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a Provide equations for position and velocity update of particles of the canonical particle swarm optimization algorithm. b Find the maximum of the function f

a Provide equations for position and velocity update of particles of the canonical particle swarm optimization algorithm.
b Find the maximum of the function f(x)=-x2+5x+20, where -10x10 using the canonical PSO algorithm. Let the initial positions of the particles at t=0 be:
x1=-9.6,x2=-6,x3=-2.6,x4=-1.1,x5=0.6,x6=2.3,x7=2.8, and x9=10.
Set all initial velocities v1=v2=v3=v4=v5=v6=v7=v8=v9=0 and let c1=c2=1,r1=0.213,r2=0.876 at t=1,r1=0.113,r2=0.706 at t=2. Calculate the objective function value f(xi) at t=0 and find the personal best for each particle at iteration 1 and 2. Also calculate the global best at the end of each iteration. Show the detailed computations for iterations 1 and 2.
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