On the integrality Gap of Small Asymmetric Travelling Salesman Problems: A Polyhedral and Computational Approach

\(\) In this paper, we investigate the integrality gap of the Asymmetric Traveling Salesman Problem (ATSP) with respect to the linear relaxation given by the Asymmetric Subtour Elimination Problem (ASEP) for small-sized instances. In particular, we focus on the geometric properties and symmetries of the ASEP polytope ( \(P_{ASEP}^n\) ) and its vertices. The polytope’s … Read more

On the generation of Metric TSP instances with a large integrality gap by branch-and-cut.

This paper introduces a computational method for generating metric Travelling Salesperson Problem (TSP) instances having a large integrality gap. The method is based on the solution of an NP-hard problem, called IH-OPT, that takes in input a fractional solution of the Subtour Elimination Problem (SEP) on a TSP instance and compute a TSP instance having … Read more