Home Exercise :

$3-$ GA Problem.

Suppose that GA is used to find the maximum of $F(x),x=0,1,$dotsdots, $275.$ Let $x=107$ and $x=254$ represent parents P$1$ and P$2.$

$($a$)$ Represent P$1$ and P$2$ as binary codes.

$($b$)$ Use uniform crossover to create C $1$ and C $2.$

$($c$)$ Create C $1$ and C $2$ using a $1-$point crossover.

$($d$)$ Create C $1$ and C $2$ using a $2-$point crossover.

$($e$)$ In Part $($b$),$ use random numbers to mutate C $1$ and C $2.$