论文标题

基准测试问题,以实现鲁棒的离散优化

Benchmarking Problems for Robust Discrete Optimization

论文作者

Goerigk, Marc, Khosravi, Mohammad

论文摘要

强大的离散优化是一个高度积极的研究领域,在该领域中,考虑决策标准,不确定性集和潜在的名义问题之间的大量组合。通常,即使它仍然处于相同的复杂性类别中,也比其名义上的问题更难解决。因此,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,需要一组基准实例,但到目前为止缺失。在本文中,我们提出了一些实例生成程序,以迈出了迈向最小,最大遗憾,两阶段和可回收的鲁棒性,以间隔,离散或预算的不确定性集的结合,提出了朝着这一目标迈出的进一步步骤。除了采样方法超出了简单的统一抽样方法(即生成实例的事实标准)外,还考虑了构建硬实例的优化模型。在标称地面问题上使用选择问题,我们能够生成比统一采样实例在用一般混合组合编程求解器求解时更难解决的实例。所有实例和发电机代码均可在线提供。

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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