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Column generation for the equilibrium route-flow traffic assignment problem

Abstract

Today efficient traffic management seems to be impossible without the support of the artificial intelligence systems based on mathematical models of traffic flow assignment since a modern road network is a large-scale system with huge amounts of elements. The present paper is devoted to the route-flow traffic assignment problem, which solution is the most valuable from decision-making perspectives. The paper aims to fill the gap in the relation between the column generation process and the uniqueness of the equilibrium route-flow traffic assignment pattern. The independence of routes is showed to be highly significant when travel time functions are arc-additive. Indeed, on the one hand, the independence of routes is proved to guarantee the uniqueness of the equilibrium route-flow traffic assignment pattern. On the other hand, the independence of routes appears to be crucial for column generation when solving the route-flow traffic assignment problem since the equilibrium travel time is proven to be decreased only by adding independent candidate route. Obtained results contribute to the development of algorithms for route-flow traffic assignment based on travel times equilibration procedure.

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Acknowledgments

The work was jointly supported by a grant from the Russian Science Foundation (No. 19-71-10012 Multi-agent systems development for automatic remote control of traffic flows in congested urban road networks).

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Correspondence to Alexander Krylatov.

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Krylatov, A. Column generation for the equilibrium route-flow traffic assignment problem. Ann Math Artif Intell (2021). https://doi.org/10.1007/s10472-020-09725-z

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  • DOI: https://doi.org/10.1007/s10472-020-09725-z

Keywords

  • Nonlinear optimization
  • Column generation
  • Traffic assignment problem
  • User-equilibrium of Wardrop

Mathematics Subject Classification (2010)

  • 90C30
  • 90C33
  • 90C35