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.
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.
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