One thing most older SF about multigenerational starships did not address
Was the ability of virtual reality to help alleviate the potential
boredom and/or social degeneration.
I could see VR advancing enough so that people aboard such a
vessel could immerse themselves in worlds that seem very real
to their minds and thus survive.
Or we could send a group of really devout religious people, who
either are "traditional" religious types or treat the mission as a
religious quest that must be fulfilled.
Yes, I know there are issues with these ideas as well - so let's
have at it!
By the way, 500 or even 10,000 years may seem like a lot to
us short-lived creatures, but they are the proverbial drop in
the bucket compared to the galaxy or the Universe's ages.