Machine Learning–Augmented Optimization of Large Bilevel and Two-Stage Stochastic Programs: Application to Cycling Network Design
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Problem definition: 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 are present. Motivated by a real-world cycling infrastructure planning application, we present a general approach to solving such problems. Methodology/results: 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 with 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 with the current practice, our approach improves Toronto’s cycling accessibility by 19.2%, equivalent to $18 million in potential cost savings. Managerial implications: Our approach is being used to inform the cycling infrastructure planning in Toronto and can be generalized to any decision problems that are formulated as bilevel programs with independent followers. Funding: This work was supported by City of Toronto Transportation Services and the Natural Sciences and Engineering Research Council of Canada [NSERC Alliance Grant ALLRP 561212-20]. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/msom.2024.1317 .
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it