Offset Dependent Uniform Delay Mathematical Optimization Model for Signalized Traffic Network Using Differential Evolution Algorithm
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32931
##### Offset Dependent Uniform Delay Mathematical Optimization Model for Signalized Traffic Network Using Differential Evolution Algorithm

Abstract:

A concept of uniform delay offset dependent mathematical optimization problem is derived as the main objective for this study using a differential evolution algorithm. Furthermore, the objectives are to control the coordination problem which mainly depends on offset selection, and to estimate the uniform delay based on the offset choice at each signalized intersection. The assumption is the periodic sinusoidal function for arrival and departure patterns. The cycle time is optimized at the entry links and the optimized value is used in the non-entry links as a common cycle time. The offset optimization algorithm is used to calculate the uniform delay at each link. The results are illustrated by using a case study and compared with the canonical uniform delay model derived by Webster and the highway capacity manual’s model. The findings show that the derived model minimizes the total uniform delay to almost half compared to conventional models; the mathematical objective function is robust; the algorithm convergence time is fast.

References:

[1] F. v. Webster, “Traffic signal settings,” Road Research Technical Paper, No.39, Road Research Laboratory, London, p. 44, 1958.
[2] W. Fawaz and J. El Khoury, “An exact modelling of the uniform control traffic delay in undersaturated signalized intersections,” Journal of Advanced Transportation, vol. 50, no. 5, pp. 918–932, 2016, doi: 10.1002/atr.1387.
[3] N. Rouphail, A. Tarko, and J. Li, “Traffic flow at signalized intersections,” in Revised Monograph on Traffic Flow Theory, 1992.
[4] S. W. Chiou, “TRANSYT derivatives for area traffic control optimisation with network equilibrium flows,” Transportation Research Part B: Methodological, vol. 37, no. 3, pp. 263–290, 2003, doi: 10.1016/S0191-2615(02)00013-9.
[5] Halim. Ceylan, “Developing combined genetic algorithm—Hill-climbing optimization method for area traffic control,” Journal of Transportation Engineering, vol. 132, no. 8, pp. 663–671, Aug. 2006, doi: 10.1061/(ASCE)0733-947X (2006)132:8(663).
[6] S. W. Chiou, “An efficient algorithm for optimal design of area traffic control with network flows,” Applied Mathematical Modelling, vol. 33, no. 6, pp. 2710–2722, 2009, doi: 10.1016/j.apm.2008.08.009.
[7] S. W. Chiou, “A novel algorithm for area traffic capacity control with elastic travel demands,” Applied Mathematical Modelling, vol. 35, no. 2, pp. 650–666, 2011, doi: 10.1016/j.apm.2010.07.016.
[8] S. W. Chiou, “Optimization of robust area traffic control with equilibrium flow under demand uncertainty,” Computers & operations, Elsevier, vol. 41, pp. 399–411, Jan. 2014.
[9] Halim. Ceylan, “A genetic algorithm approach to the equilibrium network design problem.,” University of Newcastle upon Tyne, 2002.
[10] R. E. Allsop, “Delay-minimizing settings for fixed-time traffic signals at a single road junction,” IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), vol. 8, no. 2, pp. 164–185, Oct. 1971, doi: 10.1093/imamat/8.2.164.
[11] R. E. Allsop, “Delay at a fixed time traffic signal--1. theoretical analysis” Transportation Science, vol. 6, no. 3, pp. 260–285, 1972, doi: 10.1287/TRSC.6.3.260.
[12] G. Improta and G. E. Cantarella, “Control system design for an individual signalized junction,” Transportation Research Part B, vol. 18, no. 2, pp. 147–167, 1984, doi: 10.1016/0191-2615(84)90028-6.
[13] B. Heydecker and I. Dudgeon, “Calculation of signal settings to minimise delay at a junction,” Transportation and Traffic Theory, 1987.
[14] A. Muralidharan, R. Pedarsani, and P. Varaiya, “Analysis of fixed-time control,” Transportation Research Part B: Methodological, vol. 73, pp. 81–90, Mar. 2015, doi: 10.1016/J.TRB.2014.12.002.
[15] G. Improta and A. Sforza, “Optimal offsets for traffic signal systems in urban networks,” Transportation Research Part B: Methodological, vol. 16, no. 2, pp. 143–161, Apr. 1982, doi: 10.1016/0191-2615(82)90032-7.
[16] G. E. Cantarella, G. Improta, and A. Sforza, “Iterative procedure for equilibrium network traffic signal setting,” Transportation Research Part A: General, vol. 25, no. 5, pp. 241–249, Sep. 1991, doi: 10.1016/0191-2607(91)90141-C.
[17] J. A. Hillier and R. Rothery, “The Synchronization of Traffic Signals for Minimum Delay,” Transportation Science, vol. 1, no. 2, pp. 81–94, 1967, doi: 10.1287/trsc.1.2.81.
[18] S. C. Wong, “Derivatives of the performance index for the traffic model from TRANSYT,” Transportation Research Part B, vol. 29, no. 5, pp. 303–327, Oct. 1995, doi: 10.1016/0191-2615(95)00012-3.
[19] S. Lee, S. C. Wong, and P. Varaiya, “Group-based hierarchical adaptive traffic-signal control part I: Formulation,” Transportation Research Part B: Methodological, vol. 105, pp. 1–18, 2017, doi: 10.1016/j.trb.2017.08.008.
[20] S. Coogan, G. Gomes, E. Kim, M. Arcak, and P. Varaiya, “Offset optimization for a network of signalized intersections via semidefinite relaxation,” Conference Publication IEEE, 2015. https://ieeexplore.ieee.org/document/7402531 (accessed Jan. 26, 2022).
[21] S. Coogan, E. Kim, G. Gomes, M. Arcak, and P. Varaiya, “Offset optimization in signalized traffic networks via semidefinite relaxation,” Transportation Research Part B: Methodological, vol. 100, pp. 82–92, Jun. 2017, doi: 10.1016/j.trb.2017.01.016.
[22] Z. Amini, S. Coogan, C. Flores, A. Skabardonis, and P. Varaiya, “Optimizing Offsets in Signalized Traffic Networks: A Case Study,” Conference on Control Technology and Applications (CCTA) IEEE, Aug. 2018.
[23] E. S. Kim, C. J. Wu, R. Horowitz, and M. Arcak, “Offset optimization of signalized intersections via the Burer-Monteiro method,” Proceedings of the American Control Conference, pp. 3554–3559, Jun. 2017, doi: 10.23919/ACC.2017.7963497.
[24] Y. Ouyang, R. Y. Zhang, J. Lavaei, and P. Varaiya, “Conic Approximation with Provable Guarantee for Traffic Signal Offset Optimization,” IEEE Conference on Decision and Control (CDC), pp. 229–236, Dec. 2018.
[25] Y. Ouyang, R. Y. Zhang, J. Lavaei, and P. Varaiya, “Large-Scale Traffic Signal Offset Optimization,” Transactions on Control of Network Systems IEEE, vol. 7, no. 3, pp. 1176–1187, Sep. 2020, doi: 10.1109/TCNS.2020.2966588.
[26] N. H. Gartner, J. D. C. Little, and H. Gabbay, “Optimization of Traffic Signal Settings by Mixed-Integer Linear Programming - 1. the network coordination problem.,” Transportation Science, vol. 9, no. n, pp. 321–343, Nov. 1975, doi: 10.1287/trsc.9.4.321.
[27] R. A. Vincent, A. I. Mitchell, and D. I. Robertson, “User Guide to Transyt Version 8,” Transport and Road Research Laboratory (TRRL) (No. LR 888 Monograph)., p. 86, 1980.
[28] Halim. Ceylan and M. G. H. Bell, “Traffic signal timing optimisation based on genetic algorithm approach, including drivers’ routing,” Transportation Research Part B: Methodological, vol. 38, no. 4, pp. 329–342, 2004, doi: 10.1016/S0191-2615(03)00015-8.
[29] E. Almasri and B. Friedrich, “Online offset optimisation in urban networks based on cell transmission model,” Institute of Transport, Road Engineering and Planning University of Hannover, Appelstr. 9A, 30167 Hannover, Germany, 2005.
[30] C. M. Day and D. M. Bullock, “Computational efficiency of alternative algorithms for arterial offset optimization,” Transportation Research Record, no. 2259, pp. 37–47, 2011, doi: 10.3141/2259-04.
[31] H. Ceylan, “Optimal Design of Signal Controlled Road Networks Using Differential Evolution Optimization Algorithm,” Mathematical Problems in Engineering, vol. 2013, p. 11, 2013, doi: 10.1155/2013/696374.
[32] R. Storn and K. Price, “Differential Evolution-A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces,” Journal of Global Optimization, vol. 11, pp. 341–359, 1997.
[33] S. S. Leal, P. E. M. De Almeida, and E. Chung, “Active control for traffic lights in regions and corridors: An approach based on evolutionary computation,” Transportation Research Procedia, vol. 25, pp. 1769–1780, 2017, doi: 10.1016/j.trpro.2017.05.140.
[34] R. E. Allsop and J. A. Charlesworth, “Traffic in a Signal-Controlled Road Network: An Example of Different Signal Timings Including Different Routeing,” Traffic Engineering & Control, vol. 18, no. 5, May 1977.
[35] M. Abdel-Basset, L. Abdel-Fatah, and A. K. Sangaiah, “Metaheuristic Algorithms: A Comprehensive Review,” Computational Intelligence for Multimedia Big Data on the Cloud with Engineering Applications, pp. 185–231, Jan. 2018, doi: 10.1016/B978-0-12-813314-9.00010-4.
[36] Z. Cakici and Y. S. Murat, “A Differential Evolution Algorithm-Based Traffic Control Model for Signalized Intersections,” Advances in Civil Engineering, p. 16, 2019, doi: 10.1155/2019/7360939.
[37] E. Korkmaz and AP Akgüngör, “Delay estimation models for signalized intersections using differential evolution algorithm,” Journal of Engineering Research, vol. 5(3), pp. 16–29, 2017.
[38] R. Storn and K. Price, “Differential evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces,” 1995.
[39] K. V Price, R. M. Storn, and J. A. Lampinen, Differential Evolution. A Practical Approach to Global Optimization. 2005.
[40] Highway Capacity Manual, “Highway Capacity Manual 2010,” Transportation Research Board, Washington, DC, 2, 1., Nov. 2010.