Uncertainty Sets for Robust Shortest Path Problems

A lot has been written about solving robust problems when one knows exactly what the set of possible parameter realisations looks like. With the variable-sized robustness approach we have considered an alternative setting, in which the size of uncertainty is not really known. Still, we assume that the shape is given.

In a recent paper with the title “An Experimental Comparison of Uncertainty Sets for Robust Shortest Path Problems”, we go back another step and evaluate which uncertainty sets actually make sense for shortest path problems. We use actual real-world traffic data to generate uncertainty sets and compare the performance of the resulting solutions. It turns out that hardness of the robust problem is not really an indicator for the usefulness of the resulting paths. See for yourself!

The abstract:

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 lead 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 allows us to point out which robust models should be the future focus of algorithmic development.