Q$4.$ Consider the following nonconvex programming problem.

Maximize $Z=0\mathrm{.}5x^5-6x^4+24\mathrm{.}5x^3-39x^2+20x,$

subject $to$

$,x5$

$,x0,$

Take Population size: $5$ and $c1=c2=1.$ Initialize the initial position $(x_i^t)$ and velocity $(v_i^t)$ values and then apply PSO algorithm for two iterations.