The traveling salesman problem: A Linear programming formulation

TL;DR

This paper introduces a polynomial-sized linear programming formulation for the Traveling Salesman Problem, utilizing a network flow-based model, and discusses implementation issues and results.

Contribution

It presents a novel polynomial-sized linear programming model for TSP, advancing the understanding of its mathematical formulation.

Findings

Linear program is polynomial-sized

Network flow-based model effectively represents TSP

Implementation issues are addressed and results discussed

Abstract

In this paper, we present a polynomial-sized linear programming formulation of the Traveling Salesman Problem (TSP). The proposed linear program is a network flow-based model. Numerical implementation issues and results are discussed. (The exposition and proofs are much more detailed in an edition which I wrote in collaboration with Dr. M.H. Karwan in 2012-2014 . That edition is available at http://users.business.uconn.edu/mdiaby/P=NPProofPapers/tspPaper.pdf)