How to Solve TSP Given Length of Path? I am trying to devise an algorithm in which given the length of a path that satisfies the constraints of the Traveling Salesman Problem, I can find the path.  Currently, my only solution is to find a cost matrix of every possible path and brute force adding them up until I get a solution that equals the length of the path.

Is there a better way to find a TSP path given the length?
This decision problem ("does this graph contain a tour of length at most this?") is NP-complete, so you won't find a polynomial-time algorithm most likely. 

In addition to the brute-force method you describe, you can have a look at Held-Karp, which solves the problem in $O^*(2^n)$ time using dynamic programming. For an even more practical solution, you can have a look at the Concorde TSP solver, which has been successfully used to solve instances with tens of thousands of cities optimally.