This paper presents a novel deep learning based data‐driven optimization method. A novel generative adversarial network (GAN) based data‐driven distributionally robust chance constrained programming framework is proposed. GAN is applied to fully extract distributional information from historical data in a nonparametric and unsupervised way without a priori approximation or assumption. Since GAN utilizes deep neural networks, complicated data distributions and modes can be learned, and it can model uncertainty efficiently and accurately. Distributionally robust chance constrained programming takes into consideration ambiguous probability distributions of uncertain parameters. To tackle the computational challenges, sample average approximation method is adopted, and the required data samples are generated by GAN in an end‐to‐end way through the differentiable networks. The proposed framework is then applied to supply chain optimization under demand uncertainty. The applicability of the proposed approach is illustrated through a county‐level case study of a spatially explicit biofuel supply chain in Illinois.

中文翻译：

---

带有生成对抗网络（GAN）的分布鲁棒机会受限编程

本文提出了一种新颖的基于深度学习的数据驱动优化方法。提出了一种基于数据驱动分布式鲁棒机会约束的新型生成对抗网络。GAN用于以非参数和无监督的方式从历史数据中完全提取分布信息，而无需先验近似或假设。由于GAN利用深度神经网络，因此可以学习复杂的数据分布和模式，并且可以高效，准确地对不确定性进行建模。分布鲁棒的机会约束规划考虑了不确定参数的模棱两可的概率分布。为解决计算难题，采用了样本平均逼近法，GAN通过可区分网络端到端地生成所需的数据样本。然后将提出的框架应用于需求不确定性下的供应链优化。通过对伊利诺伊州空间明确的生物燃料供应链进行县级案例研究，说明了该方法的适用性。