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Congested O-D Trip Demand Adjustment Problem: Bilevel Programming Formulation and Optimality Conditions

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Multilevel Optimization: Algorithms and Applications

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 20))

Abstract

The problem of adjusting (or estimating) an origin-destination (O-D) matrix by using observed flows on the links of a congested traffic network, which we denote DAP,is considered in this paper. After reviewing the previous contributions made in stating models and development solution algorithms for this problem, a nonlinear bilevel programming formulation is proposed to model the DAP. The existence of solutions is established under relatively mild assumptions on the link cost functions. The property of the continuous dependence of equilibrium link flows on the demand is demonstrated under a fairly weaker condition. By using the general bilevel programming theory, the DAP is reformulated as a single-level like optimization problem, where the marginal function of the lower level equilibrium problem is used explicitly in a constraint. The gradient function of the implicit marginal function is derived in terms of the link cost mapping and the link proportions in an equilibrium state. Necessary optimality conditions for the DAP are derived based on the gradient information of the marginal function, of which the significance and application for the DAP are discussed as well.

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Author information

Authors and Affiliations

  1. Centre de recherche surles transports, Université de Montréal, Montréal, Québec, Canada, H3C 3J7

    Yang Chen & Michael Florian

Authors
  1. Yang Chen
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  2. Michael Florian
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Editor information

Editors and Affiliations

  1. Division of Optimization, Department of Mathematics, Linköping Institute of Technology, Linköping, Sweden

    Athanasios Migdalas  & Peter Värbrand  & 

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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© 1998 Kluwer Academic Publishers

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Chen, Y., Florian, M. (1998). Congested O-D Trip Demand Adjustment Problem: Bilevel Programming Formulation and Optimality Conditions. In: Migdalas, A., Pardalos, P.M., Värbrand, P. (eds) Multilevel Optimization: Algorithms and Applications. Nonconvex Optimization and Its Applications, vol 20. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0307-7_1

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  • DOI: https://doi.org/10.1007/978-1-4613-0307-7_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7989-8

  • Online ISBN: 978-1-4613-0307-7

  • eBook Packages: Springer Book Archive

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