> It would take 15 to 20 generations of human beings, living their entire lives confined to a prison, to complete this journey.
From a link given by a poster in another comment, earlier, you can do it at 1g acceleration for just 12 years subjective time:
http://convertalot.com/relativistic_star_ship_calculator.htm...
... so from the look of it, the difficulty isn't having a generation ship, it's having sufficient fuel to produce the acceleration.