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A LAGRANGE NEURAL NETWORK FOR NETWORK TRAFFIC ASSIGNMENT OPTIMIZATION

Year 2023, , 82 - 95, 29.12.2023
https://doi.org/10.51477/mejs.1272077

Abstract

This study considers a nonlinear optimization problem used to achieve user equilibrium in the network traffic assignment problem. By providing the Karush Kuhn Tucker conditions of this optimization problem, it is converted into a system of differential equations using the Lagrange function. This system is then redefined as a Lagrange neural network, which is proven to be asymptotically and lyapunov stable. Finally, a numerical method are used to demonstrate that the results obtained from this neural network are a solution to the optimization problem and converge to user equilibrium.

References

  • J.G. Wardrop, "Some theoretical aspects of road traffic research," Proceedings of the Institution of Civil Engineers, Part II, vol. 1, no. 3, pp. 325-378, 1952.
  • M. Frank and P. Wolfe, "An algorithm for quadratic programming," Naval Research Logistics Quarterly, vol. 3, no. 1-2, pp. 95-110, 1956.
  • Y. Sheffi and W. B. Powell, "A survey of transportation network models," Transportation Research Part B: Methodological, vol. 19, no. 5, pp. 381-391, 1985.
  • C. F. Daganzo and Y. Sheffi, "On stochastic models of traffic assignment," Transportation Science, vol. 11, no. 3, pp. 253-274, 1977.
  • M. Beckmann, C. B. McGuire, and C. B. Winsten, "Studies in the economics of transportation," Yale University Press, 1956.
  • S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science, vol. 220, no. 4598, pp. 671-680, 1983.
  • M. J. Smith and P. J. Wieskamp, "The network design problem: Dual and primal methods," Transportation Research Part B: Methodological, vol. 13, no. 1, pp. 1-16, 1979.
  • M. Florian and S. Nguyen, "An efficient algorithm for the continuous network design problem," Transportation Science, vol. 18, no. 3, pp. 269-291, 1984.
  • S. Peeta and A. K. Ziliaskopoulos, "Foundations of dynamic traffic assignment: the past, the present and the future," Networks and Spatial Economics, vol. 1, no. 3-4, pp. 233-265, 2001.
  • A. Sumalee and W. H. Lam, "Traffic congestion modeling: A state-of-the-art review," Transportation Research Part C: Emerging Technologies, vol. 14, no. 2, pp. 89-123, 2006.
  • H. Jin, L. Sun, X. Wang, and Y. Wang, "Simulation-based dynamic traffic assignment algorithm considering driver routing behavior," Transportation Research Part C: Emerging Technologies, vol. 86, pp. 245-264, 2018.
  • J. Lin, B. Yu, H. Huang, S. Wang, and M. Zhou, "A bilevel optimization model for sustainable transportation planning with consideration of driver compliance behavior," Transportation Research Part D: Transport and Environment, vol. 76, pp. 161-180, 2019.
  • X. Hu, C. Chen, and Y. Jiang, "A network loading model with uncertain flow and travel time for sustainable urban transport," Transportation Research Part C: Emerging Technologies, vol. 112, pp. 63-81, 2020.
  • W. Xie, Y. Liu, H. Huang, and Z. Gao, "A data assimilation augmented Wolfe dual method for dynamic traffic assignment," Transportation Research Part C: Emerging Technologies, vol. 111, pp. 463-486, 2020.
  • Y. Li, J. Wu, B. Yang, and F. Peng, "A variable-penalty augmented Lagrangian method for large-scale traffic assignment," Transportation Research Part B: Methodological, vol. 149, pp. 305-326, 2021.
  • A. Krylatov, "Optimization Models and Methods for Equilibrium Traffic Assignment," Transportation Research Procedia, vol. 40, pp. 166-173, 2019.
  • S. Zhang and A. G. Constantinides, "Lagrange Programming Neural Networks," IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 39, no. 7, pp. 441-452, Jul. 1992.
  • 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 Transactions on Neural Networks, vol. 12, no. 5, pp. 1074-1083, 2001.
  • K. M. Lee, Y. J. Park and J. H. Kim, "A Lagrange programming neural network for large-scale convex programming problems," Neurocomputing, vol. 115, pp. 109-117, 2013.
  • Y. Liu, G. Li and J. Li, "Lagrange programming neural network for solving non-linear programming problems," Neurocomputing, vol. 275, pp. 1156-1165, 2018.
  • S. C. Dafermos and F. T. Sparrow, "The traffic assignment problem for a general network," J. Res. Natl. Bur. Stand. B, vol. 73, no. 2, pp. 91-118, 1969.
  • T. L. Friesz and D. Bernstein, "Foundations of Network Optimization and Games," New York, NY: Springer, 2016.
  • M. Patriksson, "The Traffic Assignment Problem: Models and Methods," Courier Dover Publications, New York, 2015.
  • A. T. Karaşahin ve A. E. Tümer, "Real-time traffic signal timing approach based on artificial neural network," MANAS Journal of Engineering, vol. 8, no. 1, pp. 49-54, 2020.
  • Q. Zhang, S.Q. Liu, ve M. Masoud, "A traffic congestion analysis by user equilibrium and system optimum with incomplete information," Journal of Combinatorial Optimization, vol. 43, no:1, pp. 1391–1404, 2022.
  • B. Javani and A. Babazadeh, "Origin-destination-based truncated quadratic programming algorithm for traffic assignment problem," Transportation Letters, vol. 9, no. 3, pp. 166-176, 2017.
  • A. Babazadeh, B. Javani, G. Gentile, and M. Florian, "Reduced gradient algorithm for user equilibrium traffic assignment problem," Transportmetrica A: Transport Science, vol. 16, no. 3, pp. 1111-1135, 2020.
  • V. Morandi, "Bridging the user equilibrium and the system optimum in static traffic assignment: a review," 4OR-Q J Oper Res, 2023, doi: 10.1007/s10288-023-00540-w.
Year 2023, , 82 - 95, 29.12.2023
https://doi.org/10.51477/mejs.1272077

Abstract

References

  • J.G. Wardrop, "Some theoretical aspects of road traffic research," Proceedings of the Institution of Civil Engineers, Part II, vol. 1, no. 3, pp. 325-378, 1952.
  • M. Frank and P. Wolfe, "An algorithm for quadratic programming," Naval Research Logistics Quarterly, vol. 3, no. 1-2, pp. 95-110, 1956.
  • Y. Sheffi and W. B. Powell, "A survey of transportation network models," Transportation Research Part B: Methodological, vol. 19, no. 5, pp. 381-391, 1985.
  • C. F. Daganzo and Y. Sheffi, "On stochastic models of traffic assignment," Transportation Science, vol. 11, no. 3, pp. 253-274, 1977.
  • M. Beckmann, C. B. McGuire, and C. B. Winsten, "Studies in the economics of transportation," Yale University Press, 1956.
  • S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science, vol. 220, no. 4598, pp. 671-680, 1983.
  • M. J. Smith and P. J. Wieskamp, "The network design problem: Dual and primal methods," Transportation Research Part B: Methodological, vol. 13, no. 1, pp. 1-16, 1979.
  • M. Florian and S. Nguyen, "An efficient algorithm for the continuous network design problem," Transportation Science, vol. 18, no. 3, pp. 269-291, 1984.
  • S. Peeta and A. K. Ziliaskopoulos, "Foundations of dynamic traffic assignment: the past, the present and the future," Networks and Spatial Economics, vol. 1, no. 3-4, pp. 233-265, 2001.
  • A. Sumalee and W. H. Lam, "Traffic congestion modeling: A state-of-the-art review," Transportation Research Part C: Emerging Technologies, vol. 14, no. 2, pp. 89-123, 2006.
  • H. Jin, L. Sun, X. Wang, and Y. Wang, "Simulation-based dynamic traffic assignment algorithm considering driver routing behavior," Transportation Research Part C: Emerging Technologies, vol. 86, pp. 245-264, 2018.
  • J. Lin, B. Yu, H. Huang, S. Wang, and M. Zhou, "A bilevel optimization model for sustainable transportation planning with consideration of driver compliance behavior," Transportation Research Part D: Transport and Environment, vol. 76, pp. 161-180, 2019.
  • X. Hu, C. Chen, and Y. Jiang, "A network loading model with uncertain flow and travel time for sustainable urban transport," Transportation Research Part C: Emerging Technologies, vol. 112, pp. 63-81, 2020.
  • W. Xie, Y. Liu, H. Huang, and Z. Gao, "A data assimilation augmented Wolfe dual method for dynamic traffic assignment," Transportation Research Part C: Emerging Technologies, vol. 111, pp. 463-486, 2020.
  • Y. Li, J. Wu, B. Yang, and F. Peng, "A variable-penalty augmented Lagrangian method for large-scale traffic assignment," Transportation Research Part B: Methodological, vol. 149, pp. 305-326, 2021.
  • A. Krylatov, "Optimization Models and Methods for Equilibrium Traffic Assignment," Transportation Research Procedia, vol. 40, pp. 166-173, 2019.
  • S. Zhang and A. G. Constantinides, "Lagrange Programming Neural Networks," IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 39, no. 7, pp. 441-452, Jul. 1992.
  • 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 Transactions on Neural Networks, vol. 12, no. 5, pp. 1074-1083, 2001.
  • K. M. Lee, Y. J. Park and J. H. Kim, "A Lagrange programming neural network for large-scale convex programming problems," Neurocomputing, vol. 115, pp. 109-117, 2013.
  • Y. Liu, G. Li and J. Li, "Lagrange programming neural network for solving non-linear programming problems," Neurocomputing, vol. 275, pp. 1156-1165, 2018.
  • S. C. Dafermos and F. T. Sparrow, "The traffic assignment problem for a general network," J. Res. Natl. Bur. Stand. B, vol. 73, no. 2, pp. 91-118, 1969.
  • T. L. Friesz and D. Bernstein, "Foundations of Network Optimization and Games," New York, NY: Springer, 2016.
  • M. Patriksson, "The Traffic Assignment Problem: Models and Methods," Courier Dover Publications, New York, 2015.
  • A. T. Karaşahin ve A. E. Tümer, "Real-time traffic signal timing approach based on artificial neural network," MANAS Journal of Engineering, vol. 8, no. 1, pp. 49-54, 2020.
  • Q. Zhang, S.Q. Liu, ve M. Masoud, "A traffic congestion analysis by user equilibrium and system optimum with incomplete information," Journal of Combinatorial Optimization, vol. 43, no:1, pp. 1391–1404, 2022.
  • B. Javani and A. Babazadeh, "Origin-destination-based truncated quadratic programming algorithm for traffic assignment problem," Transportation Letters, vol. 9, no. 3, pp. 166-176, 2017.
  • A. Babazadeh, B. Javani, G. Gentile, and M. Florian, "Reduced gradient algorithm for user equilibrium traffic assignment problem," Transportmetrica A: Transport Science, vol. 16, no. 3, pp. 1111-1135, 2020.
  • V. Morandi, "Bridging the user equilibrium and the system optimum in static traffic assignment: a review," 4OR-Q J Oper Res, 2023, doi: 10.1007/s10288-023-00540-w.
There are 28 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Article
Authors

Hasan Dalman 0009-0008-6574-3215

Publication Date December 29, 2023
Submission Date March 28, 2023
Acceptance Date October 18, 2023
Published in Issue Year 2023

Cite

IEEE H. Dalman, “A LAGRANGE NEURAL NETWORK FOR NETWORK TRAFFIC ASSIGNMENT OPTIMIZATION”, MEJS, vol. 9, no. 2, pp. 82–95, 2023, doi: 10.51477/mejs.1272077.

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