To be honest, the best way is to use human ingenuity rather than algorithms.
If a particular search can be automated, then it means a greater number of people have access, thus reducing your chances of a bargain.

The only method I'm willing to share is that I look for other airports that I can get to /from by plane, train or automobile (or ferry ... whatever) that might have cheaper fares for some reason (less popular routes, over-capacity, public holiday dates etc)