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On the Application of Saddle-Point Methods for Combined Equilibrium Transportation Models

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Mathematical Optimization Theory and Operations Research (MOTOR 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14766))

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Abstract

Travel demand modeling is an essential tool in urban planning and transportation system management. Existing practically efficient algorithms for solving multistage travel demand problems are variations of the heuristic sequential procedure. We propose a novel approach that applies saddle-point methods to a combined convex optimization formulation of the problem. Unlike all previous methods, our algorithm does not require costly shortest-paths calculations, and can be seamlessly scaled on GPUs. We show that in some cases it drastically outperforms the sequential procedures.

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Notes

  1. 1.

    https://github.com/niquepolice/mmo_tm/tree/sp-combined.

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Acknowledgments

The work of Yarmoshik D. is supported by the Ministry of Science and Higher Education of the Russian Federation (Goszadaniye) No. 075-03-2024-117, project No. FSMG-2024-0025. The work of Persiianov M. is supported by the annual income of the Endowment Fund of Moscow Institute of Physics and Technology (target capital no. 5 for the development of artificial intelligence and machine learning, https://fund.mipt.ru/capitals/ck5/).

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    Demyan Yarmoshik & Michael Persiianov

  2. Institute for Information Transmission Problems, Moscow, Russia

    Demyan Yarmoshik & Michael Persiianov

  3. The Skolkovo Institute of Science and Technology, Moscow, Russia

    Michael Persiianov

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  1. Demyan Yarmoshik
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  2. Michael Persiianov
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Correspondence to Demyan Yarmoshik .

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Editors and Affiliations

  1. Dostoevsky Omsk State University, Omsk, Russia

    Anton Eremeev

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  4. Karelia Research Center of RAS, Petrozavodsk, Russia

    Vladimir Mazalov

  5. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Yarmoshik, D., Persiianov, M. (2024). On the Application of Saddle-Point Methods for Combined Equilibrium Transportation Models. In: Eremeev, A., Khachay, M., Kochetov, Y., Mazalov, V., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2024. Lecture Notes in Computer Science, vol 14766. Springer, Cham. https://doi.org/10.1007/978-3-031-62792-7_29

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