When evaluating the optimum found by an evolutionary algorithm, how
close is "close enough" to the "true optimum" in order for this to count
as a good result/successful optimization?

For instance, if I have simple search space from x: -1000 to +1000 and
the optimum is at zero, how close do I have to be for this to be a
"valid"/successful optimization?

I.e., my result should be within +/- epsilon from the true optimum.
How to choose this epsilon value? Clearly it should be different for a
search space of -1000 to +1000 vs say -1 to +1. If anyone has any
rules/guidance that would imply statistically significant results, or
could point me to some articles or references I would be grateful.