Lecture 1

Question 1

what is the probability of generating a specific solution with a single random experiment? Solutions in the space {0,1}^n

Answer 1

2^(-n)

Question 2

what is the probability of generating a specific solution in the first k iterations?

Answer 2

1 - (1 - 2^(-n))^k
because it’s 1 - the probability that it does not happen in the first k iterations

Question 3

what is the probability of generating a specific solution in iteration k?

Answer 3

(1 - p)^(k - 1) * p
where p =2^(-n) is the probability of generating it

Question 4

how does the evolutionary search algorithm go?

Answer 4

1. randomly initialize a candidate solution
   WHILE we have not found the solution, DO:
2. create a copy of the old solution
3. flip each bit in the copy with a probability
4. calculate the hamming distance between this new copy and the optimal solution and the hamming distance between the old solution and the optimal solution
5. out of the copy and the old solution, keep the one with the smallest distance to the optimal solution

NB: this is a (1+1) EA!

Question 5

what is the upper bound for the expected number of iterations for evolutionary search?

Answer 5

E_iter(n) \in O(n ln n)