^1 = -4.4719 \, for \, x\_2$$

$$v\_1^1 = 0.0900 \, for \, x\_3$$


**Table 6.**

*Choose the particle with best fitness value as gBest [5].*

*Swarm Intelligence - Recent Advances and Current Applications*


#### **Table 7.**

*Updated velocity for every particle [5].*
