*Particle Position Update:* (**Table 7**) *Position Update for First Particle:*

$$\mathbf{x}\_1^{0+1} = \mathbf{x}\_1^0 + \boldsymbol{\nu}\_1^0$$

$$\mathbf{x}\_1^1 = \mathbf{8.8} + \mathbf{1.0667} = \mathbf{9.8667}$$

$$\mathbf{x}\_1^1 = \mathbf{9.9} + (-4.4719) = \mathbf{5.4281}$$

$$\mathbf{x}\_1^1 = \mathbf{1.1} + \mathbf{0.900} = \mathbf{2}$$

#### **STEP – 4: FITNESS EVALUATION** *f x<sup>t</sup> i* (**Table 8**) **Current Best Calculation Best [gBest] Update Minimization: Calculate Fitness Value:**

$$F(\mathbf{x}) = 10 \ast (X\_1 - 1)^\prime 2 + 20 \ast (X\_2 - 2)^\prime 2 + 30 \ast (X\_3 - 3)^\prime 2$$

$$\text{FirstParticle}$$

$$F(\mathbf{x}) = 10 \ast (9.8667 - 1)^\prime 2 + 20 \ast (5.4281 - 2)^\prime 2 + 30 \ast (2 - 3)^\prime 2 = 1.0512$$

$$\text{SecondParticle}$$

$$F(\mathbf{x}) = 10 \ast (10.71 - 1)^\prime 2 + 20 \ast (7.14 - 2)^\prime 2 + 30 \ast (1.19 - 3)^\prime 2 = 1.5695$$

$$\text{ThirdParticle}$$

$$F(\mathbf{x}) = 10 \ast (10.78 - 1)^\prime 2 + 20 \ast (8.07 - 2)^\prime 2 + 30 \ast (-7.317 - 3)^\prime 2 = 4.8866$$

$$\text{Fourparticle}$$

$$F(\mathbf{x}) = 10 \ast (10.78 - 1)^\prime 2 + 20 \ast (8.07 - 2)^\prime 2 + 30 \ast (-7.317 - 3)^\prime 2 = 3.6716$$


#### **Table 8.**

*Updated positions for every particle [5].*


#### **Table 9.**

*Updated fitness value [5].*

*FifthParticle*

*F x*ð Þ¼ <sup>10</sup> <sup>∗</sup> ð Þ <sup>9</sup>*:*<sup>78</sup> � <sup>1</sup> *^* <sup>2</sup> <sup>þ</sup> <sup>20</sup> <sup>∗</sup> ð Þ <sup>6</sup>*:*<sup>028</sup> � <sup>2</sup> *^* <sup>2</sup> <sup>þ</sup> <sup>30</sup> <sup>∗</sup> ð Þ �4*:*<sup>8635</sup> � <sup>3</sup> *^* 2 ¼ 2*:*9504
