Modeling and optimizing traffic light settings in road networks

Göttlich, Simone; Herty, Michaël; Ziegler, Ute

doi:10.1016/j.cor.2014.10.001

Cited by 42 publications

(31 citation statements)

References 53 publications

(64 reference statements)

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“…Asimismo, se han estudiado diversas formas para modelar el comportamiento en intersecciones con caminos convergentes o divergentes (Coclite el al., 2005) utilizando tal tipo de teoría. Recientemente, se ha desarrollado un modelo de optimización de semáforos en redes de tráfico combinando un modelo LWR con un enfoque numérico de optimización del tipo entero-mixto lineal (Göttlich et al, 2015). Esta metodología es muy precisa aunque puede ser muy costosa desde el punto de vista computacional para grandes redes.…”

Section: Introductionunclassified

Un Enfoque De Optimización Para El Control De Semáforos

Domínguez

Cortínez

2016

Libro De Actas CIT2016. XII Congreso De Ingeniería Del Transporte

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RESUMENEn este trabajo se presenta un modelo computacional para el diseño óptimo de configuración de semáforos basado en la combinación del modelo de tráfico LQM (Link Queue Model) desarrollado recientemente por Wen-Long Jin (2013) con una técnica de optimización denominada Recocido Simulado. El modelo LQM conduce a un sistema de ecuaciones diferenciales ordinarias no lineales de primer orden teniendo tantas incógnitas (densidades medias espaciales) como tramos existan en la red. Se ha adoptado el mencionado modelo de tráfico ya que ha demostrado una gran efectividad balanceando adecuadamente la velocidad computacional, la estabilidad numérica y el realismo físico de sus predicciones. Por otra parte, se utiliza el método de Recocido Simulado como técnica de optimización ya que el problema analizado es no convexo, es decir la función objetivo puede presentar varios mínimos (o máximos) locales. Se presentan ejemplos numéricos que ilustran las posibilidades de la presente metodología. INTRODUCCIÓNEl control de tráfico por medio de la semaforización se ha convertido en un elemento fundamental para aliviar la congestión en las grandes ciudades considerando la falta de espacio para la construcción de nuevas arterias. Un aspecto fundamental para efectuar el diseño del control de tráfico es la predicción de los patrones de flujo vehicular en la red de transporte para la infraestructura existente y sus posibles modificaciones ante diversos parámetros del funcionamiento de los semáforos. Las variables más importantes para realizar tal diseño corresponden a los tiempos de duración del ciclo así como también de la señal verde. También juega un papel de importancia la sincronización del comienzo de ciclo en diferentes intersecciones sucesivas. Luego, el problema de diseño consiste en obtener estos parámetros para las diferentes señales de tráfico de manera tal de mejorar la eficiencia del transporte con algún objetivo previamente definido. Se han empleado diferentes maneras de evaluar tal eficiencia. Una de ellas consiste en la consideración de la cantidad total de vehículos en una zona urbana o equivalentemente de la

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Section: Introductionunclassified

Un Enfoque De Optimización Para El Control De Semáforos

Domínguez

Cortínez

2016

Libro De Actas CIT2016. XII Congreso De Ingeniería Del Transporte

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“…Another signal control methodology is formulated as a quadratic programming problem to minimize and balance the link queues, therefore, minimizing the risk of queue spillback [9]. Göttlich [65] presented a numerical approach for the optimization of switching points as a function of time based upon the macroscopic traffic flow model. The numerical discussion relies on an equivalent reformulation of the original problem as well as a mixed-integer discretization of the flow dynamics.…”

Section: Introductionmentioning

confidence: 99%

A new nondominated sorting genetic algorithm based to the regression line For fuzzy traffic signal optimization problem

et al. 2017

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Traffic jam is a daily problem in nearly all major cities in the world and continues to increase with population and economic growth of urban areas. Traffic lights, as one of the key components at intersections, play an important role in control of traffic flow. Hence, study and research on phase synchronization and time optimization of the traffic lights could be an important step to avoid creating congestion and rejection queues in a urban network. Here, we describe the application of NSGA-II, a multi-objective evolutionary algorithm, to optimize both vehicle and pedestrian delays in an individual intersection. Results show that parameters found by improved NSGA-II can be superior to those defined by a traffic engineer with respect to several objectives, including total queue length of vehicles and pedestrians.In this paper, we improve NSGA-II algorithm based to the regression line to find a Pareto-optimal solution or a restrictive set of Pareto-optimal solutions based on our solution approaches to the problem, named PDNSGA (Non-dominated Sorting Genetic Algorithm based on Perpendicular Distance). In this paper, our purpose is to present a solution methodology to obtain all Pareto-optimal solutions to optimize traffic signal timing and enable the decision-makers to evaluate a greater number of alternative solutions. The proposed algorithm has the capability of searching Pareto front of the multi-objective problem domain. Further jobs should be concerned on the signal timing optimization method for the oversaturated coordinated intersections or small-scale road network and real-field applications with the traffic signal controller. The high speed of the proposed algorithm and its quick convergence makes it desirable for large scheduling with a large number of phases. Furthermore, we have used the mean deviation from the ideal point (MDI) measure to compare the performance of the MOGA, PDNSGA, NSGA-II, and WBGA by the ANOVA method. It is demonstrated that the our proposed algorithm (PDNSGA) gives better outputs than those of MOGA, NSGA-II, and WBGA in traffic signal optimization problem, statistically .

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“…Our goal in this paper is to devise efficient heuristics to approximately solve the problem of optimal traffic light settings for road networks. We base our work on the model and scenarios presented in [12] and refer the reader to the discussion therein for further references regarding the wide variety of different approaches for traffic light control or related problems such as spillover dissipation [11,23].The resulting mathematical optimization problems, which we elaborate in full detail in section 2, can be described as nonlinear mixed-integer optimal control problems constrained by scalar hyperbolic conservation laws on networks using boundary control. These problems are extremely challenging for several reasons: First, the problems are infinite dimensional in nature and must be discretized appropriately.…”

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Partial Outer Convexification for Traffic Light Optimization in Road Networks

Göttlich¹,

Potschka²,

Ziegler³

2017

SIAM J. Sci. Comput.

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Abstract. We consider the problem of computing optimal traffic light programs for urban road intersections using traffic flow conservation laws on networks. Based on a partial outer convexification approach, which has been successfully applied in the area of mixed-integer optimal control for systems of ordinary or differential algebraic equations, we develop a computationally tractable two-stage solution heuristic. The two-stage approach consists of the solution of a (smoothed) nonlinear programming problem with dynamic constraints and a reconstruction mixed-integer linear program without dynamic constraints. The two-stage approach is founded on a discrete approximation lemma for partial outer convexification, whose grid-independence properties for (smoothed) conservation laws are investigated. We use the two-stage approach to compute traffic light programs for two scenarios on different discretizations and demonstrate that the solution candidates cannot be improved in a reasonable amount of time by global state-of-the-art mixed-integer nonlinear programming solvers. The two-stage solution candidates are not only better than results obtained by global optimization of piecewise linearized traffic flow models but also can be computed at a faster rate.Key words. partial outer convexification, traffic networks, discretized conservation laws, optimization, mixed-integer programming AMS subject classifications. 35L65, 49J20, 90C11, 90C35 DOI. 10.1137/15M10481971. Introduction. With their seminal papers [22,25] in the 1950s on timedependent models for traffic flow with continuous densities instead of individual vehicles, Lighthill and Whitham and Richards established a new area of mathematical research in traffic modeling. The area is still highly active, e.g., for the case of traffic intersections (see, e.g., [5,8]), which constitute a building block of larger road networks. Our goal in this paper is to devise efficient heuristics to approximately solve the problem of optimal traffic light settings for road networks. We base our work on the model and scenarios presented in [12] and refer the reader to the discussion therein for further references regarding the wide variety of different approaches for traffic light control or related problems such as spillover dissipation [11,23].The resulting mathematical optimization problems, which we elaborate in full detail in section 2, can be described as nonlinear mixed-integer optimal control problems constrained by scalar hyperbolic conservation laws on networks using boundary control. These problems are extremely challenging for several reasons: First, the problems are infinite dimensional in nature and must be discretized appropriately. Special care has to be exercised for the discretization of the scalar conservation laws in order to guarantee well-posedness and, on the discrete level, consistency and sta-

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Modeling and optimizing traffic light settings in road networks

Cited by 42 publications

References 53 publications

Un Enfoque De Optimización Para El Control De Semáforos

Un Enfoque De Optimización Para El Control De Semáforos

A new nondominated sorting genetic algorithm based to the regression line For fuzzy traffic signal optimization problem

Partial Outer Convexification for Traffic Light Optimization in Road Networks

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