Bilevel Tolls Optimization Problem with Nonlinear Costs: A Heuristic Solution Method

By : José Guadalupe Flores- Muñiz, Vitaliy Kalashnikov, Viacheslav Kalashnikov, Nataliya Kalashnykova

Page No: 193-219

Abstract: 
In the Tolls Optimization Problem’s setting, a public or private firm assigns a series of fees on some of the roads available in a highway network. This fee, known as a toll, must be paid by the drivers that want to go through these roads. The problems of this sort are usually addressed as a bilevel single-leader-multiple-follower game where the private firm which assigns the tolls on certain roads of the highways takes the role of the leader and the drivers traveling along the roads are the followers. Certain heuristics algorithms to solve these kinds of problems have been proposed before, however, because of the complexity of bilevel problems, most of the previous works deal only with bilevel linear formulations. In this work, we extend these previous works by considering a nonlinear bilevel formulation for the Tolls Optimization Problem (TOP) and present an efficient heuristic algorithm for its solution.

Authors :
José Guadalupe Flores- Muñiz
Universidad Autónoma de Nuevo León (UANL)  Av. Universidad S/N, Ciudad Universitaria  San Nicolás de los Garza, Nuevo León, 66455, Mexico.

Vitaliy Kalashnikov
Department of Economics Universidad Autónoma de Nuevo León (UANL) Campus Mederos, Av. Lázaro Cárdenas 4600 Monterrey, Nuevo León, 64930, Mexico.

Viacheslav Kalashnikov
Instituto Tecnológico y de Estudios Superiores de Monterrey (ITESM) Campus Monterrey, Ave. Eugenio Garza Sada 2501 Sur  Monterrey, Nuevo León, 64849, Mexico.

Nataliya Kalashnykova
Universidad Autónoma de Nuevo León (UANL)  Av. Universidad S/N, Ciudad Universitaria  San Nicolás de los Garza, Nuevo León, 66455, Mexico.
 

DOI: https://doi.org/10.32381/JCISS.2020.45.1-4.4