Differential Evolution Based Numerical Variable Speed Limit Control Method with a Non-Equilibrium Traffic Model

Abstract

This paper introduces a numerical variable speed limit (VSL) control method on a motorway, modeled by the system of partial differential equations (PDEs) of a non- equilibrium continuum traffic model. The method consists of a macroscopic simulation (i.e., numerical solution of the system of PDEs of the continuum model), introduction of the solution-based cost function and numerical optimization with a differential evolution algorithm (DE). Due to the numerical solution scheme, the method enables application of a wide range of continuum traffic models without prior discretization of PDEs. In this way, the method overcomes the limitations of the basic continuum models and represents a step towards more accurate traffic modelling in control strategies. In this paper, we determine optimal variable speed limits with the DE algorithm on a motorway section modeled by the modified switching curve model, which is a non-equilibrium continuum model consistent with the three-phase traffic flow theory. The effectiveness of the determined variable speed limits is validated using microsimulations of the test section, which show promising reductions of queue lengths and number of stops.