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Turning restriction design in traffic networks with a budget constraint

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Abstract

The restriction (prohibition) of certain turns at intersections is a very common task employed by the managers of urban traffic networks. Surprisingly, this approach has received little attention in the research literature. The turning restriction design problem (TRDP) involves finding a set of turning restrictions at intersections to promote flow in a congested urban traffic network. This article uses a successive linear approximation (SLA) method for identifying approximate solutions to a nonlinear model of the TRDP. It aims to adjust the current turning restriction regime in a given network in order to minimize total user travel cost when route choice is driven by user equilibrium principles. Novel features of the method include the facts that it is based on link capacity-based arc travel costs and there is a budget constraint on the total cost of all turning restriction alterations. It has been tested using standard network examples from the literature. One of the tests utilized a multi-start approach which improved the solutions produced by the SLA method. The method was also employed to identify turning restrictions for an actual medium-sized urban traffic network in Brazil. Computational experience with the proposed method is promising.

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References

  1. Armijo, L.: Minimization of functions having Lipschitz continuous first partial derivatives. Pac. J. Math. 16(1), 1–3 (1966)

    Article  Google Scholar 

  2. Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming, Theory and Applications, 2nd edn. Wiley, New York (1993)

    Google Scholar 

  3. Bekhor, S., Toledo, B.: Investigating path-based algorithms for the stochastic user equilibrium problem. Transp. Res. A Pol. 39(3), 279–295 (2005)

    Google Scholar 

  4. Boyce, D.E.: Urban transportation network-equilibrium and design models: recent achievements and future prospects. Environ. Plan. A 16(11), 1445–1474 (1984)

    Article  Google Scholar 

  5. Braess, D., Nagurney, A., Wakolbinger, T.: On a paradox of traffic planning. Transp. Sci. 39(4), 446–450 (2005)

    Article  Google Scholar 

  6. Brønmo, G., Christiansen, M., Fagerholt, K., Nygreen, B.: A multi-start local search heuristic for ship scheduling–a computational study. Comput. Oper. Res. 34(3), 900–917 (2007)

    Article  Google Scholar 

  7. Cantarella, G.E., Pavone, C., Vitetta, A.: Heuristics for urban road network design: lane layout and signal settings. Eur. J. Oper. Res. 175(3), 1682–1695 (2006)

    Article  Google Scholar 

  8. Cascetta, E., Gallo, M., Montella, B.: Models and algorithms for the optimization of signal settings on urban networks with stochastic assignment models. Ann. Oper. Res. 144(1), 301–328 (2006)

    Article  Google Scholar 

  9. Chen, K., Luo, Z.Z.: Analysis of feature of left turn traffic at level crossing and countermeasures. Technol. Highw. Transp. 22(2), 114–118 (2006)

    Google Scholar 

  10. Cipriani, E., Fusco, G.: Combined signal setting design and traffic assignment problem. Eur. J. Oper. Res. 155(3), 569–583 (2004)

    Article  Google Scholar 

  11. Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Oper. Res. 8(1), 101–111 (1960)

    Article  Google Scholar 

  12. Drezner, Z., Salhi, S.: Selecting a good configuration of one-way and two-way routes using tabu search. Control Cybern 29(3), 725–740 (2000)

    Google Scholar 

  13. Drezner, Z., Salhi, S.: Using hybrid metaheuristics for the one-way and two-way network design problem. Nav. Res. Logist. 49(5), 449–463 (2002)

    Article  Google Scholar 

  14. Drezner, Z., Wesolowsky, G.O.: Network design: selection and design of links and facility location. Transp. Res. A Pol. 37(3), 241–256 (2003)

    Article  Google Scholar 

  15. Farahani, R.Z., Miandoabchi, E., Szeto, W., Rashidi, H.: A review of urban transportation network design problems. Eur. J. Oper. Res. 229(2), 281–302 (2013)

    Article  Google Scholar 

  16. Fisk, S.C.: Game theory and transportation systems modelling. Transp. Res. B Meth. 18(4), 301–313 (1984)

    Article  Google Scholar 

  17. Ford, L.R., Fulkerson, D.R.: A suggested computation for multi-commodity network flows. Manage. Sci. 5(1), 97–101 (1958)

    Article  Google Scholar 

  18. Foulds, L.R.: A multicommodity flow network design problem. Transp. Res. B Meth. 15(4), 273–284 (1981)

    Article  Google Scholar 

  19. Foulds, L.R.: Graph Theory Applications. Springer, New York (1991)

    Google Scholar 

  20. Foulds, L.R., do Nascimento, H.A.D., Calixto, I.C.A., Hall, B., Longo, H.: A fuzzy set approach to estimating OD matrices in congested Brazilian traffic networks. In: Proceedings of the XLIII Simpósio Brasileiro de Pesquisa Operacional (SBPO2011), pp. 1386–1397. Brazil (2011)

  21. Friesz, T.L.: Transportation network equilibrium, design and aggregation: key developments and research opportunities. Transp. Res. A Pol. 19(5–6), 413–427 (1985)

    Article  Google Scholar 

  22. Gallo, M., D’Acierno, L., Montella, B.: A meta-heuristic approach for solving the urban network design problem. Eur. J. Oper. Res. 201(1), 144–157 (2010)

    Article  Google Scholar 

  23. García-Ródenas, R., Verastegui-Rayo, D.: A column generation algorithm for the estimation of origin-destination matrices in congested traffic networks. Eur. J. Oper. Res. 184(3), 860–878 (2008)

    Article  Google Scholar 

  24. Gilmore, P.C., Gomory, R.E.: A linear programming approach to the cutting stock problem. Oper. Res. 9(6), 849–859 (1961)

    Article  Google Scholar 

  25. Gilmore, P.C., Gomory, R.E.: A linear programming approach to the cutting stock problem. Part II. Oper. Res. 11(6), 863–888 (1963)

    Article  Google Scholar 

  26. Gur, Y.J., Turnquist, M., Schneider, M., Leblanc, L., Kurth, D.: Estimation of an Origin-Destination Trip Table Based on Observed Link Volumes and Turning Movements. Department of Transportation, Federal Highway Administration, Office of Research, Traffic Systems Division, Washington, Springfield, VA (1980)

  27. Heydecker, B.G., Khoo, T.K.: The equilibrium network design problem. In: Proceedings of AIRO’90 Conference on Models and Methods for Decision Support, pp. 587–602. Sorrento, NA, Italy (1990)

  28. Jradi, W., do Nascimento, H.A.D., Longo, H., Hall, B.R.: Simulation and analysis of urban traffic the architecture of a web-based interactive decision support system. In: Proceedings of the 12th International IEEE Conference on Intelligent Transportation Systems (ITSC’09), pp. 1–6 (2009)

  29. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948 (1995)

  30. Laguna, M.: Scatter search. In: Pardalos, P.M., Resende, M.G.C. (eds.) Handbook of Applied Optimization, pp. 183–193. Oxford University Press, Oxford (2002)

    Google Scholar 

  31. Lasdon, L.S.: Optimization Theory for Large Systems. MacMillan, New York, NY (1970)

    Google Scholar 

  32. LeBlanc, L.J.: An algorithm for the discrete network design problem. Transp. Sci. 9(3), 183–199 (1975)

    Article  Google Scholar 

  33. Lee, C.K., Yang, K.I.: Network design of one-way streets with simulated annealing. Pap. Reg. Sci. 73(2), 119–134 (1994)

    Article  Google Scholar 

  34. Long, J., Gao, Z., Zhang, H., Szeto, W.Y.: A turning restriction design problem in urban road networks. Eur. J. Oper. Res. 206(3), 569–578 (2010)

    Article  Google Scholar 

  35. Magnanti, T.L., Wong, R.T.: Network design and transportation planning: models and algorithm. Transp. Sci. 18(1), 1–55 (1984)

    Article  Google Scholar 

  36. Martí, R., Laguna, M., Glover, F.: Principles of scatter search. Eur. J. Oper. Res. 169(2), 359–372 (2006)

    Article  Google Scholar 

  37. Martí, R., Moreno-Vega, J.M., Duarte, A.: Advanced multi-start methods. In: Gendreau, M., potvin, J.Y. (eds.) Handbook of Metaheuristics (International Series in Operations Research and Management Science), 2nd edn, pp. 183–193. Springer, Berlin (2002)

  38. Meneguzzer, C.: An equilibrium route choice model with explicit treatment of the effect of intersections. Transp. Res. B Meth. 29(5), 329–356 (1995)

    Article  Google Scholar 

  39. Miandoabchi, E., Farahani, R.Z.: Optimizing reserve capacity of urban road networks in a discrete network design problem. Adv. Eng. Softw. 42(12), 1041–1050 (2011)

    Article  Google Scholar 

  40. Migdalas, A.: Bilevel programming in traffic planning: models, methods and challenge. J. Global Optim. 7(4), 381–405 (1995)

    Article  Google Scholar 

  41. Oda, T., Otokita, T., Tsugui, T., Mashiyama, Y.: Application of simulated annealing to optimization of traffic signal timings. In: Papageorgiou, M., Pouliezos, A. (eds.) Preprints of 8th IFAC Symposium on Transportation Systems, vol. 2, pp. 733–736. Elsevier, Chania (2009)

    Google Scholar 

  42. Palacios-Gomez, F., Lasdon, L., Engquist, M.: Nonlinear optimization by successive linear programming. Manage. Sci. 28(10), 1106–1120 (1982)

    Article  Google Scholar 

  43. Poorzahedy, H., Rouhani, O.M.: Hybrid meta-heuristic algorithms for solving network design problem. Eur. J. Oper. Res. 182(2), 578–596 (2007)

    Article  Google Scholar 

  44. Potts, R.B., Oliver, R.M.: Flows in Transportation Networks. Academic Press, London (1972)

    Google Scholar 

  45. Russo, F., Vitetta, A.: A topological method to choose optimal solutions after solving the multicriteria urban network design problem. Transportation 33(4), 347–370 (2006)

    Article  Google Scholar 

  46. Sheffi, Y.: Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming. Prentice Hall, Englewood Cliff (1985)

    Google Scholar 

  47. Sheffi, Y., Powell, W.B.: Optimal signal settings over transportation networks. J. Transp. Eng. 109(6), 824–839 (1983)

    Article  Google Scholar 

  48. Sherali, H.D., Narayanan, A., Sivanandan, R.: Estimation of origin-destination trip-tables based on a partial set of traffic link volumes. Transp. Res. B Meth. 37(9), 815–836 (2003)

    Article  Google Scholar 

  49. Steenbrink, P.A.: Optimization of Transport Networks. Wiley, New York (1974)

    Google Scholar 

  50. Teklu, F., Sumalee, A., Watting, D.: A genetic algorithm approach for optimizing traffic control signals considering routing. Comput. Aided Civ. Infrast. Eng. 22, 31–43 (2007)

    Article  Google Scholar 

  51. USA Bureau of Public Roads: Traffic assignment manual. Technical report, US Department of Commerce, Urban Planning Division, Washington DC, USA (1964)

  52. Wardrop, J.: Some theoretical aspects of road traffic research. Proc. Inst. Civ. Eng. II 1(36), 352–362 (1952)

    Google Scholar 

  53. Wey, W.M.: Model formulation and solution algorithm of traffic signal control in an urban network. Comput. Environ. Urban 24(4), 355–377 (2000)

    Article  Google Scholar 

  54. Wong, C.S., Yang, H.: Reserve capacity of a signal-controlled road network. Transp. Res. B Meth. 31(5), 397–402 (1997)

    Article  Google Scholar 

  55. Yang, H., Bell, M.G.H.: Models and algorithms for road network design: a review and some new developments. Transp. Rev. 18(3), 257–278 (1998)

    Article  Google Scholar 

  56. Yang, H., Yagar, S.: Traffic assignment and signal control in saturated road networks. Transp. Res. A Pol. 29(2), 125–139 (1995)

    Article  Google Scholar 

  57. Ying, J.Q., Lu, H.P., Shi, J.: An algorithm for local continuous optimization of traffic signals. Eur. J. Oper. Res. 181(3), 1189–1197 (2007)

    Article  Google Scholar 

  58. Zhang, H., Gao, Z.: Two-way road network design problem with variable lanes. J. Syst. Sci. Syst. Eng. 16(1), 50–61 (2007)

    Article  Google Scholar 

  59. Ziyou, G., Yifan, S.: A reserve capacity model of optimal signal control with user-equilibrium route choice. Transp. Res. B Meth. 36(4), 313–323 (2002)

    Article  Google Scholar 

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Correspondence to Hugo A. D. do Nascimento.

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Hugo do Nascimento was partially sponsored by CNPq (Scholarship of Research Productivity—309463/ 2009-2)

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Foulds, L.R., Duarte, D.C.S., do Nascimento, H.A.D. et al. Turning restriction design in traffic networks with a budget constraint. J Glob Optim 60, 351–371 (2014). https://doi.org/10.1007/s10898-013-0127-1

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