Would time travel be useful for optimization?
Yes.  If time travel were possible, it would be a huge win for optimization and computation: it would enable us to solve computational problems that today seem very hard to solve with existing computers.

To formalize this, we must first agree on a model of physics that allows time travel and that describes what happens when you try.  There are various plausible ways to do that.  Under one plausible set of assumptions about the physics, the set of problems you can solve in polynomial time using time travel is all of PSPACE.  (If you're not familiar with it, PSPACE is the set of problems solvable by classical no-time-travel computers in  any amount of running time you want, subject only the restriction that the space usage must be polynomial.)  For instance, every problem in NP could be solved in polynomial time if time travel were possible.

For instance, there are problems that today seem to require exponential time to solve (with classical no-time-travel computers), but could be solved in polynomial time if time travel were possible.

To learn more about this subject, I suggest you take a look at Scott Aaronson's lecture notes: http://www.scottaaronson.com/democritus/lec19.html