b4swine,
To repeat what you are asking:

• A data structure that supports fast lookups
• A routine that implements that fast lookup
• More elegant code

The last two depend on the first one. One idea might be to use a single level hash instead of a HoH. Something like $lookup{"$obj_a*$obj_b"}. Another possibility is to use an array instead of a hash if there is some sort of efficient obj to index conversion that could be done since array lookups are faster. In fact, there may be no need to use a data structure at all. If you can convert your objects into an ordinal number efficiently, you could just store all the comparisons in a string and unpack the solution.

Only you are going to be able to answer if any of those ideas are viable. If you gave us some sample data with more information we might be able to propose a working solution.