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arxiv: 2605.28730 · v1 · pith:RDUPPIKFnew · submitted 2026-05-27 · 💻 cs.AI

AlphaTransit: Learning to Design City-scale Transit Routes

Bibek Poudel , Sai Swaminathan , Weizi Li This is my paper

Pith reviewed 2026-06-29 11:52 UTC · model grok-4.3

classification 💻 cs.AI
keywords transit network designMonte Carlo Tree Searchreinforcement learningbus route optimizationdelayed feedbackcity-scale planningservice rate maximization
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The pith

AlphaTransit uses Monte Carlo Tree Search guided by a neural policy-value network to design bus routes that maximize service rate under delayed feedback.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that transit network design involves sequential route choices whose quality only becomes clear after the full network is built, creating a delayed-feedback problem where local improvements can harm global performance. AlphaTransit addresses this by pairing MCTS with a neural network that proposes extensions and estimates final network quality, allowing lookahead without simulator rollouts inside the search tree. On a Bloomington benchmark with realistic roads and demand, the method reaches service rates of 54.6 percent and 82.1 percent in mixed and full demand cases, outperforming both plain reinforcement learning and unguided MCTS. These gains demonstrate that learned guidance and search together handle deceptive route interactions better than either component alone.

Core claim

AlphaTransit couples Monte Carlo Tree Search with a neural policy-value network so that the policy proposes route extensions while the value head estimates downstream network quality; this supplies decision-time lookahead during route construction without running simulator rollouts inside the search tree, and on the Bloomington network it produces the highest service rates of 54.6 percent and 82.1 percent under mixed and full transit demand.

What carries the argument

Monte Carlo Tree Search guided by a neural policy-value network that estimates final design quality without internal simulator rollouts.

If this is right

  • Coupling learned guidance with MCTS is more effective for transit network design than using either approach alone.
  • Route construction can proceed with lookahead predictions that avoid running full simulations at every search node.
  • Service rate improvements of roughly 10 to 11 percent are attainable on realistic city networks with census-derived demand.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same hybrid guidance pattern could be tested on other sequential network-design tasks that share delayed feedback, such as power-grid or water-system layout.
  • Performance on larger metropolitan areas would reveal whether the current neural estimates remain reliable when route interactions grow more complex.
  • Replacing the fixed Bloomington topology with dynamic traffic or construction data would test whether the value estimates can be updated online.

Load-bearing premise

The neural policy-value network supplies sufficiently accurate estimates of final network quality to guide MCTS decisions without any simulator rollouts inside the search tree.

What would settle it

A head-to-head comparison on the same Bloomington benchmark in which AlphaTransit without the value network or with deliberately noisy value estimates fails to exceed the service rates of plain reinforcement learning or unguided MCTS.

Figures

Figures reproduced from arXiv: 2605.28730 by Bibek Poudel, Sai Swaminathan, Weizi Li.

Figure 1
Figure 1. Figure 1: Learning dynamics and search cost under mixed demand ( [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: AlphaTransit overview. At each route-construction state [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: AlphaTransit policy-value network. Node features are projected to embeddings, then passed [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: AlphaTransit scaling behavior under mixed demand ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Mixed-demand results on the Bloomington benchmark ( [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Selected route designs under mixed demand ( [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The Bloomington, Indiana transportation network ( [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Learning dynamics and search cost under full demand ( [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Full transit demand results on the Bloomington benchmark ( [PITH_FULL_IMAGE:figures/full_fig_p027_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Selected route designs under full transit demand ( [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
read the original abstract

Designing a transit network requires many sequential route extension decisions, but their quality is often visible only after the full network is assembled. This delayed-feedback challenge lies at the heart of the Transit Route Network Design Problem (TRNDP), where route interactions can be deceptive: an extension that appears useful locally can create transfer bottlenecks, produce redundant overlap, or reduce overall throughput. To guide route construction under delayed simulator feedback, we introduce AlphaTransit, a search-based planning framework for cityscale bus network design. AlphaTransit couples Monte Carlo Tree Search (MCTS) with a neural policy-value network: the policy proposes route extensions, the value estimates downstream design quality, and search uses these predictions to refine each decision. This provides decision-time lookahead during route construction without running simulator rollouts inside the search tree. We evaluate AlphaTransit on a new Bloomington TRNDP benchmark with realistic road topology and censusderived demand, under mixed and full transit demand settings. In the Bloomington network, AlphaTransit attains the highest service rate in both demand settings, reaching 54.6% and 82.1%, respectively. Relative to reinforcement learning without search, these correspond to 9.9% and 11.4% service rate gains; relative to MCTS without learned guidance, they correspond to 2.5% and 11.2% gains. These results suggest that coupling learned guidance with MCTS is more effective than using either approach alone for transit network design. Our code and data are publicly available in https://github.com/poudel-bibek/AlphaTransit.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper presents AlphaTransit, a framework that couples Monte Carlo Tree Search (MCTS) with a neural policy-value network to solve the Transit Route Network Design Problem (TRNDP). The policy proposes route extensions while the value head estimates final network quality, enabling lookahead during sequential route construction without simulator rollouts inside the search tree. On a new Bloomington benchmark with realistic topology and census-derived demand, AlphaTransit reports the highest service rates (54.6% mixed demand, 82.1% full demand), yielding 9.9–11.4% gains over RL without search and 2.5–11.2% gains over MCTS without learned guidance. Code and data are released publicly.

Significance. If the central performance claims hold after verification, the work demonstrates that learned value estimates can usefully substitute for rollouts in MCTS for delayed-feedback network design tasks, outperforming either component alone. The public release of code and benchmark data is a clear strength that supports reproducibility and further research on TRNDP variants.

major comments (2)
  1. [Abstract] Abstract: The headline service-rate gains (54.6%/82.1%, 9.9–11.4% over RL, 2.5–11.2% over plain MCTS) rest on the claim that the learned value head supplies sufficiently accurate estimates of final network quality to replace simulator rollouts inside the MCTS tree. No diagnostics of value prediction quality—such as correlation between predicted value and realized service rate on held-out partial networks, calibration plots, or error statistics—are reported anywhere in the manuscript.
  2. [Abstract] Abstract: The reported percentage gains are presented without error bars, confidence intervals, or statistical significance tests across multiple random seeds or demand realizations. This makes it impossible to assess whether the observed improvements over the two baselines are robust or could be explained by hyperparameter choices or benchmark-specific tuning.
minor comments (1)
  1. [Abstract] Abstract and methods: No description of the training procedure for the policy-value network (e.g., loss functions, data generation, or hyperparameter settings) or any ablation isolating the contribution of the value head is provided.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback highlighting the need for value-head diagnostics and statistical reporting. We address each major comment below and will incorporate the suggested analyses in the revision.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The headline service-rate gains (54.6%/82.1%, 9.9–11.4% over RL, 2.5–11.2% over plain MCTS) rest on the claim that the learned value head supplies sufficiently accurate estimates of final network quality to replace simulator rollouts inside the MCTS tree. No diagnostics of value prediction quality—such as correlation between predicted value and realized service rate on held-out partial networks, calibration plots, or error statistics—are reported anywhere in the manuscript.

    Authors: We agree that explicit diagnostics would strengthen the evidence for the value head's utility. In the revised manuscript we will add a dedicated subsection reporting (i) Pearson/Spearman correlation between value predictions and realized service rates on held-out partial networks, (ii) calibration plots, and (iii) mean absolute error and other error statistics. These will be computed from the publicly released code and data. revision: yes

  2. Referee: [Abstract] Abstract: The reported percentage gains are presented without error bars, confidence intervals, or statistical significance tests across multiple random seeds or demand realizations. This makes it impossible to assess whether the observed improvements over the two baselines are robust or could be explained by hyperparameter choices or benchmark-specific tuning.

    Authors: We acknowledge the limitation. The revised version will rerun all methods (AlphaTransit, RL, and plain MCTS) across at least five random seeds, reporting mean service rates with standard deviations. We will also include paired statistical significance tests (e.g., Wilcoxon) between AlphaTransit and each baseline. Updated tables and abstract will reflect these results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results are empirical comparisons on held-out data

full rationale

The paper reports service-rate gains (54.6%/82.1% on Bloomington under two demand settings) from direct simulation-based evaluation of AlphaTransit against RL-without-search and MCTS-without-guidance baselines. These metrics are measured externally on held-out demand instances and do not reduce, via any equation or self-citation in the provided text, to quantities defined by the fitted network parameters or by construction. The value-network substitution for rollouts is an unverified modeling assumption (more relevant to correctness than circularity), but the derivation chain itself remains self-contained and non-tautological.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that a learned value function can stand in for full simulator rollouts inside MCTS; the paper introduces no new physical entities and treats standard MCTS and neural-network training as background.

free parameters (1)
  • neural network weights and hyperparameters
    Learned from data; number and values not stated in abstract but required for the policy-value network to function.
axioms (1)
  • domain assumption A neural network trained on past route-construction trajectories can generalize to predict final service rate for unseen partial networks.
    Invoked by the decision to replace simulator rollouts with value estimates.

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discussion (0)

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Reference graph

Works this paper leans on

71 extracted references · 9 canonical work pages · 5 internal anchors

  1. [1]

    Khalid Alkilane and Der-Horng Lee. MetroZero: Deep reinforcement learning and Monte Carlo tree search for optimized metro network expansion.IEEE Transactions on Intelligent Transportation Systems, 26(1):810–823, 2025

    2025

  2. [2]

    Surrogate assisted monte carlo tree search in combinatorial optimization.arXiv preprint arXiv:2403.09925, 2024

    Saeid Amiri, Parisa Zehtabi, Danial Dervovic, and Michael Cashmore. Surrogate assisted monte carlo tree search in combinatorial optimization.arXiv preprint arXiv:2403.09925, 2024

    work page arXiv 2024

  3. [3]

    Public transportation ridership update

    American Public Transportation Association. Public transportation ridership update. Policy brief, APTA, 2025

    2025

  4. [4]

    Neural Combinatorial Optimization with Reinforcement Learning

    Irwan Bello, Hieu Pham, Quoc V Le, Mohammad Norouzi, and Samy Bengio. Neural combina- torial optimization with reinforcement learning.arXiv preprint arXiv:1611.09940, 2016

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  5. [5]

    Data-driven transit network design at scale

    Dimitris Bertsimas, Yee Sian Ng, and Julia Yan. Data-driven transit network design at scale. Operations Research, 69(4):1118–1133, 2021

    2021

  6. [6]

    Gtfs schedule dataset.https://bloomingtontransit.com/gtfs/

    Bloomington Transit. Gtfs schedule dataset.https://bloomingtontransit.com/gtfs/

  7. [7]

    How Attentive are Graph Attention Networks?

    Shaked Brody, Uri Alon, and Eran Yahav. How attentive are graph attention networks?arXiv preprint arXiv:2105.14491, 2021

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  8. [8]

    A survey of monte carlo tree search methods.IEEE Transactions on Computational Intelligence and AI in games, 4(1):1–43, 2012

    Cameron B Browne, Edward Powley, Daniel Whitehouse, Simon M Lucas, Peter I Cowling, Philipp Rohlfshagen, Stephen Tavener, Diego Perez, Spyridon Samothrakis, and Simon Colton. A survey of monte carlo tree search methods.IEEE Transactions on Computational Intelligence and AI in games, 4(1):1–43, 2012

    2012

  9. [9]

    Ralph Buehler, John Pucher, and Oliver Dümmler. Verkehrsverbund: The evolution and spread of fully integrated regional public transport in germany, austria, and switzerland.International Journal of Sustainable Transportation, 13(1):36–50, 2019

    2019

  10. [10]

    and Texas Transportation Institute

    Cambridge Systematics, Inc. and Texas Transportation Institute. Traffic congestion and reliabil- ity: Trends and advanced strategies for congestion mitigation. Final Report FHW A-HOP-05-064, Federal Highway Administration, Washington, DC, September 2005

    2005

  11. [11]

    CRC press, 2016

    Avishai Ceder.Public transit planning and operation: Modeling, practice and behavior. CRC press, 2016

    2016

  12. [12]

    A bag of tricks for deep reinforcement learning, 2023

    Jeremiah Coholich. A bag of tricks for deep reinforcement learning, 2023

    2023

  13. [13]

    Efficient selectivity and backup operators in monte-carlo tree search

    Rémi Coulom. Efficient selectivity and backup operators in monte-carlo tree search. In International conference on computers and games, pages 72–83. Springer, 2006

    2006

  14. [14]

    Planning spatial networks with Monte Carlo tree search.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 479(2269):20220383, 2023

    Victor-Alexandru Darvariu, Stephen Hailes, and Mirco Musolesi. Planning spatial networks with Monte Carlo tree search.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 479(2269):20220383, 2023

    2023

  15. [15]

    Optimising public bus transit networks using deep reinforcement learning

    Ahmed Darwish, Momen Khalil, and Karim Badawi. Optimising public bus transit networks using deep reinforcement learning. In2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC), pages 1–7. IEEE, 2020

    2020

  16. [16]

    A survey on the transit network design and frequency setting problem.Public transport, 14(1):155–190, 2022

    Javier Durán-Micco and Pieter Vansteenwegen. A survey on the transit network design and frequency setting problem.Public transport, 14(1):155–190, 2022

    2022

  17. [17]

    The University of Texas at Austin, 2004

    Wei Fan.Optimal transit route network design problem: Algorithms, implementations, and numerical results. The University of Texas at Austin, 2004

    2004

  18. [18]

    Optimal transit route network design problem with variable transit demand: genetic algorithm approach.Journal of transportation engineering, 132(1):40– 51, 2006

    Wei Fan and Randy B Machemehl. Optimal transit route network design problem with variable transit demand: genetic algorithm approach.Journal of transportation engineering, 132(1):40– 51, 2006

    2006

  19. [19]

    Ruiz, Julian Schrittwieser, Grzegorz Swirszcz, et al

    Alhussein Fawzi, Matej Balog, Aja Huang, Thomas Hubert, Bernardino Romera-Paredes, Mohammadamin Barekatain, Alexander Novikov, Francisco J R. Ruiz, Julian Schrittwieser, Grzegorz Swirszcz, et al. Discovering faster matrix multiplication algorithms with reinforcement learning.Nature, 610(7930):47–53, 2022. 11

    2022

  20. [20]

    Setting frequencies on bus routes: Theory and practice

    Peter G Furth and Nigel HM Wilson. Setting frequencies on bus routes: Theory and practice. Transportation Research Record, 818(1981):1–7, 1981

    1981

  21. [21]

    An adaptive scaled network for public transport route optimisation.Public Transport, 11(2):379–412, 2019

    Philipp Heyken Soares, Christine L Mumford, Kwabena Amponsah, and Yong Mao. An adaptive scaled network for public transport route optimisation.Public Transport, 11(2):379–412, 2019

    2019

  22. [22]

    Augmenting transit network design algorithms with deep learning

    Andrew Holliday and Gregory Dudek. Augmenting transit network design algorithms with deep learning. In2023 IEEE 26th International Conference on Intelligent Transportation Systems (ITSC), pages 2343–2350. IEEE, 2023

    2023

  23. [23]

    A neural-evolutionary algorithm for autonomous transit network design

    Andrew Holliday and Gregory Dudek. A neural-evolutionary algorithm for autonomous transit network design. In2024 IEEE International Conference on Robotics and Automation (ICRA), pages 4457–4464. IEEE, 2024

    2024

  24. [24]

    Learning heuristics for transit network design and improvement with deep reinforcement learning.Transportmetrica B: Transport Dynamics, 13(1):2561863, 2025

    Andrew Holliday, Ahmed El-Geneidy, and Gregory Dudek. Learning heuristics for transit network design and improvement with deep reinforcement learning.Transportmetrica B: Transport Dynamics, 13(1):2561863, 2025

    2025

  25. [25]

    The 37 implementation details of proximal policy optimization.The ICLR Blog Track 2023, 2022

    Shengyi Huang, Rousslan Fernand Julien Dossa, Antonin Raffin, Anssi Kanervisto, and Weixun Wang. The 37 implementation details of proximal policy optimization.The ICLR Blog Track 2023, 2022

    2023

  26. [26]

    A closer look at invalid action masking in policy gradient algorithms.arXiv preprint arXiv:2006.14171, 2020

    Shengyi Huang and Santiago Ontañón. A closer look at invalid action masking in policy gradient algorithms.arXiv preprint arXiv:2006.14171, 2020

    work page arXiv 2006

  27. [27]

    Beyond games: a systematic review of neural monte carlo tree search applications.arXiv preprint arXiv:2303.08060, 2023

    Marco Kemmerling, Daniel Lütticke, and Robert H Schmitt. Beyond games: a systematic review of neural monte carlo tree search applications.arXiv preprint arXiv:2303.08060, 2023

    work page arXiv 2023

  28. [28]

    Transit route network design problem

    Konstantinos Kepaptsoglou and Matthew Karlaftis. Transit route network design problem. Journal of transportation engineering, 135(8):491–505, 2009

    2009

  29. [29]

    Attention, learn to solve routing problems! In International Conference on Learning Representations, 2019

    Wouter Kool, Herke van Hoof, and Max Welling. Attention, learn to solve routing problems! In International Conference on Learning Representations, 2019

    2019

  30. [30]

    Pomo: Policy optimization with multiple optima for reinforcement learning.Advances in neural information processing systems, 33:21188–21198, 2020

    Yeong-Dae Kwon, Jinho Choo, Byoungjip Kim, Iljoo Yoon, Youngjune Gwon, and Seungjai Min. Pomo: Policy optimization with multiple optima for reinforcement learning.Advances in neural information processing systems, 33:21188–21198, 2020

    2020

  31. [31]

    The traveling salesman problem: a guided tour of combinatorial optimization

    Eugene L Lawler. The traveling salesman problem: a guided tour of combinatorial optimization. Wiley-Interscience Series in Discrete Mathematics, 1985

    1985

  32. [32]

    A transit network design and frequency setting model with graph neural network and deep reinforcement learning

    Junjun Li, Hao Dong, Xuedong Zhao, Hao Tang, Aimin Yin, and Ruchen Xue. A transit network design and frequency setting model with graph neural network and deep reinforcement learning. InSixth International Conference on Computer Information Science and Application Technology (CISAT 2023), volume 12800, page 128005Y . SPIE, 2023

    2023

  33. [33]

    Microscopic traffic simulation using SUMO

    Pablo Alvarez Lopez, Michael Behrisch, Laura Bieker-Walz, Jakob Erdmann, Yun-Pang Flöt- teröd, Robert Hilbrich, Leonhard Lücken, Johannes Rummel, Peter Wagner, and Evamarie Wießner. Microscopic traffic simulation using SUMO. In2018 21st International Conference on Intelligent Transportation Systems (ITSC), pages 2575–2582. IEEE, November 2018

    2018

  34. [34]

    Evaluation and optimization of urban public transportation networks

    Christoph E Mandl. Evaluation and optimization of urban public transportation networks. European Journal of Operational Research, 5(6):396–404, 1980

    1980

  35. [35]

    Faster sorting algorithms discovered using deep reinforcement learning.Nature, 618(7964):257–263, 2023

    Daniel J Mankowitz, Andrea Michi, Anton Zhernov, Marco Gelmi, Marco Selvi, Cosmin Paduraru, Edouard Leurent, Shariq Iqbal, Jean-Baptiste Lespiau, Alex Ahern, et al. Faster sorting algorithms discovered using deep reinforcement learning.Nature, 618(7964):257–263, 2023

    2023

  36. [36]

    Designing a large-scale public transport network using agent-based microsimulation.Transportation Research Part A: Policy and Practice, 137:1–15, 2020

    Patrick Manser, Henrik Becker, Sebastian Hörl, and Kay W Axhausen. Designing a large-scale public transport network using agent-based microsimulation.Transportation Research Part A: Policy and Practice, 137:1–15, 2020. 12

    2020

  37. [37]

    Summary of travel trends: 2017 national household travel survey

    Nancy McGuckin, Anthony Fucci, et al. Summary of travel trends: 2017 national household travel survey. Technical report, United States. Department of Transportation. Federal Highway Administration, 2018

    2017

  38. [38]

    New heuristic and evolutionary operators for the multi-objective urban transit routing problem

    Christine L Mumford. New heuristic and evolutionary operators for the multi-objective urban transit routing problem. In2013 IEEE congress on evolutionary computation, pages 939–946. IEEE, 2013

    2013

  39. [39]

    Transit network design by genetic algorithm with elitism.Transportation Research Part C: Emerging Technologies, 46:30–45, 2014

    Muhammad Ali Nayeem, Md Khaledur Rahman, and M Sohel Rahman. Transit network design by genetic algorithm with elitism.Transportation Research Part C: Emerging Technologies, 46:30–45, 2014

    2014

  40. [40]

    A simplified car-following theory: a lower order model.Transportation Research Part B: Methodological, 36(3):195–205, 2002

    Gordon Frank Newell. A simplified car-following theory: a lower order model.Transportation Research Part B: Methodological, 36(3):195–205, 2002

    2002

  41. [41]

    Transit network design by bee colony optimization

    Miloš Nikoli´c and Dušan Teodorovi´c. Transit network design by bee colony optimization. Expert Systems with Applications, 40(15):5945–5955, 2013

    2013

  42. [42]

    A simulation-based optimization approach for designing transit networks.Public Transport, 15(2):377–409, 2023

    Obiora A Nnene, Johan W Joubert, and Mark HP Zuidgeest. A simulation-based optimization approach for designing transit networks.Public Transport, 15(2):377–409, 2023

    2023

  43. [43]

    Transit network design problem: a half century of methodological research

    Mahmoud Owais. Transit network design problem: a half century of methodological research. Innovative Infrastructure Solutions, 11(1):3, 2026

    2026

  44. [44]

    Roess, E.S

    R.P. Roess, E.S. Prassas, and W.R. McShane.Traffic Engineering. Pearson, 2011

    2011

  45. [45]

    Multi-armed bandits with episode context.Annals of Mathematics and Artificial Intelligence, 61(3):203–230, 2011

    Christopher D Rosin. Multi-armed bandits with episode context.Annals of Mathematics and Artificial Intelligence, 61(3):203–230, 2011

    2011

  46. [46]

    Planning and optimizing transit lines.arXiv preprint arXiv:2405.10074, 2024

    Marie Schmidt and Anita Schöbel. Planning and optimizing transit lines.arXiv preprint arXiv:2405.10074, 2024

    work page arXiv 2024

  47. [47]

    Mastering Atari, Go, chess and shogi by planning with a learned model.Nature, 588(7839):604–609, 2020

    Julian Schrittwieser, Ioannis Antonoglou, Thomas Hubert, Karen Simonyan, Laurent Sifre, Simon Schmitt, Arthur Guez, Edward Lockhart, Demis Hassabis, Thore Graepel, Timothy Lillicrap, and David Silver. Mastering Atari, Go, chess and shogi by planning with a learned model.Nature, 588(7839):604–609, 2020

    2020

  48. [48]

    High-Dimensional Continuous Control Using Generalized Advantage Estimation

    John Schulman, Philipp Moritz, Sergey Levine, Michael Jordan, and Pieter Abbeel. High- dimensional continuous control using generalized advantage estimation.arXiv preprint arXiv:1506.02438, 2015

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  49. [49]

    Proximal Policy Optimization Algorithms

    John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms.arXiv preprint arXiv:1707.06347, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  50. [50]

    Uxsim: lightweight mesoscopic traffic flow simulator in pure python.Journal of Open Source Software, 10(106):7617, 2025

    Toru Seo. Uxsim: lightweight mesoscopic traffic flow simulator in pure python.Journal of Open Source Software, 10(106):7617, 2025

    2025

  51. [51]

    David Silver, Aja Huang, Chris J. Maddison, Arthur Guez, Laurent Sifre, George van den Driess- che, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, Sander Dieleman, Dominik Grewe, John Nham, Nal Kalchbrenner, Ilya Sutskever, Timothy Lillicrap, Madeleine Leach, Koray Kavukcuoglu, Thore Graepel, and Demis Hassabis. Mastering the...

    2016

  52. [52]

    A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play.Science, 362(6419):1140–1144, 2018

    David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, Timothy Lillicrap, Karen Simonyan, and Demis Hassabis. A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play.Science, 362(6419):1140–1144, 2018

    2018

  53. [53]

    Mastering the game of Go without human knowledge.Nature, 550:354–359, 2017

    David Silver, Julian Schrittwieser, Karen Simonyan, Ioannis Antonoglou, Aja Huang, Arthur Guez, Thomas Hubert, Lucas Baker, Matthew Lai, Adrian Bolton, Yutian Chen, Timothy Lillicrap, Fan Hui, Laurent Sifre, George van den Driessche, Thore Graepel, and Demis Hassabis. Mastering the game of Go without human knowledge.Nature, 550:354–359, 2017

    2017

  54. [54]

    MIT press, 2018

    Richard S Sutton and Andrew G Barto.Reinforcement learning: An introduction. MIT press, 2018. 13

    2018

  55. [55]

    SIAM, 2014

    Paolo Toth and Daniele Vigo.Vehicle routing: problems, methods, and applications. SIAM, 2014

    2014

  56. [56]

    Who’s on board 2019: How to win back america’s transit riders

    TransitCenter. Who’s on board 2019: How to win back america’s transit riders. Technical report, TransitCenter, New York, 2019

    2019

  57. [57]

    Bloomington transit (bt) — operator details

    Transitland. Bloomington transit (bt) — operator details. https://www.transit.land/ operators/o-dnfq-bloomingtontransit

  58. [58]

    World urbanization prospects: The 2018 revision

    United Nations Department of Economic and Social Affairs. World urbanization prospects: The 2018 revision. Technical report, United Nations, 2019

    2018

  59. [59]

    Census Bureau

    U.S. Census Bureau. Tiger/line shapefiles. https://www.census.gov/cgi-bin/geo/ shapefiles/index.php, 2025. Accessed: 2025-10-06

    2025

  60. [60]

    Census Bureau, Center for Economic Studies

    U.S. Census Bureau, Center for Economic Studies. Lehd origin-destination employment statistics (lodes).https://lehd.ces.census.gov/data, 2025. Accessed: 2025-10-06

    2025

  61. [61]

    Graph Attention Networks

    Petar Veliˇckovi´c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. Graph attention networks.arXiv preprint arXiv:1710.10903, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  62. [62]

    An exact solution approach for the bus line planning problem with integrated passenger routing.Journal of Advanced Transportation, 2021(1):6684795, 2021

    Evert Vermeir, Wouter Engelen, Johan Philips, and Pieter Vansteenwegen. An exact solution approach for the bus line planning problem with integrated passenger routing.Journal of Advanced Transportation, 2021(1):6684795, 2021

    2021

  63. [63]

    Pointer networks.Advances in neural information processing systems, 28, 2015

    Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks.Advances in neural information processing systems, 28, 2015

    2015

  64. [64]

    John Wiley & Sons, 2007

    Vukan R Vuchic.Urban transit systems and technology. John Wiley & Sons, 2007

    2007

  65. [65]

    John Wiley & Sons, 2017

    Vukan R Vuchic.Urban transit: operations, planning, and economics. John Wiley & Sons, 2017

    2017

  66. [66]

    Pareto-optimal transit route planning with multi-objective monte-carlo tree search.IEEE Transactions on Intelligent Transportation Systems, 22(2):1185–1195, 2021

    Di Weng, Ran Chen, Jianhui Zhang, Jie Bao, Yu Zheng, and Yingcai Wu. Pareto-optimal transit route planning with multi-objective monte-carlo tree search.IEEE Transactions on Intelligent Transportation Systems, 22(2):1185–1195, 2021

    2021

  67. [67]

    Promoting livable cities by investing in urban mobility

    World Bank. Promoting livable cities by investing in urban mobility. Results brief, World Bank Group, 2024

    2024

  68. [68]

    Representation learning on graphs with jumping knowledge networks

    Keyulu Xu, Chengtao Li, Yonglong Tian, Tomohiro Sonobe, Ken-ichi Kawarabayashi, and Stefanie Jegelka. Representation learning on graphs with jumping knowledge networks. In International Conference on Machine Learning (ICML), 2018

    2018

  69. [69]

    Graph pointer neural networks

    Tianmeng Yang, Yujing Wang, Zhihan Yue, Yaming Yang, Yunhai Tong, and Jing Bai. Graph pointer neural networks. InProceedings of the AAAI conference on artificial intelligence, volume 36, pages 8832–8839, 2022

    2022

  70. [70]

    A reinforcement learning approach for bus network design and frequency setting optimisation.Public Transport, 15(2):503–534, 2023

    Sunhyung Yoo, Jinwoo Brian Lee, and Hoon Han. A reinforcement learning approach for bus network design and frequency setting optimisation.Public Transport, 15(2):503–534, 2023

    2023

  71. [71]

    Simulated annealing–genetic algorithm for transit network optimization.Journal of Computing in Civil Engineering, 20(1):57–68, 2006

    Fang Zhao and Xiaogang Zeng. Simulated annealing–genetic algorithm for transit network optimization.Journal of Computing in Civil Engineering, 20(1):57–68, 2006. 14 A Size of the search space The scope of the design problem is to choose K= 16 routes, each visiting 14 distinct nodes, on the Bloomington network graph G= (V, E) . Computing the exact size of ...

    2006