Capacitated Network Traffic Assignment using Lagrange Neural Networks

Öz

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.

Anahtar Kelimeler

• Nonlinear Optimization
• Neural Dynamics
• Traffic assignment
• Neural Networks

Kaynakça

1. [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. [2] M. Beckmann, C.B. McGuire, and C.B. Winsten, "Studies in the Economics of Transportation," New Haven,: CT: Yale University Press, 1956.
3. [3] J.A. Tomlin, "Minimum-cost multicommodity network flows," Oper. Res., vol. 14, no. 1, pp. 45-51, 1966.
4. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [20] R. B. Potts and R. M. Oliver, "Flows in transportation networks," New York and London: Academic Press, 1972.