Consider following particles for particle swarm optimization to solve optimization problem where optimal solution is on zero. Initialize velocities values as per your choice within the range of 0.1 to 0.9

P1=0.2

P2=0.5

P3=.34

P4=.45

P5=0.48

a) Compute the fitness of above particles using X² +X +1 functions, sort out the particle based on fitness, most optimal particle should be on top of the list.

b) Update velocity and position of each particle where w=0.7, C₁=C₂=1.4, rand₁=1, rand₂=1