Well, using this Generation Ship idea would make more of an excellent story to a game versus being a game type so to say. A sim game would make you experience the boredom of such a thing, while lets say a dramatic first person with an interesting story intro would seem a lot more interesting.

But I don't think you could make a game that is based solely on that - more particularly using the story of Generation Ship, and focusing in on some huge event that could potentially destroy the mission.

"We have been boarded by aliens!" and then like millions of kids get slaughtered, and blah blah blah - it could be a bad thing, oxygen supply runs low, plants have been killed, etc...

The whole point of the game could be you avoiding the aliens, boarding the alien ship, blowing it up, and then, end game.

Also for some reason this idea makes me think it should be a female with the lead role.

Because this idea is so wide open with possibility, one thing I'd really concentrate on at the start is what kind of aesthetic sense you're trying to capture. Is the environment the focus (the compelling nature of the ship and how it works)? Is the story the focus? Is the survival simulation such an environment implies important (consummables, weather patterns, gravitational rotation)? Or is strategy and planning, military or civic, the focus? You might even be trying to capture the sense of evolving culture, and what happens to the mindset of the people.

Once you figure out the aesthetic sense you're going for I think you'll be better able to narrow down what gameplay elements to include. Here are some off the wall ideas, some based on books I've read or heard about:

Lakeside The Long Sun: You could have a generation ship gone wrong where the crew have become posthuman/extinct, the colonists have regressed to near digital illiteracy (even worshipping tech), and a single character has to somehow save the day. This would be more a puzzle/action game on a huge scale in a very strange environment.

Civ meets Master of Orion with Greg Bear's Eon for spice: The generation ship could be massive enough to be its own mobile cylindrical planet. The interior could be partly manmade, partly bound to a wormhole which creates an infinite Way stretching through spacetime. You'd gather materials in space in order to pave / terraform the Way. But because its a wormhole linked throughout spacetime, enemy forces could pop into your terraformed land at specific points.

A thousand eyes, ten thousand mouths Don't remember the title of this book, but I read a weird generation ship story where the main character was conned into volunteering for a project which turned him into a brain in a jar. He found himself running the ship, and at first was angry and mistreated the colonists. This caused their tech and social development to decline to the point where they were a danger to the ship. He then had to war with them until, generations later, he managed to make peace. Throughout the voyage he kept having to give them goals, place pressures on them so that they wouldn't decline, aggressively take out socially cancerous elements (like a Satanist terrorist cell), and even hide or defend against hostile alien boarders. As a game, I could see this being a blend of personal interaction and Sim-cultural development, with some RTS combat thrown in for good measure. Might be fun.