In this paper, we study uncertainty set construction for robust optimization using various polyhedral norms. We first introduce the classical symmetric polyhedral-norms induced uncertainty sets and the corresponding robust counterparts of a linear uncertain constraint. Then, we introduce a novel method for asymmetric uncertainty set construction based on the distributional information of the uncertain parameters. Deterministic robust counterpart formulations for both types of uncertainty sets are derived for a general linear uncertain constraint. We further derive the robust counterpart of a linear uncertain constraint where the uncertain parameters belong to (i) an intersection of two symmetric uncertainty sets and (ii) an intersection of asymmetric and symmetric uncertainty sets. Using a numerical example and a reactor design problem, we demonstrate that appropriate uncertainty set construction reduces solution conservativeness. We also highlight the significance of integrating the data and distributional information of uncertain parameters in terms of safeguarding feasibility alongside improving the solution.

在本文中，我们研究了使用各种多面体范数进行稳健优化的不确定性集构造。我们首先介绍经典对称多面体范数引起的不确定性集和线性不确定性约束的相应鲁棒对应物。然后，我们介绍了一种基于不确定参数分布信息的非对称不确定集构造新方法。针对一般线性不确定性约束导出了两种类型不确定性集的确定性稳健对应公式。我们进一步推导出线性不确定约束的鲁棒对应物，其中不确定参数属于（i）两个对称不确定集的交集和（ii）非对称和对称不确定集的交集。使用一个数值例子和一个反应堆设计问题，我们证明了适当的不确定性集构造会降低解决方案的保守性。我们还强调了整合不确定参数的数据和分布信息在保障可行性和改进解决方案方面的重要性。