Annals of Operations Research

, Volume 249, Issue 1–2, pp 119–139 | Cite as

On the minimization of traffic congestion in road networks with tolls

  • F. Stefanello
  • L. S. Buriol
  • M. J. Hirsch
  • P. M. Pardalos
  • T. Querido
  • M. G. C. Resende
  • M. Ritt


Population growth and the massive production of automotive vehicles have lead to the increase of traffic congestion problems. Traffic congestion today is not limited to large metropolitan areas, but is observed even in medium-sized cities and highways. Traffic engineering can contribute to lessen these problems. One possibility, explored in this paper, is to assign tolls to streets and roads, with the objective of inducing drivers to take alternative routes, and thus better distribute traffic across the road network. This assignment problem is often referred to as the tollbooth problem and it is NP-hard. In this paper, we propose mathematical formulations for two versions of the tollbooth problem that use piecewise-linear functions to approximate congestion cost. We also apply a biased random-key genetic algorithm on a set of real-world instances, analyzing solutions when computing shortest paths according to two different weight functions. Experimental results show that the proposed piecewise-linear functions approximate the original convex function quite well and that the biased random-key genetic algorithm produces high-quality solutions.


Combinatorial optimization Transportation networks  Genetic algorithms Tollbooth problem 



This work has been partially supported by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), FAPERGS (Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul), and PRH PB-217—Petrobras S.A., Brazil. The work of Mauricio G. C. Resende was done when he was employed at AT&T Labs Research, in Middletown, New Jersey, USA.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • F. Stefanello
    • 1
  • L. S. Buriol
    • 1
  • M. J. Hirsch
    • 2
  • P. M. Pardalos
    • 3
  • T. Querido
    • 4
  • M. G. C. Resende
    • 5
  • M. Ritt
    • 1
  1. 1.Instituto de InformáticaUniversidade Federal do Rio Grande do SulPorto AlegreBrazil
  2. 2.ISEA TEKMaitlandUSA
  3. 3.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  4. 4.Linear Options ConsultingGainesvilleUSA
  5. 5.Mathematical Optimization and Planning Amazon.comInc.SeattleUSA

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