Fast Calibration of Car-Following Models to Trajectory Data Using the Adjoint Method

Published Online:https://doi.org/10.1287/trsc.2020.1027

References

  • Antoniou C , Azevedo CL , Lu L , Pereira F , Ben-Akiva M (2015) W-spsa in practice: Approximation of weight matrices and calibration of traffic simulation models. Transportation Res. Part C: Emerging Techl. 59:129–146.CrossrefGoogle Scholar
  • Bando M , Hasebe K , Nakayama A , Shibata A , Sugiyama Y (1995a) Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E 51(2):1035–1042.Google Scholar
  • Bando M , Hasebe K , Nakanishi K , Nakayama A , Shibata A , Sugiyama Y (1995b) Phenomenological study of dynamical model of traffic flow. J. Physique I 5(11):1389–1399.Google Scholar
  • Birgin E , Martnez J , Raydan M (2000) Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10(4):1196–1211.Google Scholar
  • Brackstone M , McDonald M (1999) Car-following: a historical review. Transportation Res. Part F: Traffic Psych. Behav. 2(4):181–196.CrossrefGoogle Scholar
  • Brockfeld E , Khne R , Wagner P (2004) Calibration and validation of microscopic traffic flow models. Transportation Res. Record 1876(1):62–70.Google Scholar
  • Brockfeld E , Khne R , Skabardonis A , Wagner P (2003) Toward benchmarking of microscopic traffic flow models. Transportation Res. Record 1852(1):124–129.Google Scholar
  • Byrd RH , Lu P , Nocedal J , Zhu C (1995) A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16(5):1190–1208.Google Scholar
  • Calver J , Enright W (2017) Numerical methods for computing sensitivities for odes and ddes. Numerical Algorithms 74(4):1101–1117.Google Scholar
  • Cao Y , Li S , Petzold L , Serban R (2003) Adjoint sensitivity analysis for differential-algebraic equations: The adjoint dae system and its numerical solution. SIAM J. Sci. Comput. 24(3):1076–1089.Google Scholar
  • Chaparro B , Thuillier S , Menezes L , Manach P , Fernandes J (2008) Material parameters identification: Gradient-based, genetic and hybrid optimization algorithms. Comput. Materials Sci. 44(2):339–346.CrossrefGoogle Scholar
  • Ciuffo B , Punzo V , Montanino M (2012a) The calibration of traffic simulation models: Report on the assessment of different goodness of fit measures and optimization algorithms. Technical Report EU Cost Action TU0903 MULTITUDE , European Commission Joint Research Centre, Luxembourg. Google Scholar
  • Ciuffo B , Punzo V , Montanino M (2012b) Thirty years of gipps’ car-following model. Transportation Res. Record 2315(1):89–99.Google Scholar
  • Coifman B , Li L (2017) A critical evaluation of the next generation simulation (ngsim) vehicle trajectory data set. Transportation Res. Part B Methodological 105:362–377.CrossrefGoogle Scholar
  • Daganzo CF (1994) The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Res. Part B: Methodological 28(4):269–287.CrossrefGoogle Scholar
  • Daganzo CF (2006) In traffic flow, cellular automata=kinematic waves. Transportation Res. Part B Methodological 40(5):396–403.CrossrefGoogle Scholar
  • Davis L (2003) Modifications of the optimal velocity traffic model to include delay due to driver reaction time. Phys. A . 319:557–567.CrossrefGoogle Scholar
  • Davis LC (2002) Comment on “analysis of optimal velocity model with explicit delay”. Phys. Rev. E 66(3 Pt 2B):038101.Google Scholar
  • Duret A , Buisson C , Chiabaut N (2008) Estimating individual speed-spacing relationship and assessing ability of newell’s car-following model to reproduce trajectories. Transportation Res. Record 2088(1):188–197.Google Scholar
  • Fletcher R , Gould N , Leyffer S , Toint P , Wchter A (2002) Global convergence of a trust-region sqp-filter algorithm for general nonlinear programming. SIAM J. Optim. 13(3):635–659.Google Scholar
  • Gao F , Han L (2012) Implementing the nelder-mead simplex algorithm with adaptive parameters. Comput. Optim. Appl. 51(1):259–277.Google Scholar
  • Gasser I , Sirito G , Werner B (2004) Bifurcation analysis of a class of car following traffic models. Phys. D 197(3):222–241.CrossrefGoogle Scholar
  • Ge HX , Dai SQ , Dong LY , Xue Y (2004) Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application. Phys. Rev. E 70(6 Pt 2):066134.Google Scholar
  • Gipps P (1981) A behavioural car-following model for computer simulation. Transportation Res. Part B: Methodological 15(2):105–111.CrossrefGoogle Scholar
  • He Z , Zheng L , Guan W (2015) A simple nonparametric car-following model driven by field data. Transportation Res. Part B: Methodological 80:185–201.CrossrefGoogle Scholar
  • Helbing D , Tilch B (1998) Generalized force model of traffic dynamics. Phys. Rev. E 58(1):133–138.Google Scholar
  • Helbing D , Hennecke A , Shvetsov V , Treiber M (2002) Micro- and macro-simulation of freeway traffic. Math. Comput. Model. 35(5):517–547.CrossrefGoogle Scholar
  • Hidas P (2005) A functional evaluation of the aimsun, paramics and vissim microsimulation models. Road Transportation Res. 14(4): 45–59.Google Scholar
  • Huang X , Sun J , Sun J (2018) A car-following model considering asymmetric driving behavior based on long short-term memory neural networks. Transportation Res. Part C: Emerging Tech. 95:346–362.CrossrefGoogle Scholar
  • Jiang R , Hu MB , Zhang H , Gao ZY , Jia B , Wu QS (2015) On some experimental features of car-following behavior and how to model them. Transportation Res. Part B: Methodological 80:338–354.CrossrefGoogle Scholar
  • Jiang R , Jin CJ , Zhang H , Huang YX , Tian JF , Wang W , Hu MB , et al. . (2018) Experimental and empirical investigations of traffic flow instability. Transportation Res. Part C: Emerging Tech. 94:83–98.Google Scholar
  • Jones DR , Perttunen CD , Stuckman BE (1993) Lipschitzian optimization without the Lipschitz constant. J. Optim. Theory Appl. 79(1):157–181.Google Scholar
  • Keane R , Gao HO (2019) A formulation of the relaxation phenomenon for lane changing dynamics in an arbitrary car following model. Preprint, submitted April 17 2019, https://arxiv.org/abs/1904.08395.Google Scholar
  • Kerner BS (2014) Three-phase theory of city traffic: Moving synchronized flow patterns in under-saturated city traffic at signals. Phys. A 397:76–110.CrossrefGoogle Scholar
  • Kerner BS , Rehborn H (1997) Experimental properties of phase transitions in traffic flow. Phys. Rev. Lett. 79(20):4030–4033.Google Scholar
  • Kesting A , Treiber M (2008) Calibrating car-following models by using trajectory data: Methodological study. Transportation Res. Record 2088(1):148–156.Google Scholar
  • Krajewski R , Bock J , Kloeker L , Eckstein L (2018) The highD data set: A drone data set of naturalistic vehicle trajectories on German highways for validation of highly automated driving systems. Proc. IEEE 21st Internat. Conf. on Intelligent Transportation Systems (ITSC) (IEEE, New York), 2118–2125.Google Scholar
  • Laval JA , Daganzo CF (2006) Lane-changing in traffic streams. Transportation Res. Part B: Methodological 40(3):251–264.CrossrefGoogle Scholar
  • Laval JA , Leclercq L (2008) Microscopic modeling of the relaxation phenomenon using a macroscopic lane-changing model. Transportation Res. Part B: Methodological 42(6):511–522.CrossrefGoogle Scholar
  • Laval JA , Toth CS , Zhou Y (2014) A parsimonious model for the formation of oscillations in car-following models. Transportation Res. Part B: Methodological 70:228–238.CrossrefGoogle Scholar
  • Li L , Chen XM , Zhang L (2016) A global optimization algorithm for trajectory data based car-following model calibration. Transportation Res. Part C: Emerging Tech. 68:311–332.CrossrefGoogle Scholar
  • Lighthill MJ , Whitham GB (1955) On kinematic waves. ii. A theory of traffic flow on long crowded roads. Proc. Royal Soc. London A: Math. Physical Engrg. Sci. 229(1178):317–345.Google Scholar
  • LINDO Systems I (2018) Lindo api 12.0 user manual. Accessed April 2, 2019, https://www.lindo.com/downloads/PDF/API.pdf.Google Scholar
  • Lu XY , Skabardonis A (2007) Freeway shockwave analysis: Exploring NGSIM trajectory data. Proc. Transportation Res. Board 86th Annual Meeting (Transportation Research Board, Washington, DC).Google Scholar
  • Montanino M , Punzo V (2015) Trajectory data reconstruction and simulation-based validation against macroscopic traffic patterns. Transportation Res. Part B: Methodological 80:82–106.CrossrefGoogle Scholar
  • Nagel K , Schreckenberg M (1992) A cellular automaton model for freeway traffic. J. Physique I 2(12):2221–2229.Google Scholar
  • Nash S (1984) Newton-type minimization via the lanczos method. SIAM J. Numerical Anal. 21(4):770–788.Google Scholar
  • Nocedal J , Wright SJ (1999) Numerical Optimization (Springer, New York).CrossrefGoogle Scholar
  • Orosz G , Stépán G (2006) Subcritical hopf bifurcations in a car-following model with reaction-time delay. Proc. Royal Soc. London A Math. Physical Engrg. Sci. 462(2073):2643–2670.Google Scholar
  • Ossen S , Hoogendoorn S , Gorte B (2006) Interdriver differences in car-following: A vehicle trajectory-based study. Transportation Res. Record 1965(1):121–129.Google Scholar
  • Papathanasopoulou V , Antoniou C (2015) Toward data-driven car-following models. Transportation Res. Part C: Emerging Tech. 55:496–509.CrossrefGoogle Scholar
  • Punzo V , Simonelli F (2005) Analysis and comparison of microscopic traffic flow models with real traffic microscopic data. Transportation Res. Record 1934(1):53–63.Google Scholar
  • Punzo V , Ciuffo B , Montanino M (2012) Can results of car-following model calibration based on trajectory data be trusted? Transportation Res. Record 2315(1):11–24.Google Scholar
  • Punzo V , Montanino M , Ciuffo B (2015) Do we really need to calibrate all the parameters? Variance-based sensitivity analysis to simplify microscopic traffic flow models. IEEE Trans. Intelligent Transportation Systems 16(1):184–193.Google Scholar
  • Rakha H , Crowther B , 2002 Comparison of greenshields, pipes, and van aerde car-following and traffic stream models. Transportation Res. Record 1802(1):248–262.Google Scholar
  • Ranjitkar P , Nakatsuji T , Asano M (2004) Performance evaluation of microscopic traffic flow models with test track data. Transportation Res. Record 1876(1):90–100.Google Scholar
  • Spall JC (1992) Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans/ Automatic Control 37(3):332–341.Google Scholar
  • Stern RE , Cui S , Delle Monache ML , Bhadani R , Bunting M , Churchill M , Hamilton N , et al. (2018) Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments. Transportation Res. Part C: Emerging Tech. 89:205–221.Google Scholar
  • Storn R , Price K (1997) Differential evolutionmbox: A simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4):341–359.Google Scholar
  • Sugiyama Y , Fukui M , Kikuchi M , Hasebe K , Nakayama A , Nishinari K , Tadaki S , et al. (2008) Traffic jams without bottlenecks—Experimental evidence for the physical mechanism of the formation of a jam. New J. Phys. 10(3):033001.Google Scholar
  • Tian J , Jiang R , Jia B , Gao Z , Ma S (2016) Empirical analysis and simulation of the concave growth pattern of traffic oscillations. Transportation Res. Part B: Methodological 93:338–354.CrossrefGoogle Scholar
  • Treiber M , Kesting A (2013a) Microscopic calibration and validation of car-following models—A systematic approach. Procedia Soc. Behav. Sci. 80:922–939.Google Scholar
  • Treiber M , Kesting A (2013b) Traffic Flow Dynamics (Springer, Berlin).CrossrefGoogle Scholar
  • Treiber M , Kesting A (2017) The intelligent driver model with stochasticity -new insights into traffic flow oscillations. Transportation Res. Procedia 23:174–187.Google Scholar
  • Treiber M , Hennecke A , Helbing D (2000) Congested traffic states in empirical observations and microscopic simulations. Physical Rev. E 62(2 Pt A):1805–1824.Google Scholar
  • Treiber M , Kesting A , Helbing D (2006) Delays, inaccuracies and anticipation in microscopic traffic models. Phys. A 360(1):71–88.CrossrefGoogle Scholar
  • Tympakianaki A , Koutsopoulos HN , Jenelius E (2015) c-spsa: Cluster-wise simultaneous perturbation stochastic approximation algorithm and its application to dynamic origin—Destination matrix estimation. Transportation Res. Part C Emerging Tech. 55:231–245.CrossrefGoogle Scholar
  • U.S. Department of Transportation(2006) Next generation simulation (NGSIM) vehicle trajectories and supporting data. Accessed May 5, 2018, https://data.transportation.gov/Automobiles/Next-Generation-Simulation-NGSIM-Vehicle-Trajector/8ect-6jqj.Google Scholar
  • Wong G , Wong S (2002) A multi-class traffic flow model—An extension of LWR model with heterogeneous drivers. Transportation Res. Part A Policy Practices 36(9):827–841.CrossrefGoogle Scholar
  • Wu C , Kreidieh A , Parvate K , Vinitsky E , Bayen A (2017) Flow: Architecture and benchmarking for reinforcement learning in traffic control. Preprint, submitted October 16, 2017, https://arxiv.org/abs/1710.05465.Google Scholar
  • Yeo H , Skabardonis A (2008) Parameter estimation for ngsim over-saturated freeway flow algorithm. Proc. of the 10th AATT Conf. (University of Athens, Athens).Google Scholar
  • Yeo H , Skabardonis A , Halkias J , Colyar J , Alexiadis V (2008) Oversaturated freeway flow algorithm for use in next generation simulation. Transportation Res. Record 2088(1):68–79.Google Scholar
  • Zhou M , Qu X , Li X (2017) A recurrent neural network based microscopic car following model to predict traffic oscillation. Transportation Res. Part C: Emerging Tech. 84:245–264.CrossrefGoogle Scholar
  • Zhu C , Byrd RH , Lu P , Nocedal J (1997) Algorithm 778: L-bfgs-b: Fortran subroutines for large-scale bound-constrained optimization. ACM Trans. Math. Software 23(4):550–560.Google Scholar
  • Zhu M , Wang X , Wang Y (2018) Human-like autonomous car-following model with deep reinforcement learning. Transportation Res. Part C: Emerging Tech. 97:348–368.CrossrefGoogle Scholar
  • Zingg DW , Nemec M , Pulliam TH , 2008 A comparative evaluation of genetic and gradient-based algorithms applied to aerodynamic optimization. Eur. J. Comput. Mechanics 17(1-2):103–126.Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.