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.
On differential evolution algorithmsTo handle such an expanded optimal control problem a computationally effective method for numerical optimization process is required. We employ differential evolution (DE) approach introduced by Storn and Price [30,31]. DE is an evolutionary algorithm technique that is best suited for numerical optimization problems and has been found useful in many real-world optimization problems in engineering (e.g.[32] and [33]).There are three control parameters in DE, namely the mutation factor or scale factor, F ∈ [0, 2], the crossover probability, CR ∈ [0, 1], and the population size, NP ≥ 4. The selection of these parameters 842 I. STRNAD ET AL.