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

2022-09-20

AI Summary

This paper addresses the computational intractability arising from millions of independent followers (e.g., cyclists) in large-scale bilevel and two-stage stochastic programming, using bicycle infrastructure planning as a motivating application. We propose an integrated optimization framework combining Monte Carlo sampling, graph neural network (GNN)-based representation learning, and ensemble regression modeling. Our contributions are threefold: (1) the first follower sampling and embedded machine learning estimation method with provable theoretical optimality guarantees; (2) a bilevel-aware follower representation learning mechanism leveraging GNNs to encode spatial and behavioral heterogeneity; and (3) scalability to real-world city-scale networks with up to one million nodes. Evaluated on Toronto’s urban transportation system, our approach improves cycling accessibility by 19.2%—equivalent to $18 million in societal cost savings—while significantly outperforming baseline methods in decision quality. The framework has been deployed in operational infrastructure planning.

Abstract

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.

Problem

• Optimize large bilevel and stochastic programs
• Improve cycling network design efficiency
• Enhance decision quality using machine learning

Innovation

• Machine learning estimates unsampled followers
• Follower sampling algorithms tighten bounds
• Representation learning enhances follower features