A novel data-driven stochastic robust optimization (DDSRO) framework is proposed for optimization under uncertainty leveraging labeled multi-class uncertainty data. Uncertainty data in large datasets are often collected from various conditions, which are encoded by class labels. Machine learning methods including Dirichlet process mixture model and maximum likelihood estimation are employed for uncertainty modeling. A DDSRO framework is further proposed based on the data-driven uncertainty model through a bi-level optimization structure. The outer optimization problem follows a two-stage stochastic programming approach to optimize the expected objective across different data classes; adaptive robust optimization is nested as the inner problem to ensure the robustness of the solution while maintaining computational tractability. A decomposition-based algorithm is further developed to solve the resulting multi-level optimization problem efficiently. Case studies on process network design and planning are presented to demonstrate the applicability of the proposed framework and algorithm.

提出了一种新颖的数据驱动的随机鲁棒优化（DDSRO）框架，用于利用标记的多类不确定性数据进行不确定性下的优化。大型数据集中的不确定性数据通常是从各种条件收集的，这些条件由类标签编码。不确定性建模采用包括Dirichlet过程混合模型和最大似然估计在内的机器学习方法。通过双层优化结构，在数据驱动的不确定性模型的基础上进一步提出了DDSRO框架。外部优化问题遵循两阶段随机规划方法，以跨不同数据类优化预期目标。嵌套的自适应鲁棒优化是内部问题，可确保解决方案的鲁棒性，同时保持计算的可处理性。进一步开发了一种基于分解的算法，以有效解决由此产生的多级优化问题。提出了关于过程网络设计和规划的案例研究，以证明所提出的框架和算法的适用性。