Cite Formal Definitions of Standard Problem in Thesis Should I cite the definition of a standard problem that is widely know by the community in my thesis? For example the travelling salesman problem (TSP) is a very well known problem in computer science (dating back to the 1800s). To ensure accuracy I would refer to other sources for the formal definition, but these sources are very far removed from the original formulation of the problem.

Not sure if it makes a difference but I would potentially using different symbols as some of them could conflict with other uses throughout the document.
It is probably best to err on the side of completeness as long as you don't get so pedantic that you can't be understood. Some people who later read your work will appreciate those citations, even if your committee doesn't need them. Appendices/annexes are good for including some of that sort of thing. 

But if you rely on a different formulation than the standard it might be especially useful to be complete. You don't, likely, need to chase the full history back (though it might help situate your work), but at least the immediate ancestors to your work. 

Complete, but not pedantic. A balance. 

And of course, your dissertation advisor has the best and most relevant advice on this. He or she needs to be happy.