Apply genetic algorithm $($GA$)$ to maximize the following fitness function:

$f(x)=12x^5-975x^4+28,000x^3-345,000x^2+1,800,000x$

subject to

$0x31.$

For simplification, Table $1$ is readily supplied with the chromosomes of initial population. Table

$2$ is meant to perform the genetic operators of selection and reproduction $($crossover and

mutation$)$ for iteration $1.$

Table $1$: Initialization

Table $2$: Selection and reproduction of iteration $1$

Fill up Tables $1$ and $2$ accordingly. Show steps to solutions whenever necessary.

$2.$ Reproduction

a$)$ For crossover, assign the uniform intervals of random number $[0,1].$ The interval $[0\mathrm{.}0000,0\mathrm{.}4999]$ corresponds to bit $0$ while the interval $[0\mathrm{.}5000,0\mathrm{.}9999]$

corresponds to bit $1$;

b$)$ Assume the random number, R$=\{0\mathrm{.}0967,0\mathrm{.}8682,0\mathrm{.}8755,0\mathrm{.}6606\}$ to implement the crossover at four genes of children $1$ and $2$;

c$)$ Assume the random number, R$=\{0\mathrm{.}2087,0\mathrm{.}8845,0\mathrm{.}6850,0\mathrm{.}3942$ to implement

the crossover at four genes of children $3$ and $4$;

d$)$ Assume the random number, R$=\{0\mathrm{.}4623,0\mathrm{.}8931,0\mathrm{.}8215,0\mathrm{.}9232\}$ to implement the crossover at four genes of children $5$ and $6$;

e$)$ For mutation, assign the uniform intervals of random number $[0,1].$ The interval

$[0\mathrm{.}0000,0\mathrm{.}0999]$ corresponds to a mutation while the interval $[0\mathrm{.}1000,0\mathrm{.}9999]$

corresponds to no mutation;

f$)$ Assume the following random numbers to implement the mutation at all $30$

genes of children:

R$=\{0\mathrm{.}3189,0\mathrm{.}7232,0\mathrm{.}3258,0\mathrm{.}3696,0\mathrm{.}9000,0\mathrm{.}2214,0\mathrm{.}4495,0\mathrm{.}0307,0\mathrm{.}5017,$

$0\mathrm{.}9751,0\mathrm{.}7496,0\mathrm{.}2130,0\mathrm{.}1778,0\mathrm{.}5735,0\mathrm{.}6161,0\mathrm{.}3709,0\mathrm{.}4477,0\mathrm{.}9108,0\mathrm{.}0846,$

$0\mathrm{.}7811,0\mathrm{.}7696,0\mathrm{.}9208,0\mathrm{.}5606,0\mathrm{.}7308,0\mathrm{.}8864,0\mathrm{.}7710,0\mathrm{.}8036,0\mathrm{.}9374,0\mathrm{.}6013,$

$0\mathrm{.}7975\}$