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A LAGRANGE NEURAL NETWORK FOR NETWORK TRAFFIC ASSIGNMENT OPTIMIZATION

Year 2023, Volume: 9 Issue: 2, 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, Volume: 9 Issue: 2, 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 Volume: 9 Issue: 2

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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