$1.$ The integer x that minimizes the function F$($x$)=$x$2-$x$-1$ in the range $[0-31]$ will be found with the Genetic Algorithm.

a$.$ Suggest a suitable coding method for this problem. Code the initial population X$1=12,$ X$2=8,$ X$3=9,$ X$4=15$ using this method. Calculate the fitness values of the population.

b$.$ Create $4$ new individuals by matching X$1$ and X$2,$ X$3$ and X$4$ using the single$-$point crossover method.

c$.$ Which individuals would you protect for the next phase? From where?