不确定网络设计模型的比较
A Comparison of Models for Uncertain Network Design
摘要：
为了解决现实世界的问题，建模者通常需要在模型的复杂性和有用性之间做出权衡。这对于鲁棒优化也是如此，其中已经提出了广泛的不确定性模型，即所谓的不确定性集。然而，虽然这些集主要是从理论的角度研究，很少有研究比较不同的集对现实世界的问题的有用性。在本文中，我们认为在电信方面的网络设计问题。我们需要投资于基础设施，以便有足够的能力满足未来的需求，而未来的需求并不确定。对于未满足的已实现需求，需要进行外包。我们考虑三种方法来建模需求：使用离散的不确定性集，使用多面体的不确定性集，并使用每商品拟合零膨胀均匀分布的平均值。虽然前两个模型被用作鲁棒优化设置的一部分，但最后一个模型表示简单的随机最优化设置。我们比较这些方法的效率前沿的真实世界的数据取自在线图书馆SNDlib，并观察到，相反，目前的研究趋势，强大的优化使用多面体的不确定性集可能会导致不太有效解。
英文摘要：
To solve a real-world problem, the modeler usually needs to make a trade-off between model complexity and usefulness. This is also true for robust optimization, where a wide range of models for uncertainty, so-called uncertainty sets, have been proposed. However, while these sets have been mainly studied from a theoretical perspective, there is little research comparing different sets regarding their usefulness for a real-world problem. In this paper we consider a network design problem in a telecommunications context. We need to invest into the infrastructure, such that there is sufficient capacity for future demand which is not known with certainty. There is a penalty for an unsatisfied realized demand, which needs to be outsourced. We consider three approaches to model demand: using a discrete uncertainty set, using a polyhedral uncertainty set, and using the mean of a per-commodity fitted zero-inflated uniform distribution. While the first two models are used as part of a robust optimization setting, the last model represents a simple stochastic optimization setting. We compare these approaches on an efficiency frontier real-world data taken from the online library SNDlib and observe that, contrary to current research trends, robust optimization using the polyhedral uncertainty set may result in less efficient solutions.
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