Question $4$: Genetic Algorithms

$[19]$

Consider the function

$f_5=2x+y^2$

where xin$[0,5]$ and yin$[-3,3]$

We want to use a Genetic Algorithm $($GA$)$ to find values for $x$ and $y$ to get $f_3$ as

close as possible to $10.$

$($a$)$ Define the following for this GA task:

An appropriate chromosome

Fitness function

Crossover operator

Justify your choice for each of these.

$($b$)$ Generate an initial population of $10$ members. Justify your answer.

$($c$)$ Calculate the fitness value of all $10$ members of the initial population. Show all

your calculations.

$($d$)$ Select the top $2$ members using your fitness function. Apply your crossover

operator to generate two new members.

Show all your steps and calculations.

$($e$)$ Calculate four exact solution for this task.