$9$:$47$

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$2.$ In a Genetic Algorithm, suppose that two potential parents are given by

$\backslash$table$[[1,1,0,0,1,1,0,1]]\backslash$right$.$

$\backslash$table$[[0,0,1,1,1,0,1,0]]$

Assume that the indices are numbered from left to right with the values $1$ to $8,$ and that a split point of i implies dividing the chromosome between the indices $i-1$ and $i.$ Show the result of two$-$point crossover for the split points ${}_1=3$ and ${}_2=7.$

$3.$ Suppose that $p_m=0\mathrm{.}1$ and a chromosome, $C,$ is given by

$1,1,0,0,1,0,0,1$

Assume that the indices are numbered from left to right with the values $1$ to $8.$ In each case below, start over each time with the given $C$ and the parameters: ${}_{1}U(1,8)$ and ${}_{2}U(0,1)$ supplied. Let ${}_1$ be the selected gene index and let ${}_2$ be the random number that is used to decide if mutation will occur at that gene $($i$.$e$.$ mutation occurs if ${}_2{p}_m).$ Show the result of a GA mutation step for the following parameters:

i$){}_1=3$;${}_2=0\mathrm{.}25$

ii$){}_1=2$;${}_2=0\mathrm{.}05$

iii$){}_1=6$;${}_2=0\mathrm{.}09$

iv$){}_1=8$;${}_2=0\mathrm{.}11$

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