Shortest common supersequence with Genetic Algorithm
As is usual, you will really have to think for yourself what makes sense for the
crossover function.  But here is the naive approach (without really knowing your
problem).

Let $s_1$ and $s_2$ be the strings you want to find the shortest common
supersequence for.  Let $\text{superseq}(x, s_1)$ be the number of characters in
$x$ that form a supersequence.

For individuals $x$, $x'$, define


fitness: $f(x) = \text{length}(x) - \text{superseq}(x, s_1) - \text{superseq}(x, s_2)$ (we want to minimize $f$)
mutation: $m(x) = \hat x$, where we obtain $\hat x$ from $x$ by randomly changing, deleting, or adding a character
crossover: $c(x, x') = x[i, j] + x'[i', j']$ for randomly drawn $i \leq j$, $i' \leq j'$.


In other words, the crossover simply picks a random (consecutive) substring of
each of the individuals and concatenates it to make a new.  There are many more
options, you can pick a string smarter (keeping only certain missing
characters), you can interleave the strings, e.g. shuffle the string $\chi =
0^{\text{length(x)}}1^{\text{lenth(x')}}$ and let the result of the crossover be

$$ \left[ x[i] \text{ if } \chi_i = 0 \text{ else } x'[i] \text{ for } i \in \text{range}(\text{length}(\chi) \right]. $$