Macroscopic traffic flow model calibration using different optimization algorithms

This study tests and compares different optimization algorithms employed for the calibration of a macroscopic traffic flow model. In particular, the deterministic Nelder–Mead algorithm, a stochastic genetic algorithm and the stochastic cross-entropy method are utilized to estimate the parameter values of the METANET model for a particular freeway site, using real traffic data. The resulting models are validated using various traffic data sets and the optimization algorithms are evaluated and compared with respect to the accuracy of the produced validated models as well as the convergence speed and the required computation time. The validation results showed that all utilized optimization algorithms were able to converge to robust model parameter sets, albeit achieving different performances considering the convergence speed and the required computation time.

[1]  Markos Papageorgiou,et al.  Macroscopic modelling of traffic flow on the Boulevard Périphérique in Paris , 1989 .

[2]  Dirk Helbing.  Derivation and empirical validation of a refined traffic flow model , 1996 .

[3]  Ping Yi,et al.  Continuum modelling of traffic dynamics for congested freeways , 1993 .

[4]  Markos Papageorgiou,et al.  Overview of nonlinear programming methods suitable for calibration of traffic flow models , 2015, Oper. Res..

[5]  Martin Treiber,et al.  Traffic Flow Dynamics , 2013 .

[6]  Serge P. Hoogendoorn,et al.  State-of-the-art of vehicular traffic flow modelling , 2001 .

[7]  M. J. Box.  A New Method of Constrained Optimization and a Comparison With Other Methods , 1965, Comput. J..

[8]  Dirk P. Kroese,et al.  The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning , 2004 .

[9]  Markos Papageorgiou,et al.  Traffic Simulation with METANET , 2010 .

[10]  Markos Papageorgiou,et al.  METANET: A MACROSCOPIC SIMULATION PROGRAM FOR MOTORWAY NETWORKS , 1990 .

[11]  Markos Papageorgiou,et al.  The Importance of Traffic Flow Modeling for Motorway Traffic Control , 2001 .

[12]  Jeffrey C. Lagarias,et al.  Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions , 1998, SIAM J. Optim..

[13]  Habib Haj-Salem,et al.  A Macroscopic Node Model Related to Capacity Drop , 2012 .

[14]  Shie Mannor,et al.  A Tutorial on the Cross-Entropy Method , 2005, Ann. Oper. Res..

[15]  Markos Papageorgiou,et al.  Traffic flow modeling of large-scale motorwaynetworks using the macroscopic modeling tool METANET , 2002, IEEE Trans. Intell. Transp. Syst..

[16]  Mohinder S. Grewal,et al.  Identification of Parameters in a Freeway Traffic Model , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[17]  M. Cremer,et al.  An Extended Traffic Flow Model for Inner Urban Freeways , 1987 .

[18]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[19]  Apostolos Kotsialos,et al.  METANET Model Validation Using a Genetic Algorithm , 2012 .

[20]  D. Ngoduy,et al.  Comparison of Numerical Schemes for Macroscopic Traffic Flow Models , 2004 .

[21]  Markos Papageorgiou,et al.  Parameter identification for a traffic flow model , 1979, Autom..

[22]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[23]  M. Maher,et al.  Calibration of second order traffic models using continuous cross entropy method , 2012 .

[24]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[25]  M. Papageorgiou.  MODELLING AND REAL-TIME CONTROL OF TRAFFIC FLOW ON THE SOUTHERN PART OF BOULEVARD PERIPHERIQUE DE PARIS , 1988 .

[26]  Markos Papageorgiou,et al.  Modelling and real-time control of traffic flow on the southern part of Boulevard Peripherique in Paris: Part I: Modelling , 1990 .

[27]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[28]  Karl Petty,et al.  An extended macroscopic model for traffic flow , 1996 .

[29]  Markos Papageorgiou,et al.  Macroscopic traffic flow model validation at congested freeway off-ramp areas , 2014 .