TY - JOUR

T1 - Column generation for the equilibrium route-flow traffic assignment problem

AU - Krylatov, Alexander

N1 - Funding Information: 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). Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/1/8

Y1 - 2021/1/8

N2 - 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.

AB - 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.

KW - Column generation

KW - Nonlinear optimization

KW - Traffic assignment problem

KW - User-equilibrium of Wardrop

KW - DECOMPOSITION

KW - CONVERGENT

UR - http://www.scopus.com/inward/record.url?scp=85099262176&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/61c21d18-5d9c-3cb8-bee1-0b916632fb91/

U2 - 10.1007/s10472-020-09725-z

DO - 10.1007/s10472-020-09725-z

M3 - Article

AN - SCOPUS:85099262176

JO - Annals of Mathematics and Artificial Intelligence

JF - Annals of Mathematics and Artificial Intelligence

SN - 1012-2443

ER -