The best requirement to relax, in my opinion, is that of optimality (which, incidentally, is a strong reason to be an adaptation executor rather than a utility maximizer!). My professional research is into optimization heuristics that just focus on getting good solutions and not worrying if they're the best ones- which allows tackling problems that are immensely larger. For many problems, it's simply not worth the time to ensure that no better solution exists- it's a lot of effort for little payout.
Admitting to being wrong isn't easy, but it's something we want to encourage.
So ... were you convinced by someone's arguments lately? Did you realize a heated disagreement was actually a misunderstanding? Here's the place to talk about it!