Cross the fittest two individuals using one$-$point crossover at the middle point. $(1$ mark$)$ Cross the second and third fittest individuals using a two$-$point crossover $($points b and $f).(1)$ mark$)$

$($iii$)$ Suppose the new population consists of the four offspring individuals received by the crossover operations in the above question. Evaluate the fitness of the new population. Has the overall fitness improved? $(1$ mark$)$

$($b$)$ Roulette$-$wheel selection is a fitness proportionate selection procedure where individual chromosome in the population is assigned a roulette$-$wheel slot sized in proportion to its fitness. Using the roulette$-$wheel selection procedure, complete the table below and determine the selected chromosome, when a random number $r$ is selected to be $0\mathrm{.}585.(4$ marks$)$

$\backslash$table$[[$Chromosome #$,1,2,3,4,5],[$Fitness$,f,28,18,14,9,26],[$Probability$,p_i,,,,,],[\backslash$table$[[$Cumulative probabil$-],[$ity$,q_i$