Column generation for the equilibrium route-flow traffic assignment problem

• Published in: Annals of mathematics and artificial intelligence Vol. 90; no. 7-9; pp. 697 - 713
• Main Author: Krylatov, Alexander
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.09.2022; Springer; Springer Nature B.V
• Subjects: Algorithms; Analysis; Artificial Intelligence; Assignment problem; Complex Systems; Computer Science; Equilibrium; Mathematics; Operations research; Roads & highways; Time functions; Traffic assignment; Traffic flow; Traffic management; Traffic models; Travel time; Uniqueness; Column generation; 90C30; 90C35; 90C33; Nonlinear optimization; Traffic assignment problem; User-equilibrium of Wardrop
• ISSN: 1012-2443; 1573-7470
• DOI: 10.1007/s10472-020-09725-z

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.