A Scatter Search Algorithm for Solving a Bilevel Optimization Model for Determining Highway Tolls
José Luis González Velarde1, José-Fernando Camacho-Vallejo2 and Gabriel Pinto Serrano1
1 Tecnológico de Monterrey, México. gonzalez.velarde@itesm.mx, gabrielpinto_s@hotmail.com
2 Universidad Autónoma de Nuevo León, Facultad de Ciencias Físico-Matemáticas, México. jose.camachovl@uanl.edu.mx
Corresponding author is José Fernando Camacho Vallejo.
]]>Article received on 27/11/2013.
Accepted on 08/11/2014.
Abstract
The problem of determining optimal tolls established on a subset of arcs in a multicommodity capacitated transportation network is presented. The problem is formulated as a bilevel optimization problem where the upper level consists of an administrator who establishes tolls in some arcs of a network, while the lower level is represented by a group of users who travel along the shortest paths with respect to the travel cost. The objective is not only to increase the tolls, but also to maintain an optimal flow on the arcs of the network in order to maximize the leader's profit. If the leader sets very high toll values, the followers will be discouraged from using the tolled arcs, so the profit obtained from that decision is not going to be convenient for the leader. A methodology to solve this problem using optimization software at the lower level and the metaheuristic Scatter Search at the upper level is proposed.
Keywords: Bilevel programming, scatter search, toll optimization problem.
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]]> Acknowledgements
This research has been supported by Tecnológico de Monterrey-Research Group in Industrial Engineering and Numerical Methods 0822B01006, the Mexican National Council for Science and Technology (CONACyT) through grant SEP-CONACyT CB-2011-01-166397 and the Secretary of Public Education (SEP) within the Consolidation of the Academic Groups Program with the project PROMEP/103.5/12/4953 and the UANL within the PAICYT support for the project CE960-11. The authors also gratefully acknowledge the comments and suggestions of the reviewers.
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