Question $2,[20$ marks$]$

Given the following particle positions in a PSO minimization optimization process:

X$1$ X$2$ X$3$ X$4$

$11-1-1$

$2212$

$0-1-10$

and given that each particle's attached velocity is:

V$1$ V$2$ V$3$ V$4$

$-2\mathrm{.}0-0\mathrm{.}0-0\mathrm{.}8-0\mathrm{.}9$

$0\mathrm{.}7-0\mathrm{.}20\mathrm{.}30\mathrm{.}1$

$2\mathrm{.}00\mathrm{.}62\mathrm{.}60\mathrm{.}4$

and given each particle's local best as:

P$1$ P$2$ P$3$ P$4$

$-2-111$

$-20-21$

$-1-2-21$

assuming the global best is:$[-2,-2,-1,]$

Calculate the updated positions and velocities for the next $3$ iterations

Assume $\backslash$Phi $1=0\mathrm{.}8$ and $\backslash$Phi $2=0\mathrm{.}7$

The function to be minimized is:$6$x$11+9$x$23+2$x$34$