Swarm intelligence algorithms for macroscopic traffic flow model validation with automatic assignment of fundamental diagrams

Abstract

This paper is concerned with the problem of macroscopic road traffic flow model calibration and verification. Thoroughly validated models are necessary for both control system design and scenario evaluation purposes. Here, the second order traffic flow model METANET was calibrated and verified using real data. A powerful optimisation problem formulation is proposed for identifying a set of model parameters that makes the model fit to measurements. For the macroscopic traffic flow model validation problem, this set of parameters characterise the aggregate traffic flow features over a road network. In traffic engineering, one of the most important relationships whose parameters need to be determined is the fundamental diagram of traffic, which models the non-linear relationship between vehicular flow and density. Typically, a real network does not exhibit the same traffic flow aggregate behaviour everywhere and different fundamental diagrams are used for covering different network areas. As a result, one of the initial steps of the validation process rests on expert engineering opinion assigning the spatial extension of fundamental diagrams. The proposed optimisation problem formulation allows for automatically determining the number of different fundamental diagrams to be used and their corresponding spatial extension over the road network, simplifying this initial step. Although the optimisation problem suffers from local minima, good solutions which generalise well were obtained. The design of the system used is highly generic and allows for a number of evolutionary and swarm intelligence algorithms to be used. Two UK sites have been used for testing it. Calibration and verification results are discussed in detail. The resulting models are able to capture the dynamics of traffic flow and replicate shockwave propagation. A total of ten different algorithms were considered and compared with respect to their ability to converge to a solution, which remains valid for different sets of data. Particle swarm optimisation (PSO) algorithms have proven to be particularly effective and provide the best results both in terms of speed of convergence and solution generalisation. An interesting result reported is that more recently proposed PSO algorithms were outperformed by older variants, both in terms of speed of convergence and model error minimisation.