Abstract
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.
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Notes
We use the term tollbooth to refer to both traditional tollbooths as well as to sensors that read radio-frequency identification (RFID) tags from vehicles.
References
Bai, L., Hearn, D. W., & Lawphongpanich, S. (2004). Decomposition techniques for the minimum toll revenue problem. Networks, 44(2), 142–150. doi:10.1002/net.20024.
Bai, L., Hearn, D. W., & Lawphongpanich, S. (2010). A heuristic method for the minimum toll booth problem. Journal of Global Optimization, 48, 533–548. doi:10.1007/s10898-010-9527-7. ISSN 0925-5001.
Bar-Gera, H. (2013). Transportation networks test problems. http://www.bgu.ac.il/~bargera/tntp
Bean, J. C. (1994). Genetic algorithms and random keys for sequencing and optimization. ORSA Journal on Computing, 6, 154–160.
Beckmann, M. J., McGuire, C. B., & Winsten, C. B. (1956). Studies in the economics of transportation. New Haven, CT: Yale University Press.
Broström, P., & Holmberg, K. (2006). Multiobjective design of survivable ip networks. Annals of Operations Research, 147, 235–253. doi:10.1007/s10479-006-0067-y. ISSN 0254-5330.
Bureau of Public Roads. (1964). Bureau of public roads: Traffic assignment manual. US Department of Commerce, Urban Planning Division.
Buriol, L. S., Resende, M. G. C., & Thorup, M. (2008). Speeding up dynamic shortest-path algorithms. INFORMS Journal on Computing, 20, 191–204.
Buriol, L. S., Hirsch, M. H., Pardalos, P. M., Querido, T., Resende, M. G. C., & Ritt, M. (2010). A biased random-key genetic algorithm for road congestion minimization. Optimization Letters, 4(619–633), 1862. doi:10.1007/s11590-010-0226-6. ISSN-4472.
Dial, R. B. (1999a). Minimal-revenue congestion pricing part II: An efficient algorithm for the general case. Transportation Research Part B, 34, 645–665.
Dial, R. B. (1999b). Minimal-revenue congestion pricing part I: A fast algorithm for the single origin case. Transportation Research Part B, 33, 189–202.
Ekström, J., Sumalee, A., & Lo, H. K. (2012). Optimizing toll locations and levels using a mixed integer linear approximation approach. Transportation Research Part B: Methodological, 46(7):834–854. doi:10.1016/j.trb.2012.02.006, http://www.sciencedirect.com/science/article/pii/S0191261512000318. ISSN 0191-2615.
Fortz, B., & Thorup, M. (2004). Increasing internet capacity using local search. Computational Optimization and Applications, 29(1), 189–202.
Gonçalves, J. F., & Resende, M. G. C. (2011). Biased random-key genetic algorithms for combinatorial optimization. Journal of Heuristics, 17, 487–525.
Gonçalves, J. F., Resende, M. G. C., & Toso, R. F. (2014). An experimental comparison of biased and unbiased random-key genetic algorithms. Pesquisa Operacional, 34, 143–164.
Hearn, D. W., & Ramana, M. V. (1998). Solving congestion toll pricing models. Equilibrium and Advanced Transportation Modeling, 109–124. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.141.4999
Hearn, D. W., & Yildirim, M. B. (2002). A toll pricing framework for traffic assignment problems with elastic demand. In Transportation and network analysis: Current trends. Miscellanea in honor of Michael Florian (p. 149). Dordrecht: Kluwer.
Schrank, D., Lomax, T., & Eisele, B. (2011). Urban mobility report. Technical report, Texas Transportation Institute. http://mobility.tamu.edu/files/2011/09/congestion-cost.pdf
Spears, W. M., & DeJong, K. A. (1991) On the virtues of parameterized uniform crossover. In Proceedings of the fourth international conference on genetic algorithms (pp. 230–236).
Tsekeris, T., & Voß, S. (2009). Design and evaluation of road pricing: State-of-the-art and methodological advances. Netnomics, 10, 5–52. doi:10.1007/s11066-008-9024-z. ISSN 1385-9587.
Wardrop, J. G. (1952). Some theoretical aspects of road traffic research. Proceedings of the Institution of Civil Engineers, Part II, 1, 325–378.
Wen, W. (2008). A dynamic and automatic traffic light control expert system for solving the road congestion problem. Expert Systems with Applications, 34(4), 2370–238. doi:10.1016/j.eswa.2007.03.007. http://www.sciencedirect.com/science/article/pii/S09574174070013031. ISSN 0957-4174.
Yang, H., & Zhang, X. (2003). Optimal toll design in second-best link-based congestion pricing. Transportation Research Record: Journal of the Transportation Research Board, 1857(1), 85–92. doi:10.3141/1857-10.
Acknowledgments
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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Stefanello, F., Buriol, L.S., Hirsch, M.J. et al. On the minimization of traffic congestion in road networks with tolls. Ann Oper Res 249, 119–139 (2017). https://doi.org/10.1007/s10479-015-1800-1
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DOI: https://doi.org/10.1007/s10479-015-1800-1