Second order macroscopic traffic flow model validation using automatic differentiation with resilient backpropagation and particle swarm optimisation algorithms

The problem of validating the Modéle d'Écoulement de Trafic sur Autoroute NETworks (METANET) model of a motorway section is considered. Model calibration is formulated as a least squares error minimisation problem with explicit penalisation of fundamental diagram parameter variation. The Automatic Differentiation by Overloading in C++ (ADOL-C) library is incorporated into the METANET source code and is coupled with the Resilient Back Propagation (RPROP) heuristic for solving the minimisation problem. The result is a very efficient system which is able to be calibrate METANET by determining the density and speed equation parameters as well as the fundamental diagrams used. Information obtained from the system's Jacobian provides extra insight into the dynamics showing how sensitivities propagate into the network. A 22 km site near Sheffield, UK, using data from three different days is considered. In addition to the ADOL-C/RPROP system, three particle swarm optimisation algorithms are used for solving the calibration problem. In all cases, the optimal parameter sets found are verified on data not used during calibration. Although, all three sets of data display a similar congestion pattern, the verification process showed that only one of them is capable of leading to parameter sets that capture the underlying dynamics of the traffic flow process.