The Steiner Traveling Salesman Problem and its extensions

Jessica Rodríguez-Pereira, Elena Fernández, Gilbert Laporte, Enrique Benavent, Antonio Martínez-Sykora

Research output: Contribution to journalArticlepeer-review

14 Citations (SciVal)


This paper considers the Steiner Traveling Salesman Problem, an extension of the classical Traveling Salesman Problem on an incomplete graph where not all vertices have demand. Some extensions including several depots or location decisions are introduced, modeled and solved. A compact integer linear programming formulation is proposed for each problem, where the routes are represented with two-index decision variables, and parity conditions are modeled using cocircuit inequalities. Exact branch-and-cut algorithms are developed for all formulations. Computational results obtained confirm the good performance of the algorithms. Instances with up to 500 vertices are solved optimally.

Original languageEnglish
Pages (from-to)615-628
Number of pages14
JournalEuropean Journal of Operational Research
Issue number2
Publication statusPublished - 16 Oct 2019


  • Branch-and-cut
  • Integer linear programming
  • Steiner Traveling Salesman Problem
  • Valid inequalities

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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