I am taking an extra course this semester and we were given a series of questions for exam preparation. But I was unable to attend the discussion session and so I have no access to the solutions. I hope that can get some help here.
Within an Evolutionary Algorithm a parent individual X(i) with a genome of L bit has created N offsprings X(i) = Y(i)n identical to the parent X(i).
To yield the new generation Y(i+1)n the mutation operator is modifying each of these N offspring Y(i)n by flipping each of the N∗L bits with a probability of p.
Derive a formula that calculates the probability Q for the case that none of the N new individuals Y(i+1)n is identical to the parent X(i).
I've got absolutely no idea on how to approach this. Any suggestions?