An Experimental Comparison of Uncertainty Sets for Robust Shortest Path Problems

Authors Trivikram Dokka, Marc Goerigk

Thumbnail PDF


  • Filesize: 0.54 MB
  • 13 pages

Document Identifiers

Author Details

Trivikram Dokka
Marc Goerigk

Cite AsGet BibTex

Trivikram Dokka and Marc Goerigk. An Experimental Comparison of Uncertainty Sets for Robust Shortest Path Problems. In 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017). Open Access Series in Informatics (OASIcs), Volume 59, pp. 16:1-16:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Through the development of efficient algorithms, data structures and preprocessing techniques, real-world shortest path problems in street networks are now very fast to solve. But in reality, the exact travel times along each arc in the network may not be known. This led to the development of robust shortest path problems, where all possible arc travel times are contained in a so-called uncertainty set of possible outcomes. Research in robust shortest path problems typically assumes this set to be given, and provides complexity results as well as algorithms depending on its shape. However, what can actually be observed in real-world problems are only discrete raw data points. The shape of the uncertainty is already a modelling assumption. In this paper we test several of the most widely used assumptions on the uncertainty set using real-world traffic measurements provided by the City of Chicago. We calculate the resulting different robust solutions, and evaluate which uncertainty approach is actually reasonable for our data. This anchors theoretical research in a real-world application and gives an indicator which robust models should be the future focus of algorithmic development.
  • robust shortest paths
  • uncertainty sets
  • real-world data
  • experimental study


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Hassene Aissi, Cristina Bazgan, and Daniel Vanderpooten. Min-max and min-max regret versions of combinatorial optimization problems: A survey. European journal of operational research, 197(2):427-438, 2009. Google Scholar
  2. Hannah Bast, Daniel Delling, Andrew Goldberg, Matthias Müller-Hannemann, Thomas Pajor, Peter Sanders, Dorothea Wagner, and Renato F Werneck. Route planning in transportation networks. In Algorithm Engineering, pages 19-80. Springer, 2016. Google Scholar
  3. Aharon Ben-Tal and Arkadi Nemirovski. Robust convex optimization. Mathematics of operations research, 23(4):769-805, 1998. Google Scholar
  4. Aharon Ben-Tal and Arkadi Nemirovski. Robust solutions of uncertain linear programs. Operations research letters, 25(1):1-13, 1999. Google Scholar
  5. Dimitris Bertsimas and David B. Brown. Constructing uncertainty sets for robust linear optimization. Operations research, 57(6):1483-1495, 2009. Google Scholar
  6. Dimitris Bertsimas and Melvyn Sim. Robust discrete optimization and network flows. Mathematical programming, 98(1):49-71, 2003. Google Scholar
  7. Dimitris Bertsimas and Melvyn Sim. The price of robustness. Operations research, 52(1):35-53, 2004. Google Scholar
  8. Christina Büsing. Recoverable robust shortest path problems. Networks, 59(1):181-189, 2012. Google Scholar
  9. André Chassein and Marc Goerigk. Alternative formulations for the ordered weighted averaging objective. Information Processing Letters, 115(6):604-608, 2015. Google Scholar
  10. André Chassein and Marc Goerigk. A new bound for the midpoint solution in minmax regret optimization with an application to the robust shortest path problem. European Journal of Operational Research, 244(3):739-747, 2015. Google Scholar
  11. André Chassein and Marc Goerigk. A bicriteria approach to robust optimization. Computers &Operations Research, 66:181-189, 2016. Google Scholar
  12. André Chassein and Marc Goerigk. Performance analysis in robust optimization. In Robustness Analysis in Decision Aiding, Optimization, and Analytics, pages 145-170. Springer, 2016. Google Scholar
  13. André Chassein and Marc Goerigk. Variable-sized uncertainty and inverse problems in robust optimization. European Journal of Operational Research, 2017. Available online, to appear. Google Scholar
  14. Marc Goerigk and Anita Schöbel. Algorithm engineering in robust optimization. In Algorithm engineering, pages 245-279. Springer, 2016. Google Scholar
  15. Adam Kasperski and Paweł Zieliński. Robust discrete optimization under discrete and interval uncertainty: A survey. In Robustness Analysis in Decision Aiding, Optimization, and Analytics, pages 113-143. Springer, 2016. Google Scholar
  16. Roberto Montemanni and Luca Maria Gambardella. An exact algorithm for the robust shortest path problem with interval data. Computers &Operations Research, 31(10):1667-1680, 2004. Google Scholar
  17. Evdokia Nikolova. High-performance heuristics for optimization in stochastic traffic engineering problems. In International Conference on Large-Scale Scientific Computing, pages 352-360. Springer, 2009. Google Scholar
  18. Gang Yu and Jian Yang. On the robust shortest path problem. Computers &Operations Research, 25(6):457-468, 1998. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail