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Solving multi-objective traffic assignment

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Abstract

Traffic assignment is a key component in transport planning models. It models travel behaviour in terms of route choice. This is essential to accurately forecast travel demand and most importantly to enable the correct assessment of the benefits of changes in transport policies and infrastructure developments. The route choice of travellers may be influenced by multiple objectives, for example travel time but also travel associated toll costs. Here, travellers may avoid a fast route because of toll costs associated with it. We explicitly distinguish those functions as separate route choice objectives. This leads to the concept of multi-objective traffic assignment (MTA). We discuss the concept of MTA, and develop heuristic solution methods to obtain equilibrium solutions of MTA and present some computational results.

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References

  • Beckmann, M., McGuire, C. B., & Winsten, C. B. (1956). Studies in the economics of transportation. New Haven: Yale University Press.

    Google Scholar 

  • Bernstein, D., & Gabriel, S. A. (1997). Solving the nonadditive traffic equilibrium problem. In P. M. Pardalos, D. W. Hearn, & W. W. Hager (Eds.), Network optimization (pp. 72–102). Berlin: Springer.

    Chapter  Google Scholar 

  • Bureau of Public Roads (1964). Traffic assignment manual. Washington: U.S. Department of Commerce, Urban Planning Division.

    Google Scholar 

  • Chen, G. Y., & Yen, N. D. (1993). On the variational inequality model for network equilibrium (Technical Report 3.196 (724)). Department of Mathematics, University of Pisa.

  • Chen, G. Y., Goh, C. J., & Yang, X. Q. (1999). Vector network equilibrium problems and nonlinear scalarization methods. Mathematical Methods of Operations Research, 49, 239–253.

    Google Scholar 

  • Clímaco, J. C. N., & Martins, E. Q. V. (1982). A bicriterion shortest path problem. European Journal of Operational Research, 11, 399–404.

    Article  Google Scholar 

  • Dafermos, S. (1983). A multicriteria route-mode choice traffic equilibrium model. Bulletin of the Greek Mathematical Society, 24, 13–32.

    Google Scholar 

  • Dafermos, S., & Sparrow, F. T. (1969). The traffic assignment problem for a general network. Journal of Research of the National Bureau of Standards. B, Mathematical Sciences, 73B, 91–118.

    Article  Google Scholar 

  • Dearnaley, M. (June 2010). Toll-dodger faces $26,500 in fines. New Zealand Herald. URL http://www.nzherald.co.nz/nz/news/article.cfm?c_id=1&objectid=10648815. Last visited 10/01/2011.

  • Dial, R. B. (1979). A model and algorithm for multicriteria route-mode choice. Transportation Research, 13B, 311–316.

    Article  Google Scholar 

  • Dial, R. B. (1996). Bicriterion traffic assignment: basic theory and elementary algorithms. Transportation Science, 30, 93–111.

    Article  Google Scholar 

  • Dial, R. B. (1997). Bicriterion traffic assignment: efficient algorithms plus examples. Transportation Research B, 31, 357–379.

    Article  Google Scholar 

  • Dial, R. B. (1999a). Network-optimized road pricing: Part I: A parable and a model. Operations Research, 47, 54–64.

    Article  Google Scholar 

  • Dial, R. B. (1999b). Network-optimized road pricing: Part II: Algorithms and examples. Operations Research, 47, 327–336.

    Article  Google Scholar 

  • Eliasson, J. (2000). Transport and location analysis. PhD thesis, Kungliga Tekniska Hogskolan (Sweden). Chapter “The use of average values of time in road pricing. A note on a common misconception”.

  • Gabriel, S. A., & Bernstein, D. (1997). The traffic equilibrium problem with nonadditive path costs. Transportation Science, 31, 337–348.

    Article  Google Scholar 

  • Goh, C. J., & Yang, X. Q. (1999). Vector equilibrium problem and vector optimization. European Journal of Operational Research, 116, 615–628.

    Article  Google Scholar 

  • Guerriero, F., & Musmanno, R. (2001). Label correcting methods to solve multicriteria shortest path problems. Journal of Optimization Theory and Applications, 111(3), 589–613.

    Article  Google Scholar 

  • Huang, H.-J., & Li, Z.-C. (2007). A multiclass, multicriteria logit-based traffic equilibrium assignment model under ATIS. European Journal of Operational Research, 176, 1464–1477.

    Article  Google Scholar 

  • Khan, A., & Raciti, F. (2005). On time dependent vector equilibrium problems. In F. Giannessi & A. Maugeri (Eds.), Variational analysis and applications (pp. 579–587). Berlin: Springer.

    Chapter  Google Scholar 

  • Larsson, T., Lindberg, P. O., Patriksson, M., & Rydergren, C. (2002). On traffic equilibrium models with a nonlinear time/money relation. In M. Patriksson & M. Labbé (Eds.), Transportation planning (pp. 19–31). Norwell: Kluwer Academic.

    Google Scholar 

  • Leurent, F. (1993). Cost versus time equilibrium over a network. European Journal of Operational Research, 71, 205–221.

    Article  Google Scholar 

  • Leurent, F. (1995). The practice of dual criteria assignment model with continuously distributed values-of-time. In 23rd European transport forum, 11–15 September 1995, proceedings of seminar E.

    Google Scholar 

  • Leurent, F. (1996). The theory and practice of a dual criteria assignment model with a continuously distributed value-of-time. In Transportation and traffic theory: proceedings of the 13th international symposium on transportation and traffic theory, Lyon, France, 24–26 July 1996.

    Google Scholar 

  • Leurent, F. (1998). Les valeurs du temps des automobilistes à Marseille en 1995. Recherche, Transports, Sécurité, 60, 19–38 (in French).

    Google Scholar 

  • Leurent, F. (2001). Route choice and urban tolling: the Prado-Carénage tunnel in Marseille. Recherche, Transports, Sécurité, 71, 21–23.

    Article  Google Scholar 

  • Leventhal, T., Nemhauser, G., & Trotter, J. (1973). A column generation algorithm for optimal traffic assignment. Transportation Science, 7, 168–176.

    Article  Google Scholar 

  • Li, S. J., Teo, K. L., & Yang, X. Q. (2007). Vector equilibrium problems with elastic demands and capacity constraints. Journal of Global Optimization, 37, 647–660.

    Article  Google Scholar 

  • Li, S. J., Teo, K. L., & Yang, X. Q. (2008). A remark on a standard and linear vector network equilibrium problem with capacity constraints. European Journal of Operational Research, 184, 13–23.

    Article  Google Scholar 

  • Marcotte, P. (1995). Advantages and drawbacks of variational inequalities formulations. In F. Gianessi & A. Maugeri (Eds.), Variational inequalities and network equilibrium problems (pp. 179–194). New York: Plenum.

    Google Scholar 

  • Marcotte, P., & Zhu, D. L. (1997). Equilibria with infinitely many differentiated classes of customers. In M. J. Ferris & J.-S. Pang (Eds.), Complementarity and variational problems—state of the art, proceedings of the international conference on complementarity problems. Philadelphia: SIAM.

    Google Scholar 

  • McNally, M. G. (2000). The four-step model. In D. A. Hensher & K. J. Button (Eds.), Handbook of transport modelling (Vol. 1, pp. 35–52). Elmsford: Pergamon.

    Google Scholar 

  • Mote, J., Murthy, I., & Olson, D. L. (1991). A parametric approach to solving bicriterion shortest path problems. European Journal of Operational Research, 53, 81–92.

    Article  Google Scholar 

  • Nagurney, A. (1993). Advances in computational economics: Vol. 1. Network economics a variational inequality approach. Norwell: Kluwer Academic.

    Book  Google Scholar 

  • Nagurney, A. (2000). A multiclass, multicriteria traffic network equilibrium model. Mathematical and Computer Modelling, 32, 393–411.

    Article  Google Scholar 

  • Nagurney, A., & Dong, J. (2002). A multiclass, multicriteria traffic network equilibrium model with elastic demand. Transportation Research B, 36, 445–469.

    Article  Google Scholar 

  • Nagurney, A., Dong, J., & Mokhtarian, P. L. (2001). Teleshopping versus shopping: a multicriteria network equilibrium framework. Mathematical and Computer Modelling, 34, 783–798.

    Article  Google Scholar 

  • Nagurney, A., Dong, J., & Mokhtarian, P. L. (2002a). Multicriteria network equilibrium modeling with variable weights for decision-making in the information age with applications to telecommuting and teleshopping. Journal of Economic Dynamics & Control, 26, 1629–1650.

    Article  Google Scholar 

  • Nagurney, A., Dong, J., & Mokhtarian, P. L. (2002b). Traffic network equilibrium and the environment. A multicriteria decision-making perspective. In E. J. Kontoghiorghes, B. Rustem, & S. Siokos (Eds.), Computational methods in decision-making, economics and finance (pp. 501–523). Norwell: Kluwer Academic.

    Chapter  Google Scholar 

  • NZTA. Benefits of the toll road. URL http://www.tollroad.govt.nz/About/Benefits. Last visited 10/01/2011.

  • Ortúzar, J. de D., & Willumsen, L. G. (2002). Modelling transport (3rd ed.). New York: Wiley.

    Google Scholar 

  • Powell, W. B., & Sheffi, Y. (1982). The convergence of equilibrium algorithms with predetermined step sizes. Transportation Science, 16, 45–55.

    Article  Google Scholar 

  • Raith, A., & Ehrgott, M. (2009). A comparison of solution strategies for biobjective shortest path problems. Computers & Operations Research, 36, 1299–1331. doi:10.1016/j.cor.2008.02.002.

    Article  Google Scholar 

  • Raith, A., & Ehrgott, M. (2011). On vector equilibria, vector optimization and vector variational inequalities. Journal of Multi-Criteria Decision Analysis, 18, 39–54.

    Article  Google Scholar 

  • Schneider, M. (1968). Urban development models. Chapter “Access and land development” (pp. 164–177). Highway Research Board Special Report.

  • Sheffi, Y. (1985). Urban transportation networks: equilibrium analysis with mathematical programming methods. New York: Prentice Hall.

    Google Scholar 

  • Wang, J. Y. T., Raith, A., & Ehrgott, M. (2010). Tolling analysis with biobjective traffic assignment. In M. Ehrgott, B. Naujoks, T. J. Stewart, & J. Wallenius (Eds.), Lecture notes in economics and mathematical systems: Vol. 634. Multiple criteria decision making for sustainable energy and transportation systems, proceedings of the 19th international conference on multiple criteria decision making, Auckland, New Zealand, 7th–12th January 2008 (pp. 117–123).

    Chapter  Google Scholar 

  • Wardrop, J. G. (1952). Some theoretical aspects of road traffic research. Proceedings of the Institution of Civil Engineers. Part 2. Research and Theory, 1, 325–378.

    Google Scholar 

  • Yang, X. Q., & Goh, C. J. (1997). On vector variational inequalities: applications to vector equilibria. Journal of Optimization Theory and Applications, 95, 431–443.

    Article  Google Scholar 

  • Yang, X. Q., & Goh, C. J. (2000). Vector variational inequalities, vector equilibrium flow and vector optimization. In F. Gianessi (Ed.), Vector variational inequalities and vector equilibria. Norwell: Kluwer Academic.

    Google Scholar 

  • Yang, X. Q., & Yu, H. (2005). Vector variational inequalities and dynamic traffic equilibria. In F. Giannessi & A. Maugeri (Eds.), Variational analysis and applications (pp. 1141–1157). Berlin: Springer.

    Chapter  Google Scholar 

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Acknowledgements

This research was partially supported by Marsden grant 9075 362506.

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Raith, A., Wang, J.Y.T., Ehrgott, M. et al. Solving multi-objective traffic assignment. Ann Oper Res 222, 483–516 (2014). https://doi.org/10.1007/s10479-012-1284-1

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