Assume your agent uses genetic algorithm for certain optimization task. The

description of a chromosome $($or state$)$ is of the form

a b c d

in which a$,$ b$,$ c and d can take any value from $0$ to $9.$ The fitness function f$($x$)$

is as below:

f$($x$)=($a $+$ b$)+($c$-$d$)$

The initial population x$1,$ x$2,$ x$3$ and x$4$ are as below

x$1=2913$

x$2=1258$

x$3=6284$

x$3=1597$

The agent attempts to find a$,$b$,$c and d such that it maximize f$($x$)$

$(3-$b$)$ Use a simple cross over operation $($as discussed in the class$)$ to generate offsprings O$1$

$,$ O$2$

$,$ O$3$ and O$4$ as follows:

Generate O$1$

$,$ O$2$

$,$ using first and third fittest individuals $($among x$1$

$,$ x$2$

$,$ x$3$ and x$4$

$)$

Generate O$3$

$,$ O$4$

$,$ using second and fourth fittest individuals $($among x$1$

$,$ x$2$

$,$ x$3$ and x$4$

$)$

Comment on the overall fitness of O$1$

$,$ O$2$

$,$ O$3$ and O$4$

in comparison to x$1$

$,$ x$2$

$,$ x$3$ and x$4$

$.$ Show all the necessary

computations.

$(3-$c$)$ Is it possible to reach the optimal solution without a mutation operation? Why or Why not? $[$Note: Answer in at

most two well articulated statements$]$