Consider the following optimization problem:

min :

$8$x$1+12$x$2+16$x$320$x$424$x$528$x$6(1)$

s$.$t$.$ :

x$1+3$x$2+3$x$3=5(2)$

x$4+$ x$5+$ x$6<=10(3)$

$0<=$ xi $<=9$i $=1,...,6(4)$

where the variables of the multivariable optimization problem are integers. Use Extension$-2$ type

approach, $($i$.$e$.,$ Treat the multiple variables together as one structure or as one vector$).$ Answer

the following:$($e$)$ Execute $4$ iterations of the simulated annealing with following parameters: Initial temperature

be $1000,$ and starting solution be $[3,0,1,1,1,1]$T

$.$ Neighborhood type $=$ Extended neighborhood, Move type $=$ Random walk, Pool size $=1,$ Max # tries $=4.$ Cooling mechanism $=$

After $2$ iterations $($irrespective of success or failure in the iteration$),$ reduce the temperature

to $500,$ and continue with the remaining iterations. Handle Constraint$(2)$ & $(3)$ by creating a

penalized objective function. Assume all the penalty coefficients are equal to $1000.$