论文标题
鲁棒优化的简要介绍
A Brief Introduction to Robust Bilevel Optimization
论文作者
论文摘要
二元优化是建模层次决策过程的强大工具。但是，在理论和实践中，由此产生的问题都具有挑战性。幸运的是，该领域已经取得了重大算法的进步，因此与二十年前可以解决的问题相比，今天我们可以解决更大，更复杂的问题。这导致了研究人员今天试图解决的越来越具有挑战性的二聚体问题。在本文中，我们简要介绍了这些更具挑战性的二聚体问题类别：使用强大的优化技术在不确定的情况下进行双光线优化。为此，我们简要地陈述了不同版本的不确定的二聚体问题，这些问题是从不同级别的跟随者合作以及何时揭示不确定性的情况下引起的。我们使用一个学术示例来强调这些概念，并讨论有关复杂性以及解决方案方法的最新结果。最后，我们讨论了双层优化中不确定性的来源比单级优化要丰富得多，并且为此，介绍了决策不确定性的概念。
Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic advances in the field so that we can solve much larger and also more complicated problems today compared to what was possible to solve two decades ago. This results in more and more challenging bilevel problems that researchers try to solve today. In this article, we give a brief introduction to one of these more challenging classes of bilevel problems: bilevel optimization under uncertainty using robust optimization techniques. To this end, we briefly state different versions of uncertain bilevel problems that result from different levels of cooperation of the follower as well as on when the uncertainty is revealed. We highlight these concepts using an academic example and discuss recent results from the literature concerning complexity as well as solution approaches. Finally, we discuss that the sources of uncertainty in bilevel optimization are much richer than in single-level optimization and, to this end, introduce the concept of decision uncertainty.
