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, budgeted or ellipsoidal 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.

中文翻译：

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鲁棒离散优化的基准问题

鲁棒离散优化是一个高度活跃的研究领域，其中考虑了决策标准、不确定性集和潜在名义问题之间的大量组合。通常，一个稳健的问题比其名义上的对应问题更难解决，即使它保持在相同的复杂性类别中。为此，开发了专门的求解算法。为了进一步推动更强大的解决方案算法的开发并促进方法之间的比较，一组基准实例是必要的，但迄今为止还缺少。在本文中，我们提出了实现这一目标的进一步步骤，提出了几种实例生成程序，用于最小-最大、最小-最大后悔、两阶段和可恢复鲁棒性与区间、离散、预算或椭圆体不确定性集的组合。除了超越简单均匀采样方法（生产实例的事实上的标准）之外的采样方法之外，还考虑了构建硬实例的优化模型。使用标称基础问题的选择问题，当使用通用混合整数规划求解器求解时，我们能够生成比均匀采样实例更难解决几个数量级的实例。所有实例和生成器代码均可在线获取。