"The problem under consideration" vs "The considered problem" vs "The problem considered"

I'm writing a research essay.

Is there any difference between the provided three variants? If there is, which is best to use?

You wouldn't say "the considered problem". Usually, a past participle used as adjective appears after the noun it modifies (Practical English Usage, second ed., Michael Swan, p. 405).

We often use participles after nouns in order to define or identify the nouns, in the same way as we use identifying relative clauses.

• We couldn't agree on any of the problems discussed.
  (=… the problems that were discussed
  (NOT …the discussed problems.)
  […] I got the only ticket left.

Difference of meaning
A few past participles change their meaning with their position.
Compare:
an adopted child/the solution adopted

There exists certain nouns for which "considered" is placed before, such as typically "opinion".

• a considered opinion, a considered thought, …

In this case the word means "that is the result of careful thinking". (free dictionary)

As this sense of the participle is not that given in its use with "problem", you have to say "the problem considered".

The meaning is the same as that of "problem under consideration" because as explained above, this is equivalent to "that is being considered".