Formulations and Branch-and-cut algorithms for the Period Travelling Salesman Problem

Abstract

In this work, we address two variants of the Period Travelling Salesman Problem: one where some nodes cannot be visited consecutively over the time horizon, and another one where this restriction is not imposed. A new flow-based formulation that uses specific information about the visit patterns of nodes is studied and empirical tests show that it is able to solve test instances where a flow-based formulation based on the Single Commodity Flow formulation for the Travelling Salesman Problem reached the time limit. Non-compact formulations are studied in this work as well. We propose two new sets of exponentially-sized valid inequalities that have not been studied yet in the literature. A formulation which is based on connectivity cuts per period enhanced with these sets of valid inequalities proved to be the most efficient and it was able to solve several instances.