The following algorithm is used to implement crossover in a genetic algorithm: I

Question

The following algorithm is used to implement crossover in a genetic algorithm: Input: Two strings of n bits x and y Output: Two strings of n bits x' and y' The crossover operator is applied as follows: A crossover site is selected at random (with equal probability) that divides each string into two sub-strings of non-zero length. That is x = [x1 x2] y = [y1 y2], with length of x1 = length of y1. The outputs are generated as x' = [x1 y2] and y' = [y1 x2] Given that you start with (x1, y1) = ((0 1 0 1 0 1) (1 1 1 1 1 1)), specify which 6-bit strings are possible values obtained through crossover alone. Justify your answer.

Explanation / Answer

well, your problem is saying that you are swapping parts of stringx to stringy
so..possiblilities = n for 1-point crossovers

(x1, y1) = ((1 0 1 0) (1 1 1 1))

becomes one of these:
......... x'1..,.y'1
1st bit: 1111 , 1010
2nd bit: 1011 , 1110
3rd bit: 1011 , 1111
4th bit: 1010 , 1111

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