Research Article
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Year 2023, , 81 - 87, 31.12.2023
https://doi.org/10.36222/ejt.1320824

Abstract

References

  • [1] J. G. Wardrop, "Some theoretical aspects of road traffic research," in Proc. Inst. Civ. Eng., Part II, vol. 1, no. 3, pp. 325-378, 1952.
  • [2] M. Beckmann, C.B. McGuire, and C.B. Winsten, "Studies in the Economics of Transportation," New Haven,: CT: Yale University Press, 1956.
  • [3] J.A. Tomlin, "Minimum-cost multicommodity network flows," Oper. Res., vol. 14, no. 1, pp. 45-51, 1966.
  • [4] C.F. Daganzo, "On the traffic assignment problem with flow dependent costs—I," Transp. Res., vol. 11, no. 6, pp. 433-437, 1977.
  • [5] C.F. Daganzo, "On the traffic assignment problem with flow dependent costs—II," Transportation Res., vol. 11, no. 6, pp. 439-441, 1977.
  • [6] H. Inouye, "Traffic equilibria and its solution in congested road networks," in R. Genser (Ed.), Proc. IFAC Conf. Control in Transportation Systems, Vienna, pp. 267-272, 1987.
  • [7] H. Yang and S. Yagar, "Traffic assignment and traffic control in general freeway-arterial corridor systems," Transp. Res., vol. 28, no. 6, pp. 463-486, 1994.
  • [8] T. Larsson and M. Patriksson, "An augmented Lagrangean dual algorithm for link capacity side constrained traffic assignment problems," Transp. Res. Part B: Methodol., vol. 29, no. 6, pp. 433-455, 1995.
  • [9] Y. Nie, H. M. Zhang, and D. H. Lee, "Models and algorithms for the traffic assignment problem with link capacity constraints," Transp. Res. Part B: Methodol., vol. 38, no. 4, pp. 285-312, 2004.
  • [10] D. W. Tank and J. J. Hopfield, "Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit," IEEE Trans. Circuits Syst., vol. CAS-33, pp. 533-541, May 1986.
  • [11] S. Zhang and A. G. Constantinides, "Lagrange programming neural networks," IEEE Trans. Circuits Syst. II, vol. 39, no. 7, pp. 441-452, 1992.
  • [12] R. Feng, C. S. Leung, A. G. Constantinides, and W. J. Zeng, "Lagrange programming neural network for nondifferentiable optimization problems in sparse approximation," IEEE Trans. Neural Netw. Learn. Syst., vol. 28, no. 10, pp. 2395-2407, Oct. 2016.
  • [13] Y. Lv, T. Hu, G. Wang, and Z. Wan, "A neural network approach for solving nonlinear bilevel programming problem," Comput. Math. Appl., vol. 55, no. 12, pp. 2823-2829, 2008.
  • [14] H. S. Shih, U. P. Wen, E. S. Lee, et al., "A neural network approach to multi-objective and multilevel programming problems," Comput. Math. Appl., vol. 48, no. 1-2, pp. 95-108, 2004.
  • [15] K. M. Lan, U. P. Wen, et al., "A hybrid neural network approach to bilevel programming problems," Appl. Math. Lett., vol. 20, no. 8, pp. 880-884, Aug. 2007.
  • [16] M. P. Kennedy and L. O. Chua, "Neural Network for nonlinear programming," IEEE Trans. Circuits Syst., vol. 35, no. 5, pp. 554-562, 1998.
  • [17] Y. Leung, K.Z. Chen, Y.C. Jiao, X.B. Gao, and K.S. Leung, "A new gradient-based neural network for solving linear and quadratic programming problems," IEEE Trans. Neural Netw., vol. 12, no. 5, pp. 1074-1083, 2001.
  • [18] A. R. Nazemi, "A dynamic system model for solving convex nonlinear optimization problems," Commun. Nonlinear Sci. Numer. Simulat., vol. 17, no. 4, pp. 1696-1705, 2012.
  • [19] L. Jin, S. Li, B. Hu, and M. Liu, "A survey on projection neural networks and their applications," Appl. Soft Comput., vol. 76, pp. 533-544, 2019.
  • [20] R. B. Potts and R. M. Oliver, "Flows in transportation networks," New York and London: Academic Press, 1972.

Capacitated Network Traffic Assignment using Lagrange Neural Networks

Year 2023, , 81 - 87, 31.12.2023
https://doi.org/10.36222/ejt.1320824

Abstract

In this study, we utilize a neural network methodology to obtain user equilibrium for network traffic assignment problems with capacity constraints. The optimization problem associated with network traffic assignment is first transformed into a Lagrange problem. By considering the gradient method, a system of differential equations is obtained. Subsequently, the system of differential equations is solved using the Runge-Kutta method. The effectiveness of the proposed neural network approach is demonstrated through a numerical example.

References

  • [1] J. G. Wardrop, "Some theoretical aspects of road traffic research," in Proc. Inst. Civ. Eng., Part II, vol. 1, no. 3, pp. 325-378, 1952.
  • [2] M. Beckmann, C.B. McGuire, and C.B. Winsten, "Studies in the Economics of Transportation," New Haven,: CT: Yale University Press, 1956.
  • [3] J.A. Tomlin, "Minimum-cost multicommodity network flows," Oper. Res., vol. 14, no. 1, pp. 45-51, 1966.
  • [4] C.F. Daganzo, "On the traffic assignment problem with flow dependent costs—I," Transp. Res., vol. 11, no. 6, pp. 433-437, 1977.
  • [5] C.F. Daganzo, "On the traffic assignment problem with flow dependent costs—II," Transportation Res., vol. 11, no. 6, pp. 439-441, 1977.
  • [6] H. Inouye, "Traffic equilibria and its solution in congested road networks," in R. Genser (Ed.), Proc. IFAC Conf. Control in Transportation Systems, Vienna, pp. 267-272, 1987.
  • [7] H. Yang and S. Yagar, "Traffic assignment and traffic control in general freeway-arterial corridor systems," Transp. Res., vol. 28, no. 6, pp. 463-486, 1994.
  • [8] T. Larsson and M. Patriksson, "An augmented Lagrangean dual algorithm for link capacity side constrained traffic assignment problems," Transp. Res. Part B: Methodol., vol. 29, no. 6, pp. 433-455, 1995.
  • [9] Y. Nie, H. M. Zhang, and D. H. Lee, "Models and algorithms for the traffic assignment problem with link capacity constraints," Transp. Res. Part B: Methodol., vol. 38, no. 4, pp. 285-312, 2004.
  • [10] D. W. Tank and J. J. Hopfield, "Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit," IEEE Trans. Circuits Syst., vol. CAS-33, pp. 533-541, May 1986.
  • [11] S. Zhang and A. G. Constantinides, "Lagrange programming neural networks," IEEE Trans. Circuits Syst. II, vol. 39, no. 7, pp. 441-452, 1992.
  • [12] R. Feng, C. S. Leung, A. G. Constantinides, and W. J. Zeng, "Lagrange programming neural network for nondifferentiable optimization problems in sparse approximation," IEEE Trans. Neural Netw. Learn. Syst., vol. 28, no. 10, pp. 2395-2407, Oct. 2016.
  • [13] Y. Lv, T. Hu, G. Wang, and Z. Wan, "A neural network approach for solving nonlinear bilevel programming problem," Comput. Math. Appl., vol. 55, no. 12, pp. 2823-2829, 2008.
  • [14] H. S. Shih, U. P. Wen, E. S. Lee, et al., "A neural network approach to multi-objective and multilevel programming problems," Comput. Math. Appl., vol. 48, no. 1-2, pp. 95-108, 2004.
  • [15] K. M. Lan, U. P. Wen, et al., "A hybrid neural network approach to bilevel programming problems," Appl. Math. Lett., vol. 20, no. 8, pp. 880-884, Aug. 2007.
  • [16] M. P. Kennedy and L. O. Chua, "Neural Network for nonlinear programming," IEEE Trans. Circuits Syst., vol. 35, no. 5, pp. 554-562, 1998.
  • [17] Y. Leung, K.Z. Chen, Y.C. Jiao, X.B. Gao, and K.S. Leung, "A new gradient-based neural network for solving linear and quadratic programming problems," IEEE Trans. Neural Netw., vol. 12, no. 5, pp. 1074-1083, 2001.
  • [18] A. R. Nazemi, "A dynamic system model for solving convex nonlinear optimization problems," Commun. Nonlinear Sci. Numer. Simulat., vol. 17, no. 4, pp. 1696-1705, 2012.
  • [19] L. Jin, S. Li, B. Hu, and M. Liu, "A survey on projection neural networks and their applications," Appl. Soft Comput., vol. 76, pp. 533-544, 2019.
  • [20] R. B. Potts and R. M. Oliver, "Flows in transportation networks," New York and London: Academic Press, 1972.
There are 20 citations in total.

Details

Primary Language English
Subjects Computer Software, Software Engineering (Other)
Journal Section Research Article
Authors

Hasan Dalman 0009-0008-6574-3215

Publication Date December 31, 2023
Published in Issue Year 2023

Cite

APA Dalman, H. (2023). Capacitated Network Traffic Assignment using Lagrange Neural Networks. European Journal of Technique (EJT), 13(2), 81-87. https://doi.org/10.36222/ejt.1320824

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