论文标题

机器学习的优化大型二聚体和两阶段随机程序:应用于骑自行车网络设计

Machine Learning-Augmented Optimization of Large Bilevel and Two-stage Stochastic Programs: Application to Cycling Network Design

论文作者

Chan, Timothy C. Y., Lin, Bo, Saxe, Shoshanna

论文摘要

各种各样的决策问题可以作为具有独立关注者的双重计划提出,作为特殊情况,其中包括两阶段的随机计划。众所周知,这些问题很难解决,尤其是当大量关注者出现时。由现实世界中的骑自行车基础设施计划应用程序的激励,我们提出了一种解决此类问题的一般方法。我们提出了一个优化模型,该模型明确考虑了追随者的采样子集,并利用机器学习模型来估计未采样关注者的客观值。我们证明了由原始目标函数衡量的生成领导者决策的最佳差距,该目标函数考虑了完整的追随者集。然后,我们开发追随者采样算法来收紧界限和表示追随者功能的表示方法,这些方法被用作嵌入式机器学习模型的输入。通过数值研究,我们表明我们的方法与基线相比会产生更高质量的领导者决策。最后,与多伦多市合作,我们在多伦多进行了一项现实世界中的案例研究,在那里我们解决了一个超过一百万关注者的自行车网络设计问题。与当前的做法相比,我们的方法将多伦多的自行车可及性提高了19.2%,相当于节省的1800万美元。我们的方法被用来告知多伦多的骑自行车基础设施计划,并以大幅度的优于当前的做法。可以将其推广到与独立关注者一起制定为双重计划的任何决策问题。

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.

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