Primal-dual gradient methods for searching network equilibria in combined models with nested choice structure and capacity constraints

Meruza Kubentayeva (), Demyan Yarmoshik, Mikhail Persiianov, Alexey Kroshnin, Ekaterina Kotliarova, Nazarii Tupitsa, Dmitry Pasechnyuk, Alexander Gasnikov, Vladimir Shvetsov, Leonid Baryshev and Alexey Shurupov
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Meruza Kubentayeva: Moscow Institute of Physics and Technology
Demyan Yarmoshik: Moscow Institute of Physics and Technology
Mikhail Persiianov: Moscow Institute of Physics and Technology
Alexey Kroshnin: Institute for Information Transmission Problems RAS
Ekaterina Kotliarova: Moscow Institute of Physics and Technology
Nazarii Tupitsa: Moscow Institute of Physics and Technology
Dmitry Pasechnyuk: Moscow Institute of Physics and Technology
Alexander Gasnikov: Moscow Institute of Physics and Technology
Vladimir Shvetsov: Moscow Institute of Physics and Technology
Leonid Baryshev: Russian University of Transport
Alexey Shurupov: Russian University of Transport

Computational Management Science, 2024, vol. 21, issue 1, No 15, 33 pages

Abstract: Abstract We consider a network equilibrium model (i.e. a combined model), which was proposed as an alternative to the classic four-step approach for travel forecasting in transportation networks. This model can be formulated as a convex minimization program. We extend the combined model to the case of the stable dynamics model in the traffic assignment stage, which imposes strict capacity constraints in the network. We propose a way to solve corresponding dual optimization problems with accelerated gradient methods and give theoretical guarantees of their convergence. We conducted numerical experiments with considered optimization methods on Moscow and Berlin networks.

Keywords: Forecasting; Combined model; Trip distribution; Traffic assignment; Capacity constraints; Gradient method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10287-023-00494-8

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