Benchmarking Problems for Robust Discrete Optimization

TL;DR

This paper introduces new benchmark instances and generation methods for robust discrete optimization problems, aiming to facilitate the development and comparison of solution algorithms by providing harder-to-solve instances.

Contribution

It proposes several instance generation procedures, including sampling and optimization-based methods, for various robust optimization problem types and uncertainty sets.

Findings

Generated instances are significantly harder to solve than uniform samples.

Optimization-based generation produces more challenging instances.

All instances and code are publicly available online.

Abstract

Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to solve than its nominal counterpart, even if it remains in the same complexity class. For this reason, specialized solution algorithms have been developed. To further drive the development of stronger solution algorithms and to facilitate the comparison between methods, a set of benchmark instances is necessary but so far missing. In this paper we propose a further step towards this goal by proposing several instance generation procedures for combinations of min-max, min-max regret, two-stage and recoverable robustness with interval, discrete or budgeted uncertainty sets. Besides sampling methods that go beyond the simple uniform sampling method that is the de-facto standard to produce instances, also optimization models to construct hard instances are considered. Using a selection problem for the nominal ground problem, we are able to generate instances that are several orders of magnitudes harder to solve than uniformly sampled instances when solving them with a general mixed-integer programming solver. All instances and generator codes are made available online.