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

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  • Henriques, Sofia
  • Paias, Ana

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.

Suggested Citation

  • Henriques, Sofia & Paias, Ana, 2025. "Formulations and Branch-and-cut algorithms for the Period Travelling Salesman Problem," European Journal of Operational Research, Elsevier, vol. 323(3), pages 739-752.
    • Handle: RePEc:eee:ejores:v:323:y:2025:i:3:p:739-752
    DOI: 10.1016/j.ejor.2025.01.015
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