Oh, you're thinking of NP-hard yes-no problems. Many if not most NP-hard problems of practical importance, including the traveling salesman, involve integer rather than boolean scores.
NP-hardness by definition is only yes-no decision problems. The NP-hard formulation of Traveling Salesman is "given the weighted graph G and an integer X, is there a Hamiltonian cycle in G with total weight less than X?"
