A New Integer Programming Formulation of the Graphical Traveling Salesman Problem

TL;DR

This paper introduces a novel integer programming formulation for the Graphical TSP that simplifies constraints and addresses an open problem, potentially improving solution efficiency for sparse graphs.

Contribution

It proposes a new integer programming model for the Graphical TSP with fewer and more manageable constraints, solving an open question in the field.

Findings

Formulation uses only two classes of constraints.

Constraints are either polynomial in number or separable.

Addresses an open problem by Naddef.

Abstract

In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost $c_{ij}$ of traveling from city $i$ to city $j$, which is the same in either direction for the Symmetric TSP. The objective is to visit each city exactly once, minimizing total travel costs. In the Graphical TSP, a city may be visited more than once, which may be necessary on a sparse graph. We present a new integer programming formulation for the Graphical TSP requiring only two classes of constraints that are either polynomial in number or polynomially separable, while addressing an open question proposed by Denis Naddef.