机器学习增强的大规模双层与两阶段随机规划优化：应用于自行车网络设计
Machine Learning-Augmented Optimization of Large Bilevel and Two-stage Stochastic Programs: Application to Cycling Network Design
AI总结：
针对大规模双层规划问题，提出结合跟随者采样与机器学习估计目标值的方法，在多伦多自行车网络设计中提升可达性19.2%。
摘要：
广泛的决策问题可以建模为具有独立跟随者的双层规划，其特殊情况包括两阶段随机规划。这些问题尤其难以求解，特别是当存在大量跟随者时。受现实世界自行车基础设施规划应用的启发，我们提出了一种求解此类问题的一般方法。我们提出了一个优化模型，该模型显式考虑跟随者的采样子集，并利用机器学习模型来估计未采样跟随者的目标值。我们证明了所生成的领导者决策在考虑完整跟随者集合的原始目标函数下的最优性间隙的界限。然后，我们开发了跟随者采样算法以收紧界限，以及一种表示学习方法以学习跟随者特征，这些特征用作嵌入机器学习模型的输入。通过数值研究，我们表明与基线相比，我们的方法生成的领导者决策质量更高。最后，我们与多伦多市合作，在多伦多进行了一项现实世界案例研究，我们解决了具有超过一百万个跟随者的自行车网络设计问题。与当前实践相比，我们的方法将多伦多的自行车可达性提高了19.2%，相当于潜在成本节省1800万美元。我们的方法正被用于为多伦多的自行车基础设施规划提供信息，并大幅优于当前实践。它可以推广到任何建模为具有独立跟随者的双层规划的决策问题。
英文摘要：
A wide range of decision problems can be formulated as bilevel programs with independent followers, which as a special case include two-stage stochastic programs. These problems are notoriously difficult to solve especially when a large number of followers present. Motivated by a real-world cycling infrastructure planning application, we present a general approach to solving such problems. We propose an optimization model that explicitly considers a sampled subset of followers and exploits a machine learning model to estimate the objective values of unsampled followers. We prove bounds on the optimality gap of the generated leader decision as measured by the original objective function that considers the full follower set. We then develop follower sampling algorithms to tighten the bounds and a representation learning approach to learn follower features, which are used as inputs to the embedded machine learning model. Through numerical studies, we show that our approach generates leader decisions of higher quality compared to baselines. Finally, in collaboration with the City of Toronto, we perform a real-world case study in Toronto where we solve a cycling network design problem with over one million followers. Compared to the current practice, our approach improves Toronto's cycling accessibility by 19.2%, equivalent to $18M in potential cost savings. Our approach is being used to inform the cycling infrastructure planning in Toronto and outperforms the current practice by a large margin. It can be generalized to any decision problems that are formulated as bilevel programs with independent followers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
