鲁棒离散最优化的基准问题
Benchmarking Problems for Robust Discrete Optimization
摘要：
鲁棒离散最优化是一个非常活跃的研究领域，它考虑了决策准则、不确定集和潜在标称问题之间的大量组合。通常，一个鲁棒问题比其名义上的对应问题更难解决，即使它仍然处于相同的复杂性类别。为此，已经开发了专门的解决方案算法。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，但到目前为止还没有。在本文中，我们提出了进一步实现这一目标，提出了几个实例生成程序的组合最小最大，最小最大遗憾，两阶段和可恢复的鲁棒性区间，离散或预算的不确定性集。除了超越简单的均匀抽样方法，这是事实上的标准产生的实例的抽样方法，也最优化模型构造硬实例被认为是。使用一个选择问题的名义地面问题，我们能够生成的实例是几个数量级更难解决比均匀采样的实例时，解决他们与一般的混合整数规划求解器。所有实例和生成器代码都可以在线获得。
英文摘要：
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.
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