- Let S
_{1}={*0**11***0**} and S_{2}={*****0*1****} be two schemata.
- Give the order and the defining length of S
_{1} and S_{2}.
- What is the probability for one-point crossover with crossover

rate *p*_{c} that crossover breaks S_{1}, or S_{2}? (i.e., the probability that the child created by the operator does not belong to the given schema.)
- What is the probability that mutation with mutation rate
*p*_{m}

breaks S_{1}, or S_{2}?
- What is the probability that S
_{1} or S_{2 }survives the application of both crossover and mutation?
- Is it correct to call one of these two schemata a

“building block”? Explain why, or why not.

- Whilst optimising a three-bit problem, you notice that your

population, of size 100, consists of 25 copies each of strings

100 (with fitness 10), 111 (with fitness 20), 011 (with fitness

15), and 010 (with fitness 15).
- What is the estimated fitness of schema 1\#\# ?
- Assuming fitness proportionate selection with no

crossover or mutation, show one way by which you could

calculate the estimated fitness of that schema in the

next generation.

- In a simple two-dimensional model of protein structure

prediction, a solution consists of a sequence of moves

(north/east/west/south) on a square grid. The amino acid

residues, which compose the protein, are then mapped onto this

path, giving the structure of the folded protein. Good solutions

typically exhibit a high degree of local structure. That is to

say that they can be seen as the concatenation of secondary

structure “motifs”. Explain how this domain knowledge may be

used to guide the choice of recombination operators for this

problem.

## The on-line accompaniment to the book Introduction to Evolutionary Computing