So, forced abortion.
Or, forced contraception measures, and working the occasional extra kid into your long term plan. We are talking about decades and centuries of travel time - the plan is long term population control, not "OMG, we have one extra kid, we are DOOOOOOooooooOOOOOmed!" If you have one unplanned kid, you just cut down on the planned births next year, and it evens out.
Your approach to this seems... always catastrophic. We have centuries to work with, not minutes.
We're stripping away the reproductive rights of thousands of people without their permission. Now, we can certainly do that. Sure. But, let's not pretend that we're not committing massive human rights violations to do so. "Some sacrifices" seems a tad euphemistic.
For everyone who gets on board to start with, it is entirely voluntary.
For people who are born in flight - they are taught from a young age exactly what the stakes are. They can be taught the plan, and about population dynamics. They can understand that population growth needs to be controlled. And note for most of these people, it isn't that they *cannot* have kids. It is a question of when, and how many. And, if we are smart, some of that will be negotiable, and we can plan around it. If one couple doesn't want kids, that's cool, another couple that does want them can have more.
I think you're failing to note how that we here on this board are, for the most part, highly privileged people. Most of the population of the planet you are standing on still aren't. Humans are already born into cultures they cannot control, many with aspects we think of as human rights violations, and they have no way out of them either. You are speaking as if the ship failing to be a utopia is somehow a major failing.
Hard to plant in space.
No, it isn't. You spin the ship anyway to create a centrifugal gravity to make sure human bone development happens normally, which gives you planting surfaces. Use lots of hydroponics. The plants become part of your biological and air recycling systems.