Numerical optimal control method for shockwaves reduction at stationary bottlenecks

The paper introduces an optimal control method for traffic management with variable speed limits. It consists of traffic flow dynamics prediction with a non‐linearized Lighthill–Whitham–Richards macroscopic traffic flow model, introduction of a cost functional, which enables stable shockwaves optimization, and numerical implementation of the optimization process with differential evolution. The method overcomes the discretization issues and provides speed limits that are in general not limited to small number of successive discrete points, i.e. variable message signs locations, nor in rounded speed limits. Performance of the method is demonstrated on a case study, which shows promising reduction of the backward moving shockwave that occurs because of a stationary bottleneck. Copyright © 2016 John Wiley & Sons, Ltd.