The multiverse solution to the problem(s) of evil (and the problem of suboptimality) is a systematic response to these problems, and one that is fairly popular. Still, lot’s of people have argued against the view (see, for instance, Monton, 2010, Almeida, 2008, 2010) and some use multiverses for other purposes (see O’Connor, 2008). For a nice overview of multiverse approaches (and bibliographic citations) see Klaas Kraay here.
The thought, according to multiverse theorists, is that God necessarily actualizes a possible world W that includes lots of cosmoi, or lots of universes, U0, U1, . . ., Un. All of the universes are actual, so the multiverse is not a pluriverse (for instance, it is not a Lewisian pluriverse). The universes “chosen” (don’t take this too literally) for actualization are the universes (of those worlds) that include an on balance positive value. It is of course a much longer story, and I would argue that it is probably not a coherent story (and, further, not the story that multiverse theorists think they are telling), but this is the basic multiverse thought.
What we know about W is that it contains lots of universes Un. Many of the Un include instances of evil E that are gratuitous relative to Un. For instance, our “world” @ would in fact be just one of the universes U@ in W that includes evil E that serves no greater purpose in U@. But the E in U@ would be necessary to the greatest possible overall good, viz., the good in W. There is no world w’ such that w’ is at least as good as W and w’ does not include E; so E is necessary to the best possible world W or, ☐(W ⊃ E) & ~(∃w)((w ≧ W) & ~☐(w ⊃ E))
So, the modal problem of evil seems solved: there is no evil in any world (recall, there is just one world, W) that is gratuitous. All of the evil in every world (all of the evil in every universe Un in W) is necessary to the greater possible good.
But here’s a question worth thinking about. How could God allow evil E in Un of W that is not necessary to any greater good in Un? The quick and simple answer is that E is necessary to the greater good in W, as spelled out above. But is that true? Had God prevented E in Un, Un would have been better, that’s for sure. But had God prevented E in Un, W would have been better, too, not worse, than it is. So, it certainly looks like E is not necessary to any greater good in W, either. But then W includes gratuitous evil and God could not actualize it. I think this is a deeper problem than it appears to be.