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A penalized nonlinear ADMM algorithm applied to the multi-constrained traffic assignment problem

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Abstract

We formulate the Multi-Constrained Dynamic Traffic Assignment (DTA) problem as an instance of the nonlinear composite problem. To solve the problem, this paper introduces then the penalized nonlinear alternating direction method of multipliers (ADMM), a numerical algorithm that combines the nonlinear ADMM algorithm with the external penalty method. Numerical results are then presented, analyzed and compared against those obtained by applying the Reformulation-Linearization Technique (RLT)-based convex relaxation method together with piecewise linear approximation of the objective function.

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Data availability

The network topology datasets generated during and/or analyzed during the current study are available in the SNDlib repository [20], http://sndlib.zib.de/problems.overview.action. The demand and path datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. 3nLab & Belgium Research Center (BeRC), Huawei, 3001, Leuven, Belgium

    Dimitri Papadimitriou

  2. Belgium Research Center (BeRC), Huawei, 3001, Leuven, Belgium

    Bằng Công Vũ

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  1. Dimitri Papadimitriou
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  2. Bằng Công Vũ
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Correspondence to Dimitri Papadimitriou.

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Papadimitriou, D., Vũ, B.C. A penalized nonlinear ADMM algorithm applied to the multi-constrained traffic assignment problem. Numer Algor 92, 2219–2242 (2023). https://doi.org/10.1007/s11075-022-01384-x

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  • DOI: https://doi.org/10.1007/s11075-022-01384-x

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