Which form is correct?
My advance search. My advanced search.
I ask this in comparison to "simple" that does not have a 'ed' form.
My simple search.
"Advance search" suggests a search that you did before some event, e.g. "my advance search led me to this particular car dealer". "Advanced search" means that the search operation was in some way advanced, which sounds like the case you're describing.
However, I'm not used to seeing "advanced" (or "simple") used in this way. If I'm talking about an operation I just performed on Google, I'm far more likely to just say "my search". What nuance are you trying to capture?
My advanced search is correct.
"Advance" is a verb, suggesting that you are advancing or moving forward, while "advanced" is an adjective describing that your search is more complex. "Simple" is also an adjective indicating that your search is not complex.