Solving a Class of Traveling Salesman Problems Analytically

5 Pages Posted: 3 Nov 2008

Date Written: June 2003

Abstract

This paper addresses a class of Traveling Salesman Problems (TSP) in which a route must be made to a series of nodes and return to the original location and attempts to solve it using analytical methods. The problem will be presented as a matrix of routes, much as might be seen in a national road map, excepting for there being in this case less entries. This familiar arrangement of routes will be cast as a matrix problem and solved using familiar formulations of quadratic forms. This solution, should it prove successful, can be contrasted with differing numeric or even iterative methods, such as the well-known Gomory cut method of solving integer linear programs. The advantage, should it prove tenable, will be theoretic in that a familiar and accessible form of quadratic forms can be readily applied to the problem and to similar cases.

Suggested Citation

Tashjian, Richard, Solving a Class of Traveling Salesman Problems Analytically (June 2003). Statistics Working Papers Series, Vol. , pp. -, 2003. Available at SSRN: https://ssrn.com/abstract=1293608

Richard Tashjian (Contact Author)

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